TSTP Solution File: SYN660-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN660-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 23:56:50 EDT 2022
% Result : Unsatisfiable 0.22s 0.53s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 42
% Syntax : Number of formulae : 77 ( 25 unt; 12 typ; 0 def)
% Number of atoms : 307 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 427 ( 203 ~; 190 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 124 ( 114 !; 0 ?; 124 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f11_type,type,
f11: ( $i * $i ) > $i ).
tff(c34_type,type,
c34: $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(c33_type,type,
c33: $i ).
tff(c32_type,type,
c32: $i ).
tff(p25_type,type,
p25: ( $i * $i ) > $o ).
tff(c36_type,type,
c36: $i ).
tff(f16_type,type,
f16: ( $i * $i ) > $i ).
tff(f9_type,type,
f9: $i > $i ).
tff(f17_type,type,
f17: $i > $i ).
tff(c31_type,type,
c31: $i ).
tff(1,plain,
^ [X35: $i] :
refl(
( p2(X35,X35)
<=> p2(X35,X35) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X35: $i] : p2(X35,X35)
<=> ! [X35: $i] : p2(X35,X35) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X35: $i] : p2(X35,X35)
<=> ! [X35: $i] : p2(X35,X35) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X35: $i] : p2(X35,X35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_6) ).
tff(5,plain,
! [X35: $i] : p2(X35,X35),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X35: $i] : p2(X35,X35),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X35: $i] : p2(X35,X35),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X35: $i] : p2(X35,X35)
| p2(f11(f4(c33),c34),f11(f4(c33),c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p2(f11(f4(c33),c34),f11(f4(c33),c34)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X43: $i] :
refl(
( ( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
<=> ( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
<=> ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
<=> ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X43: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
<=> ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) )),
( ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) )
<=> ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) ) )),
rewrite(
( ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) )
<=> ( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) )),
( ( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) )
<=> ( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X43: $i] :
( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) )
<=> ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X43: $i] :
( p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36)
| ~ p25(c32,X43) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_50) ).
tff(16,plain,
! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p25(c32,c33)
<=> p25(c32,c33) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p25(c32,c33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25_14) ).
tff(22,plain,
p25(c32,c33),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( p25(c33,c36)
<=> p25(c33,c36) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
p25(c33,c36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25_12) ).
tff(25,plain,
p25(c33,c36),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ~ ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
| ~ p25(c32,c33)
| p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p25(c33,c36) )
<=> ( ~ ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
| ~ p25(c32,c33)
| p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p25(c33,c36) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
| ~ p25(c32,c33)
| p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p25(c33,c36) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [X43: $i] :
( ~ p25(c32,X43)
| p2(f11(f4(X43),c34),f11(f4(c32),c34))
| ~ p25(X43,c36) )
| ~ p25(c32,c33)
| p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p25(c33,c36) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
p2(f11(f4(c33),c34),f11(f4(c32),c34)),
inference(unit_resolution,[status(thm)],[28,25,22,19]) ).
tff(30,plain,
^ [X37: $i,X35: $i,X36: $i] :
refl(
( ( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
<=> ( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
<=> ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
<=> ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
^ [X37: $i,X35: $i,X36: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X36,X37)
| ~ p2(X35,X36) )
<=> ( ~ p2(X35,X36)
| p2(X36,X37) ) )),
( ( p2(X36,X37)
| ~ p2(X35,X36)
| ~ p2(X35,X37) )
<=> ( ~ p2(X35,X36)
| p2(X36,X37)
| ~ p2(X35,X37) ) )),
rewrite(
( ( ~ p2(X35,X36)
| p2(X36,X37)
| ~ p2(X35,X37) )
<=> ( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) )),
( ( p2(X36,X37)
| ~ p2(X35,X36)
| ~ p2(X35,X37) )
<=> ( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [X37: $i,X35: $i,X36: $i] :
( p2(X36,X37)
| ~ p2(X35,X36)
| ~ p2(X35,X37) )
<=> ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [X37: $i,X35: $i,X36: $i] :
( p2(X36,X37)
| ~ p2(X35,X36)
| ~ p2(X35,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_30) ).
tff(36,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) )
<=> ( ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c33),c34),f11(f4(c32),c34))
| ~ p2(f11(f4(c33),c34),f11(f4(c33),c34))
| p2(f11(f4(c32),c34),f11(f4(c33),c34)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
p2(f11(f4(c32),c34),f11(f4(c33),c34)),
inference(unit_resolution,[status(thm)],[45,39,29,9]) ).
tff(47,plain,
^ [X96: $i] :
refl(
( ~ p2(X96,f16(X96,f9(f17(c31))))
<=> ~ p2(X96,f16(X96,f9(f17(c31)))) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31))))
<=> ! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31))))
<=> ! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_19) ).
tff(51,plain,
! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31)))),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [X96: $i] : ~ p2(X96,f16(X96,f9(f17(c31))))
| ~ p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
~ p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
( p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
<=> p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_39) ).
tff(58,plain,
p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31)))),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) )
<=> ( ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) )
<=> ( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) ) ),
inference(transitivity,[status(thm)],[61,59]) ).
tff(63,plain,
( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [X37: $i,X35: $i,X36: $i] :
( ~ p2(X35,X37)
| ~ p2(X35,X36)
| p2(X36,X37) )
| ~ p2(f11(f4(c32),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| p2(f11(f4(c33),c34),f16(f11(f4(c33),c34),f9(f17(c31))))
| ~ p2(f11(f4(c32),c34),f11(f4(c33),c34)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,39,58,55,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SYN660-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Sep 5 05:50:25 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 0.22/0.53 % SZS status Unsatisfiable
% 0.22/0.53 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------