TSTP Solution File: SYN652-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN652-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 23:56:47 EDT 2022
% Result : Unsatisfiable 0.51s 0.61s
% Output : Proof 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 60
% Syntax : Number of formulae : 110 ( 35 unt; 18 typ; 0 def)
% Number of atoms : 395 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 524 ( 242 ~; 238 |; 0 &)
% ( 44 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 9 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 241 ( 219 !; 0 ?; 241 :)
% Comments :
%------------------------------------------------------------------------------
tff(p4_type,type,
p4: ( $i * $i ) > $o ).
tff(f15_type,type,
f15: ( $i * $i ) > $i ).
tff(c34_type,type,
c34: $i ).
tff(f17_type,type,
f17: ( $i * $i ) > $i ).
tff(c31_type,type,
c31: $i ).
tff(c36_type,type,
c36: $i ).
tff(f5_type,type,
f5: ( $i * $i ) > $i ).
tff(c32_type,type,
c32: $i ).
tff(c35_type,type,
c35: $i ).
tff(p14_type,type,
p14: ( $i * $i ) > $o ).
tff(c33_type,type,
c33: $i ).
tff(p27_type,type,
p27: ( $i * $i ) > $o ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(f10_type,type,
f10: ( $i * $i ) > $i ).
tff(f13_type,type,
f13: ( $i * $i ) > $i ).
tff(c30_type,type,
c30: $i ).
tff(c29_type,type,
c29: $i ).
tff(c28_type,type,
c28: $i ).
tff(1,plain,
^ [X6: $i] :
refl(
( p14(X6,X6)
<=> p14(X6,X6) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X6: $i] : p14(X6,X6)
<=> ! [X6: $i] : p14(X6,X6) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X6: $i] : p14(X6,X6)
<=> ! [X6: $i] : p14(X6,X6) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X6: $i] : p14(X6,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_14) ).
tff(5,plain,
! [X6: $i] : p14(X6,X6),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X6: $i] : p14(X6,X6),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X6: $i] : p14(X6,X6),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X6: $i] : p14(X6,X6)
| p14(f17(c36,c31),f17(c36,c31)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p14(f17(c36,c31),f17(c36,c31)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X57: $i,X56: $i,X59: $i,X58: $i] :
refl(
( ( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) )
<=> ( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) )
<=> ! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) )
<=> ! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X57: $i,X56: $i,X59: $i,X58: $i] :
trans(
monotonicity(
rewrite(
( ( p4(f15(X56,X57),f15(X58,X59))
| ~ p14(X56,X58) )
<=> ( ~ p14(X56,X58)
| p4(f15(X56,X57),f15(X58,X59)) ) )),
( ( p4(f15(X56,X57),f15(X58,X59))
| ~ p14(X56,X58)
| ~ p4(X57,X59) )
<=> ( ~ p14(X56,X58)
| p4(f15(X56,X57),f15(X58,X59))
| ~ p4(X57,X59) ) )),
rewrite(
( ( ~ p14(X56,X58)
| p4(f15(X56,X57),f15(X58,X59))
| ~ p4(X57,X59) )
<=> ( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) ) )),
( ( p4(f15(X56,X57),f15(X58,X59))
| ~ p14(X56,X58)
| ~ p4(X57,X59) )
<=> ( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X57: $i,X56: $i,X59: $i,X58: $i] :
( p4(f15(X56,X57),f15(X58,X59))
| ~ p14(X56,X58)
| ~ p4(X57,X59) )
<=> ! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X57: $i,X56: $i,X59: $i,X58: $i] :
( p4(f15(X56,X57),f15(X58,X59))
| ~ p14(X56,X58)
| ~ p4(X57,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_41) ).
tff(16,plain,
! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p4(c34,f5(c35,c32))
<=> p4(c34,f5(c35,c32)) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p4(c34,f5(c35,c32)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_16) ).
tff(22,plain,
p4(c34,f5(c35,c32)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) )
| ~ p14(f17(c36,c31),f17(c36,c31))
| ~ p4(c34,f5(c35,c32))
| p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),f5(c35,c32))) )
<=> ( ~ ! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) )
| ~ p14(f17(c36,c31),f17(c36,c31))
| ~ p4(c34,f5(c35,c32))
| p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),f5(c35,c32))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) )
| ~ p14(f17(c36,c31),f17(c36,c31))
| ~ p4(c34,f5(c35,c32))
| p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),f5(c35,c32))) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X57: $i,X56: $i,X59: $i,X58: $i] :
( ~ p14(X56,X58)
| ~ p4(X57,X59)
| p4(f15(X56,X57),f15(X58,X59)) )
| ~ p14(f17(c36,c31),f17(c36,c31))
| ~ p4(c34,f5(c35,c32))
| p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),f5(c35,c32))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),f5(c35,c32))),
inference(unit_resolution,[status(thm)],[25,22,19,9]) ).
