## TSTP Solution File: LAT270-2 by Faust---1.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : LAT270-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art05.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 13:36:46 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   13 (   9 unt;   0 def)
%            Number of atoms       :   22 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   22 (  13   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-4 aty)
%            Number of variables   :    9 (   0 sgn   3   !;   0   ?)

%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_2,plain,
c_lessequals(v_s,c_tarski_ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT270-2.tptp',unknown),
[] ).

cnf(151267376,plain,
c_lessequals(v_s,c_tarski_ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).

fof(cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0,plain,
! [A,B,C] :
( ~ c_in(A,v_a,t_a)
| ~ c_in(B,v_a,t_a)
| ~ c_lessequals(C,c_tarski_ointerval(v_r,B,A,t_a),tc_set(t_a))
| c_lessequals(C,v_a,tc_set(t_a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT270-2.tptp',unknown),
[] ).

cnf(151308536,plain,
( ~ c_in(A,v_a,t_a)
| ~ c_in(B,v_a,t_a)
| ~ c_lessequals(C,c_tarski_ointerval(v_r,B,A,t_a),tc_set(t_a))
| c_lessequals(C,v_a,tc_set(t_a)) ),
inference(rewrite,[status(thm)],[cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0]),
[] ).

fof(cls_conjecture_6,plain,
~ c_lessequals(v_s,v_a,tc_set(t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT270-2.tptp',unknown),
[] ).

cnf(151272320,plain,
~ c_lessequals(v_s,v_a,tc_set(t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_6]),
[] ).

cnf(167109552,plain,
( ~ c_in(A,v_a,t_a)
| ~ c_in(B,v_a,t_a)
| ~ c_lessequals(v_s,c_tarski_ointerval(v_r,B,A,t_a),tc_set(t_a)) ),
inference(resolution,[status(thm)],[151308536,151272320]),
[] ).

fof(cls_conjecture_0,plain,
c_in(v_a,v_a,t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT270-2.tptp',unknown),
[] ).

cnf(151258656,plain,
c_in(v_a,v_a,t_a),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).

cnf(167173184,plain,
( ~ c_in(A,v_a,t_a)
| ~ c_lessequals(v_s,c_tarski_ointerval(v_r,v_a,A,t_a),tc_set(t_a)) ),
inference(resolution,[status(thm)],[167109552,151258656]),
[] ).

fof(cls_conjecture_1,plain,
c_in(v_b,v_a,t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT270-2.tptp',unknown),
[] ).

cnf(151262760,plain,
c_in(v_b,v_a,t_a),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).

\$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[151267376,167173184,151262760]),
[] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_2,plain,(c_lessequals(v_s,c_tarski_ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT270-2.tptp',unknown),[]).
%
% cnf(151267376,plain,(c_lessequals(v_s,c_tarski_ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% fof(cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0,plain,(~c_in(A,v_a,t_a)|~c_in(B,v_a,t_a)|~c_lessequals(C,c_tarski_ointerval(v_r,B,A,t_a),tc_set(t_a))|c_lessequals(C,v_a,tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT270-2.tptp',unknown),[]).
%
% cnf(151308536,plain,(~c_in(A,v_a,t_a)|~c_in(B,v_a,t_a)|~c_lessequals(C,c_tarski_ointerval(v_r,B,A,t_a),tc_set(t_a))|c_lessequals(C,v_a,tc_set(t_a))),inference(rewrite,[status(thm)],[cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0]),[]).
%
% fof(cls_conjecture_6,plain,(~c_lessequals(v_s,v_a,tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT270-2.tptp',unknown),[]).
%
% cnf(151272320,plain,(~c_lessequals(v_s,v_a,tc_set(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_6]),[]).
%
% cnf(167109552,plain,(~c_in(A,v_a,t_a)|~c_in(B,v_a,t_a)|~c_lessequals(v_s,c_tarski_ointerval(v_r,B,A,t_a),tc_set(t_a))),inference(resolution,[status(thm)],[151308536,151272320]),[]).
%
% fof(cls_conjecture_0,plain,(c_in(v_a,v_a,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT270-2.tptp',unknown),[]).
%
% cnf(151258656,plain,(c_in(v_a,v_a,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(167173184,plain,(~c_in(A,v_a,t_a)|~c_lessequals(v_s,c_tarski_ointerval(v_r,v_a,A,t_a),tc_set(t_a))),inference(resolution,[status(thm)],[167109552,151258656]),[]).
%
% fof(cls_conjecture_1,plain,(c_in(v_b,v_a,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LAT/LAT270-2.tptp',unknown),[]).
%
% cnf(151262760,plain,(c_in(v_b,v_a,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%