TSTP Solution File: SYN626-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN626-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 23:56:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 62
% Syntax : Number of formulae : 122 ( 33 unt; 14 typ; 0 def)
% Number of atoms : 517 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 691 ( 319 ~; 315 |; 0 &)
% ( 57 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 10 >; 7 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 283 ( 252 !; 0 ?; 283 :)
% Comments :
%------------------------------------------------------------------------------
tff(p6_type,type,
p6: ( $i * $i ) > $o ).
tff(c22_type,type,
c22: $i ).
tff(p7_type,type,
p7: ( $i * $i ) > $o ).
tff(f12_type,type,
f12: $i > $i ).
tff(f13_type,type,
f13: $i > $i ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(c24_type,type,
c24: $i ).
tff(c23_type,type,
c23: $i ).
tff(f5_type,type,
f5: $i > $i ).
tff(c20_type,type,
c20: $i ).
tff(p11_type,type,
p11: ( $i * $i ) > $o ).
tff(p16_type,type,
p16: ( $i * $i ) > $o ).
tff(p15_type,type,
p15: ( $i * $i ) > $o ).
tff(1,plain,
^ [X47: $i] :
refl(
( p6(X47,X47)
<=> p6(X47,X47) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X47: $i] : p6(X47,X47)
<=> ! [X47: $i] : p6(X47,X47) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X47: $i] : p6(X47,X47)
<=> ! [X47: $i] : p6(X47,X47) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X47: $i] : p6(X47,X47),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_3) ).
tff(5,plain,
! [X47: $i] : p6(X47,X47),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X47: $i] : p6(X47,X47),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X47: $i] : p6(X47,X47),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X47: $i] : p6(X47,X47)
| p6(c22,c22) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p6(c22,c22),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X5: $i] :
refl(
( p11(f13(f12(X5)),X5)
<=> p11(f13(f12(X5)),X5) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X5: $i] : p11(f13(f12(X5)),X5)
<=> ! [X5: $i] : p11(f13(f12(X5)),X5) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X5: $i] : p11(f13(f12(X5)),X5)
<=> ! [X5: $i] : p11(f13(f12(X5)),X5) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X5: $i] : p11(f13(f12(X5)),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_6) ).
tff(14,plain,
! [X5: $i] : p11(f13(f12(X5)),X5),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X5: $i] : p11(f13(f12(X5)),X5),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X5: $i] : p11(f13(f12(X5)),X5),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X5: $i] : p11(f13(f12(X5)),X5)
| p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24)))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X0: $i,X2: $i,X1: $i] :
refl(
( ( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) )
<=> ( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [X0: $i,X2: $i,X1: $i] :
trans(
monotonicity(
rewrite(
( ( p11(X1,X2)
| ~ p11(X0,X1) )
<=> ( ~ p11(X0,X1)
| p11(X1,X2) ) )),
( ( p11(X1,X2)
| ~ p11(X0,X1)
| ~ p11(X0,X2) )
<=> ( ~ p11(X0,X1)
| p11(X1,X2)
| ~ p11(X0,X2) ) )),
rewrite(
( ( ~ p11(X0,X1)
| p11(X1,X2)
| ~ p11(X0,X2) )
<=> ( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) ) )),
( ( p11(X1,X2)
| ~ p11(X0,X1)
| ~ p11(X0,X2) )
<=> ( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( p11(X1,X2)
| ~ p11(X0,X1)
| ~ p11(X0,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [X0: $i,X2: $i,X1: $i] :
( p11(X1,X2)
| ~ p11(X0,X1)
| ~ p11(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_16) ).
tff(25,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) )
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24)))) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) )
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24)))) )
<=> ( ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) )
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24)))) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) )
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24)))) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) )
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24)))) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) )
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24)))) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) )
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p11(X0,X2)
| ~ p11(X0,X1)
| p11(X1,X2) )
| ~ p11(f13(f12(f13(f8(f5(c20),f9(c23,c24))))),f13(f8(f5(c20),f9(c23,c24))))
| p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24)))) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24)))),
inference(unit_resolution,[status(thm)],[34,28,18]) ).