tff(27,plain,
^ [X53: $i] :
refl(
( p4(X53,X53)
<=> p4(X53,X53) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X53: $i] : p4(X53,X53)
<=> ! [X53: $i] : p4(X53,X53) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X53: $i] : p4(X53,X53)
<=> ! [X53: $i] : p4(X53,X53) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [X53: $i] : p4(X53,X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_5) ).
tff(31,plain,
! [X53: $i] : p4(X53,X53),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [X53: $i] : p4(X53,X53),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X53: $i] : p4(X53,X53),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [X53: $i] : p4(X53,X53)
| p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),c34)),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
^ [X53: $i,X55: $i,X54: $i] :
refl(
( ( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
<=> ( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
<=> ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
<=> ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [X53: $i,X55: $i,X54: $i] :
trans(
monotonicity(
rewrite(
( ( p4(X54,X55)
| ~ p4(X53,X54) )
<=> ( ~ p4(X53,X54)
| p4(X54,X55) ) )),
( ( p4(X54,X55)
| ~ p4(X53,X54)
| ~ p4(X53,X55) )
<=> ( ~ p4(X53,X54)
| p4(X54,X55)
| ~ p4(X53,X55) ) )),
rewrite(
( ( ~ p4(X53,X54)
| p4(X54,X55)
| ~ p4(X53,X55) )
<=> ( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) ) )),
( ( p4(X54,X55)
| ~ p4(X53,X54)
| ~ p4(X53,X55) )
<=> ( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X53: $i,X55: $i,X54: $i] :
( p4(X54,X55)
| ~ p4(X53,X54)
| ~ p4(X53,X55) )
<=> ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X53: $i,X55: $i,X54: $i] :
( p4(X54,X55)
| ~ p4(X53,X54)
| ~ p4(X53,X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_23) ).
tff(42,plain,
! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),c34))
| ~ p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),f5(c35,c32)))
| p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34)) )
<=> ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),c34))
| ~ p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),f5(c35,c32)))
| p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),c34))
| ~ p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),f5(c35,c32)))
| p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),c34))
| ~ p4(f15(f17(c36,c31),c34),f15(f17(c36,c31),f5(c35,c32)))
| p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34)),
inference(unit_resolution,[status(thm)],[48,45,35,26]) ).
tff(50,plain,
^ [X60: $i,X61: $i] :
refl(
( p4(f15(f17(c36,X60),f5(c35,X61)),f5(X60,X61))
<=> p4(f15(f17(c36,X60),f5(c35,X61)),f5(X60,X61)) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X60: $i,X61: $i] : p4(f15(f17(c36,X60),f5(c35,X61)),f5(X60,X61))
<=> ! [X60: $i,X61: $i] : p4(f15(f17(c36,X60),f5(c35,X61)),f5(X60,X61)) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X60: $i,X61: $i] : p4(f15(f17(c36,X60),f5(c35,X61)),f5(X60,X61))
<=> ! [X60: $i,X61: $i] : p4(f15(f17(c36,X60),f5(c35,X61)),f5(X60,X61)) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
! [X60: $i,X61: $i] : p4(f15(f17(c36,X60),f5(c35,X61)),f5(X60,X61)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_34) ).
tff(54,plain,
! [X60: $i,X61: $i] : p4(f15(f17(c36,X60),f5(c35,X61)),f5(X60,X61)),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [X60: $i,X61: $i] : p4(f15(f17(c36,X60),f5(c35,X61)),f5(X60,X61)),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [X60: $i,X61: $i] : p4(f15(f17(c36,X60),f5(c35,X61)),f5(X60,X61)),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [X60: $i,X61: $i] : p4(f15(f17(c36,X60),f5(c35,X61)),f5(X60,X61))
| p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32)) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32)),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
( ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32))
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34))
| p4(f5(c31,c32),f15(f17(c36,c31),c34)) )
<=> ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32))
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34))
| p4(f5(c31,c32),f15(f17(c36,c31),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ~ p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34))
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32))
| p4(f5(c31,c32),f15(f17(c36,c31),c34)) )
<=> ( ~ p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32))
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34))
| p4(f5(c31,c32),f15(f17(c36,c31),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34))
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32))
| p4(f5(c31,c32),f15(f17(c36,c31),c34)) )
<=> ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32))
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34))
| p4(f5(c31,c32),f15(f17(c36,c31),c34)) ) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34))
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32))
| p4(f5(c31,c32),f15(f17(c36,c31),c34)) )
<=> ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32))
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34))
| p4(f5(c31,c32),f15(f17(c36,c31),c34)) ) ),
inference(transitivity,[status(thm)],[61,59]) ).
tff(63,plain,
( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34))
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32))
| p4(f5(c31,c32),f15(f17(c36,c31),c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f5(c31,c32))
| ~ p4(f15(f17(c36,c31),f5(c35,c32)),f15(f17(c36,c31),c34))
| p4(f5(c31,c32),f15(f17(c36,c31),c34)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
p4(f5(c31,c32),f15(f17(c36,c31),c34)),
inference(unit_resolution,[status(thm)],[64,45,58,49]) ).
