## TSTP Solution File: SYN259-1 by Z3---4.8.9.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN259-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 23:54:25 EDT 2022

% Result   : Unsatisfiable 0.20s 0.49s
% Output   : Proof 0.20s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   30 (  11 unt;   4 typ;   0 def)
%            Number of atoms       :   67 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   78 (  40   ~;  28   |;   0   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    3 (   3 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   2   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   44 (  39   !;   0   ?;  44   :)

%------------------------------------------------------------------------------
tff(p1_type,type,
p1: ( \$i * \$i * \$i ) > \$o ).

tff(d_type,type,
d: \$i ).

tff(p0_type,type,
p0: ( \$i * \$i ) > \$o ).

tff(b_type,type,
b: \$i ).

tff(1,plain,
^ [B: \$i,C: \$i] :
refl(
( ( ~ p0(C,B)
| p1(B,B,B) )
<=> ( ~ p0(C,B)
| p1(B,B,B) ) )),
inference(bind,[status(th)],]) ).

tff(2,plain,
( ! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) )
<=> ! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
( ! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) )
<=> ! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(rewrite,[status(thm)],]) ).

tff(4,plain,
^ [B: \$i,C: \$i] :
rewrite(
( ( p1(B,B,B)
| ~ p0(C,B) )
<=> ( ~ p0(C,B)
| p1(B,B,B) ) )),
inference(bind,[status(th)],]) ).

tff(5,plain,
( ! [B: \$i,C: \$i] :
( p1(B,B,B)
| ~ p0(C,B) )
<=> ! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
! [B: \$i,C: \$i] :
( p1(B,B,B)
| ~ p0(C,B) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_085) ).

tff(7,plain,
! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
p0(b,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_10) ).

tff(13,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
( ( ~ ! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) )
<=> ( ~ ! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).

tff(15,plain,
( ~ ! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).

tff(16,plain,
( ~ ! [B: \$i,C: \$i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ),
inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
p1(d,d,d),
inference(unit_resolution,[status(thm)],[16,13,10]) ).

tff(18,plain,
^ [X: \$i] :
refl(
( ~ p1(X,d,X)
<=> ~ p1(X,d,X) )),
inference(bind,[status(th)],]) ).

tff(19,plain,
( ! [X: \$i] : ~ p1(X,d,X)
<=> ! [X: \$i] : ~ p1(X,d,X) ),
inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
( ! [X: \$i] : ~ p1(X,d,X)
<=> ! [X: \$i] : ~ p1(X,d,X) ),
inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
! [X: \$i] : ~ p1(X,d,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

tff(22,plain,
! [X: \$i] : ~ p1(X,d,X),
inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
! [X: \$i] : ~ p1(X,d,X),
inference(skolemize,[status(sab)],[22]) ).

tff(24,plain,
! [X: \$i] : ~ p1(X,d,X),
inference(modus_ponens,[status(thm)],[23,19]) ).

tff(25,plain,
( ~ ! [X: \$i] : ~ p1(X,d,X)
| ~ p1(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).

tff(26,plain,
\$false,
inference(unit_resolution,[status(thm)],[25,24,17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN259-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Sep  5 02:14:35 EDT 2022
% 0.13/0.35  % CPUTime  :
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.49  % SZS status Unsatisfiable
% 0.20/0.49  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------
```