## TSTP Solution File: SYN259-1 by Faust---1.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SYN259-1 : TPTP v3.4.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art07.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 17:30:44 EDT 2009

% Result   : Unsatisfiable 0.4s
% Output   : Refutation 0.4s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   28 (  20 unt;   0 def)
%            Number of atoms       :   42 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   30 (  16   ~;  14   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   34 (  12 sgn  13   !;   0   ?)

%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_this,plain,
! [A] : ~ p1(A,d,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),
[] ).

cnf(182015984,plain,
~ p1(A,d,A),
inference(rewrite,[status(thm)],[prove_this]),
[] ).

fof(rule_071,plain,
! [A,B,C,D] :
( p1(A,B,A)
| ~ l0(C)
| ~ p1(B,D,A)
| ~ s0(b) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),
[] ).

fof(axiom_5,plain,
s0(b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),
[] ).

cnf(177671720,plain,
s0(b),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).

cnf(178633392,plain,
( p1(A,B,A)
| ~ l0(C)
| ~ p1(B,D,A) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_071,177671720]),
[] ).

fof(axiom_20,plain,
l0(a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),
[] ).

cnf(177746648,plain,
l0(a),
inference(rewrite,[status(thm)],[axiom_20]),
[] ).

cnf(190712976,plain,
( p1(A,B,A)
| ~ p1(B,C,A) ),
inference(resolution,[status(thm)],[178633392,177746648]),
[] ).

fof(rule_082,plain,
! [A,B,C,D] :
( p1(A,B,C)
| ~ m0(C,A,D)
| ~ p1(C,A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),
[] ).

cnf(178737768,plain,
( p1(A,B,C)
| ~ m0(C,A,D)
| ~ p1(C,A,D) ),
inference(rewrite,[status(thm)],[rule_082]),
[] ).

fof(axiom_19,plain,
! [A,B] : m0(A,d,B),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),
[] ).

cnf(177742288,plain,
m0(A,d,B),
inference(rewrite,[status(thm)],[axiom_19]),
[] ).

cnf(194502280,plain,
( p1(d,A,B)
| ~ p1(B,d,C) ),
inference(resolution,[status(thm)],[178737768,177742288]),
[] ).

fof(axiom_12,plain,
! [A] : m0(a,A,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),
[] ).

cnf(177711920,plain,
m0(a,A,a),
inference(rewrite,[status(thm)],[axiom_12]),
[] ).

fof(rule_087,plain,
( p1(a,b,a)
| ~ r0(b)
| ~ p1(a,a,a) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),
[] ).

fof(rule_075,plain,
( p1(a,a,a)
| ~ p0(b,a) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),
[] ).

fof(axiom_14,plain,
! [A] : p0(b,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),
[] ).

cnf(177719520,plain,
p0(b,A),
inference(rewrite,[status(thm)],[axiom_14]),
[] ).

cnf(178652168,plain,
p1(a,a,a),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_075,177719520]),
[] ).

fof(axiom_9,plain,
r0(b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),
[] ).

cnf(177691576,plain,
r0(b),
inference(rewrite,[status(thm)],[axiom_9]),
[] ).

cnf(178791016,plain,
p1(a,b,a),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_087,178652168,177691576]),
[] ).

cnf(195119984,plain,
p1(b,A,a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177711920,178737768,178791016]),
[] ).

cnf(195229736,plain,
p1(d,A,b),
inference(resolution,[status(thm)],[194502280,195119984]),
[] ).

cnf(195444720,plain,
p1(b,d,b),
inference(resolution,[status(thm)],[190712976,195229736]),
[] ).

\$false,
inference(resolution,[status(thm)],[182015984,195444720]),
[] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_this,plain,(~p1(A,d,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),[]).
%
% cnf(182015984,plain,(~p1(A,d,A)),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% fof(rule_071,plain,(p1(A,B,A)|~l0(C)|~p1(B,D,A)|~s0(b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),[]).
%
% fof(axiom_5,plain,(s0(b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),[]).
%
% cnf(177671720,plain,(s0(b)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% cnf(178633392,plain,(p1(A,B,A)|~l0(C)|~p1(B,D,A)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_071,177671720]),[]).
%
% fof(axiom_20,plain,(l0(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),[]).
%
% cnf(177746648,plain,(l0(a)),inference(rewrite,[status(thm)],[axiom_20]),[]).
%
% cnf(190712976,plain,(p1(A,B,A)|~p1(B,C,A)),inference(resolution,[status(thm)],[178633392,177746648]),[]).
%
% fof(rule_082,plain,(p1(A,B,C)|~m0(C,A,D)|~p1(C,A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),[]).
%
% cnf(178737768,plain,(p1(A,B,C)|~m0(C,A,D)|~p1(C,A,D)),inference(rewrite,[status(thm)],[rule_082]),[]).
%
% fof(axiom_19,plain,(m0(A,d,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),[]).
%
% cnf(177742288,plain,(m0(A,d,B)),inference(rewrite,[status(thm)],[axiom_19]),[]).
%
% cnf(194502280,plain,(p1(d,A,B)|~p1(B,d,C)),inference(resolution,[status(thm)],[178737768,177742288]),[]).
%
% fof(axiom_12,plain,(m0(a,A,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),[]).
%
% cnf(177711920,plain,(m0(a,A,a)),inference(rewrite,[status(thm)],[axiom_12]),[]).
%
% fof(rule_087,plain,(p1(a,b,a)|~r0(b)|~p1(a,a,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),[]).
%
% fof(rule_075,plain,(p1(a,a,a)|~p0(b,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),[]).
%
% fof(axiom_14,plain,(p0(b,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),[]).
%
% cnf(177719520,plain,(p0(b,A)),inference(rewrite,[status(thm)],[axiom_14]),[]).
%
% cnf(178652168,plain,(p1(a,a,a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_075,177719520]),[]).
%
% fof(axiom_9,plain,(r0(b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN259-1.tptp',unknown),[]).
%
% cnf(177691576,plain,(r0(b)),inference(rewrite,[status(thm)],[axiom_9]),[]).
%
% cnf(178791016,plain,(p1(a,b,a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_087,178652168,177691576]),[]).
%
% cnf(195119984,plain,(p1(b,A,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177711920,178737768,178791016]),[]).
%
% cnf(195229736,plain,(p1(d,A,b)),inference(resolution,[status(thm)],[194502280,195119984]),[]).
%
% cnf(195444720,plain,(p1(b,d,b)),inference(resolution,[status(thm)],[190712976,195229736]),[]).
%