tff(66,plain,
^ [X73: $i,X74: $i] :
refl(
( ( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) )
<=> ( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) )
<=> ! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) )
<=> ! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
^ [X73: $i,X74: $i] :
rewrite(
( ( p4(f5(c31,X73),f5(c31,X74))
| ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74) )
<=> ( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [X73: $i,X74: $i] :
( p4(f5(c31,X73),f5(c31,X74))
| ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74) )
<=> ! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [X73: $i,X74: $i] :
( p4(f5(c31,X73),f5(c31,X74))
| ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_46) ).
tff(72,plain,
! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( p27(f8(f10(c28,f13(c29,c30)),c32),c33)
<=> p27(f8(f10(c28,f13(c29,c30)),c32),c33) ),
inference(rewrite,[status(thm)],]) ).
tff(77,axiom,
p27(f8(f10(c28,f13(c29,c30)),c32),c33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27_17) ).
tff(78,plain,
p27(f8(f10(c28,f13(c29,c30)),c32),c33),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( ( ~ ! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) )
| ~ p27(f8(f10(c28,f13(c29,c30)),c32),c33)
| p4(f5(c31,c32),f5(c31,c33)) )
<=> ( ~ ! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) )
| ~ p27(f8(f10(c28,f13(c29,c30)),c32),c33)
| p4(f5(c31,c32),f5(c31,c33)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ~ ! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) )
| ~ p27(f8(f10(c28,f13(c29,c30)),c32),c33)
| p4(f5(c31,c32),f5(c31,c33)) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [X73: $i,X74: $i] :
( ~ p27(f8(f10(c28,f13(c29,c30)),X73),X74)
| p4(f5(c31,X73),f5(c31,X74)) )
| ~ p27(f8(f10(c28,f13(c29,c30)),c32),c33)
| p4(f5(c31,c32),f5(c31,c33)) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
p4(f5(c31,c32),f5(c31,c33)),
inference(unit_resolution,[status(thm)],[81,78,75]) ).
tff(83,plain,
( ~ p4(f5(c31,c33),f15(f17(c36,c31),c34))
<=> ~ p4(f5(c31,c33),f15(f17(c36,c31),c34)) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
~ p4(f5(c31,c33),f15(f17(c36,c31),c34)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p4_18) ).
tff(85,plain,
~ p4(f5(c31,c33),f15(f17(c36,c31),c34)),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| p4(f5(c31,c33),f15(f17(c36,c31),c34))
| ~ p4(f5(c31,c32),f5(c31,c33))
| ~ p4(f5(c31,c32),f15(f17(c36,c31),c34)) )
<=> ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| p4(f5(c31,c33),f15(f17(c36,c31),c34))
| ~ p4(f5(c31,c32),f5(c31,c33))
| ~ p4(f5(c31,c32),f15(f17(c36,c31),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( ~ p4(f5(c31,c32),f15(f17(c36,c31),c34))
| ~ p4(f5(c31,c32),f5(c31,c33))
| p4(f5(c31,c33),f15(f17(c36,c31),c34)) )
<=> ( p4(f5(c31,c33),f15(f17(c36,c31),c34))
| ~ p4(f5(c31,c32),f5(c31,c33))
| ~ p4(f5(c31,c32),f15(f17(c36,c31),c34)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f5(c31,c32),f15(f17(c36,c31),c34))
| ~ p4(f5(c31,c32),f5(c31,c33))
| p4(f5(c31,c33),f15(f17(c36,c31),c34)) )
<=> ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| p4(f5(c31,c33),f15(f17(c36,c31),c34))
| ~ p4(f5(c31,c32),f5(c31,c33))
| ~ p4(f5(c31,c32),f15(f17(c36,c31),c34)) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f5(c31,c32),f15(f17(c36,c31),c34))
| ~ p4(f5(c31,c32),f5(c31,c33))
| p4(f5(c31,c33),f15(f17(c36,c31),c34)) )
<=> ( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| p4(f5(c31,c33),f15(f17(c36,c31),c34))
| ~ p4(f5(c31,c32),f5(c31,c33))
| ~ p4(f5(c31,c32),f15(f17(c36,c31),c34)) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| ~ p4(f5(c31,c32),f15(f17(c36,c31),c34))
| ~ p4(f5(c31,c32),f5(c31,c33))
| p4(f5(c31,c33),f15(f17(c36,c31),c34)) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [X53: $i,X55: $i,X54: $i] :
( ~ p4(X53,X55)
| ~ p4(X53,X54)
| p4(X54,X55) )
| p4(f5(c31,c33),f15(f17(c36,c31),c34))
| ~ p4(f5(c31,c32),f5(c31,c33))
| ~ p4(f5(c31,c32),f15(f17(c36,c31),c34)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
$false,
inference(unit_resolution,[status(thm)],[91,85,45,82,65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN652-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 06:21:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.51/0.61 % SZS status Unsatisfiable
% 0.51/0.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------