tff(36,plain,
^ [X57: $i,X58: $i] :
refl(
( ( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) )
<=> ( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) )
<=> ! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) )
<=> ! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [X57: $i,X58: $i] :
rewrite(
( ( p7(f12(X57),f12(X58))
| ~ p11(X57,X58) )
<=> ( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X57: $i,X58: $i] :
( p7(f12(X57),f12(X58))
| ~ p11(X57,X58) )
<=> ! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X57: $i,X58: $i] :
( p7(f12(X57),f12(X58))
| ~ p11(X57,X58) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_12) ).
tff(42,plain,
! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) )
| ~ p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24))))
| p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f12(f13(f8(f5(c20),f9(c23,c24))))) )
<=> ( ~ ! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) )
| ~ p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24))))
| p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f12(f13(f8(f5(c20),f9(c23,c24))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) )
| ~ p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24))))
| p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f12(f13(f8(f5(c20),f9(c23,c24))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X57: $i,X58: $i] :
( ~ p11(X57,X58)
| p7(f12(X57),f12(X58)) )
| ~ p11(f13(f8(f5(c20),f9(c23,c24))),f13(f8(f5(c20),f9(c23,c24))))
| p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f12(f13(f8(f5(c20),f9(c23,c24))))) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f12(f13(f8(f5(c20),f9(c23,c24))))),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
( p15(c22,f8(f5(c20),f9(c23,c24)))
<=> p15(c22,f8(f5(c20),f9(c23,c24))) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
p15(c22,f8(f5(c20),f9(c23,c24))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_9) ).
tff(52,plain,
p15(c22,f8(f5(c20),f9(c23,c24))),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
^ [X14: $i,X15: $i] :
refl(
( ( ~ p15(X14,X15)
| p16(X14,X15) )
<=> ( ~ p15(X14,X15)
| p16(X14,X15) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) )
<=> ! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) )
<=> ! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
^ [X14: $i,X15: $i] :
rewrite(
( ( p16(X14,X15)
| ~ p15(X14,X15) )
<=> ( ~ p15(X14,X15)
| p16(X14,X15) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [X14: $i,X15: $i] :
( p16(X14,X15)
| ~ p15(X14,X15) )
<=> ! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,axiom,
! [X14: $i,X15: $i] :
( p16(X14,X15)
| ~ p15(X14,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_8) ).
tff(59,plain,
! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) ),
inference(modus_ponens,[status(thm)],[61,54]) ).
tff(63,plain,
( ( ~ ! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) )
| ~ p15(c22,f8(f5(c20),f9(c23,c24)))
| p16(c22,f8(f5(c20),f9(c23,c24))) )
<=> ( ~ ! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) )
| ~ p15(c22,f8(f5(c20),f9(c23,c24)))
| p16(c22,f8(f5(c20),f9(c23,c24))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ~ ! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) )
| ~ p15(c22,f8(f5(c20),f9(c23,c24)))
| p16(c22,f8(f5(c20),f9(c23,c24))) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
( ~ ! [X14: $i,X15: $i] :
( ~ p15(X14,X15)
| p16(X14,X15) )
| ~ p15(c22,f8(f5(c20),f9(c23,c24)))
| p16(c22,f8(f5(c20),f9(c23,c24))) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
p16(c22,f8(f5(c20),f9(c23,c24))),
inference(unit_resolution,[status(thm)],[65,62,52]) ).
tff(67,plain,
^ [X20: $i] :
refl(
( ( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) )
<=> ( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) )
<=> ! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) )
<=> ! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,axiom,
! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_15) ).
tff(71,plain,
! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( ( ~ ! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) )
| p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f8(f5(c20),f9(c23,c24)))
| ~ p16(c22,f8(f5(c20),f9(c23,c24))) )
<=> ( ~ ! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) )
| p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f8(f5(c20),f9(c23,c24)))
| ~ p16(c22,f8(f5(c20),f9(c23,c24))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ~ ! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) )
| p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f8(f5(c20),f9(c23,c24)))
| ~ p16(c22,f8(f5(c20),f9(c23,c24))) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [X20: $i] :
( p7(f12(f13(X20)),X20)
| ~ p16(c22,X20) )
| p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f8(f5(c20),f9(c23,c24)))
| ~ p16(c22,f8(f5(c20),f9(c23,c24))) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f8(f5(c20),f9(c23,c24))),
inference(unit_resolution,[status(thm)],[76,73,66]) ).
tff(78,plain,
^ [X56: $i,X55: $i,X54: $i] :
refl(
( ( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) )
<=> ( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) )
<=> ! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) )
<=> ! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [X56: $i,X55: $i,X54: $i] :
trans(
monotonicity(
rewrite(
( ( p7(X55,X56)
| ~ p7(X54,X55) )
<=> ( ~ p7(X54,X55)
| p7(X55,X56) ) )),
( ( p7(X55,X56)
| ~ p7(X54,X55)
| ~ p7(X54,X56) )
<=> ( ~ p7(X54,X55)
| p7(X55,X56)
| ~ p7(X54,X56) ) )),
rewrite(
( ( ~ p7(X54,X55)
| p7(X55,X56)
| ~ p7(X54,X56) )
<=> ( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) ) )),
( ( p7(X55,X56)
| ~ p7(X54,X55)
| ~ p7(X54,X56) )
<=> ( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [X56: $i,X55: $i,X54: $i] :
( p7(X55,X56)
| ~ p7(X54,X55)
| ~ p7(X54,X56) )
<=> ! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [X56: $i,X55: $i,X54: $i] :
( p7(X55,X56)
| ~ p7(X54,X55)
| ~ p7(X54,X56) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_17) ).
tff(84,plain,
! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ( ~ ! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) )
| ~ p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f8(f5(c20),f9(c23,c24)))
| ~ p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f12(f13(f8(f5(c20),f9(c23,c24)))))
| p7(f8(f5(c20),f9(c23,c24)),f12(f13(f8(f5(c20),f9(c23,c24))))) )
<=> ( ~ ! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) )
| ~ p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f8(f5(c20),f9(c23,c24)))
| ~ p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f12(f13(f8(f5(c20),f9(c23,c24)))))
| p7(f8(f5(c20),f9(c23,c24)),f12(f13(f8(f5(c20),f9(c23,c24))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ~ ! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) )
| ~ p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f8(f5(c20),f9(c23,c24)))
| ~ p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f12(f13(f8(f5(c20),f9(c23,c24)))))
| p7(f8(f5(c20),f9(c23,c24)),f12(f13(f8(f5(c20),f9(c23,c24))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [X56: $i,X55: $i,X54: $i] :
( ~ p7(X54,X55)
| ~ p7(X54,X56)
| p7(X55,X56) )
| ~ p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f8(f5(c20),f9(c23,c24)))
| ~ p7(f12(f13(f8(f5(c20),f9(c23,c24)))),f12(f13(f8(f5(c20),f9(c23,c24)))))
| p7(f8(f5(c20),f9(c23,c24)),f12(f13(f8(f5(c20),f9(c23,c24))))) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
p7(f8(f5(c20),f9(c23,c24)),f12(f13(f8(f5(c20),f9(c23,c24))))),
inference(unit_resolution,[status(thm)],[90,87,77,49]) ).
tff(92,plain,
^ [X12: $i,X11: $i,X13: $i,X10: $i] :
refl(
( ( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) )
<=> ( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) )
<=> ! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) )
<=> ! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
^ [X12: $i,X11: $i,X13: $i,X10: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p15(X10,X11)
| ~ p6(X12,X10) )
<=> ( ~ p6(X12,X10)
| p15(X10,X11) ) )),
( ( p15(X10,X11)
| ~ p6(X12,X10)
| ~ p7(X13,X11) )
<=> ( ~ p6(X12,X10)
| p15(X10,X11)
| ~ p7(X13,X11) ) )),
rewrite(
( ( ~ p6(X12,X10)
| p15(X10,X11)
| ~ p7(X13,X11) )
<=> ( ~ p6(X12,X10)
| ~ p7(X13,X11)
| p15(X10,X11) ) )),
( ( p15(X10,X11)
| ~ p6(X12,X10)
| ~ p7(X13,X11) )
<=> ( ~ p6(X12,X10)
| ~ p7(X13,X11)
| p15(X10,X11) ) )),
( ( p15(X10,X11)
| ~ p6(X12,X10)
| ~ p7(X13,X11)
| ~ p15(X12,X13) )
<=> ( ~ p6(X12,X10)
| ~ p7(X13,X11)
| p15(X10,X11)
| ~ p15(X12,X13) ) )),
rewrite(
( ( ~ p6(X12,X10)
| ~ p7(X13,X11)
| p15(X10,X11)
| ~ p15(X12,X13) )
<=> ( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) ) )),
( ( p15(X10,X11)
| ~ p6(X12,X10)
| ~ p7(X13,X11)
| ~ p15(X12,X13) )
<=> ( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [X12: $i,X11: $i,X13: $i,X10: $i] :
( p15(X10,X11)
| ~ p6(X12,X10)
| ~ p7(X13,X11)
| ~ p15(X12,X13) )
<=> ! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,axiom,
! [X12: $i,X11: $i,X13: $i,X10: $i] :
( p15(X10,X11)
| ~ p6(X12,X10)
| ~ p7(X13,X11)
| ~ p15(X12,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_31) ).
tff(98,plain,
! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ~ p15(c22,f12(f13(f8(f5(c20),f9(c23,c24)))))
<=> ~ p15(c22,f12(f13(f8(f5(c20),f9(c23,c24))))) ),
inference(rewrite,[status(thm)],]) ).
tff(103,axiom,
~ p15(c22,f12(f13(f8(f5(c20),f9(c23,c24))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p15_24) ).
tff(104,plain,
~ p15(c22,f12(f13(f8(f5(c20),f9(c23,c24))))),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( ( ~ ! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) )
| ~ p6(c22,c22)
| ~ p15(c22,f8(f5(c20),f9(c23,c24)))
| ~ p7(f8(f5(c20),f9(c23,c24)),f12(f13(f8(f5(c20),f9(c23,c24)))))
| p15(c22,f12(f13(f8(f5(c20),f9(c23,c24))))) )
<=> ( ~ ! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) )
| ~ p6(c22,c22)
| ~ p15(c22,f8(f5(c20),f9(c23,c24)))
| ~ p7(f8(f5(c20),f9(c23,c24)),f12(f13(f8(f5(c20),f9(c23,c24)))))
| p15(c22,f12(f13(f8(f5(c20),f9(c23,c24))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ~ ! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) )
| ~ p6(c22,c22)
| ~ p15(c22,f8(f5(c20),f9(c23,c24)))
| ~ p7(f8(f5(c20),f9(c23,c24)),f12(f13(f8(f5(c20),f9(c23,c24)))))
| p15(c22,f12(f13(f8(f5(c20),f9(c23,c24))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [X12: $i,X11: $i,X13: $i,X10: $i] :
( ~ p6(X12,X10)
| ~ p15(X12,X13)
| ~ p7(X13,X11)
| p15(X10,X11) )
| ~ p6(c22,c22)
| ~ p15(c22,f8(f5(c20),f9(c23,c24)))
| ~ p7(f8(f5(c20),f9(c23,c24)),f12(f13(f8(f5(c20),f9(c23,c24)))))
| p15(c22,f12(f13(f8(f5(c20),f9(c23,c24))))) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
$false,
inference(unit_resolution,[status(thm)],[107,52,104,101,91,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN626-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 06:13:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50 % SZS output start Proof
% See solution above
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