TSTP Solution File: SYN693-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN693-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 23:56:58 EDT 2022
% Result : Unsatisfiable 1.02s 0.87s
% Output : Proof 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 51
% Syntax : Number of formulae : 98 ( 29 unt; 12 typ; 0 def)
% Number of atoms : 411 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 572 ( 267 ~; 261 |; 0 &)
% ( 44 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 8 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 237 ( 217 !; 0 ?; 237 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f11_type,type,
f11: ( $i * $i ) > $i ).
tff(c43_type,type,
c43: $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(f23_type,type,
f23: ( $i * $i ) > $i ).
tff(f9_type,type,
f9: $i > $i ).
tff(f20_type,type,
f20: $i > $i ).
tff(c37_type,type,
c37: $i ).
tff(c44_type,type,
c44: $i ).
tff(c46_type,type,
c46: $i ).
tff(p10_type,type,
p10: ( $i * $i ) > $o ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(1,plain,
^ [X43: $i] :
refl(
( p2(X43,X43)
<=> p2(X43,X43) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X43: $i] : p2(X43,X43)
<=> ! [X43: $i] : p2(X43,X43) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X43: $i] : p2(X43,X43)
<=> ! [X43: $i] : p2(X43,X43) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X43: $i] : p2(X43,X43),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_12) ).
tff(5,plain,
! [X43: $i] : p2(X43,X43),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X43: $i] : p2(X43,X43),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X43: $i] : p2(X43,X43),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X43: $i] : p2(X43,X43)
| p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ p2(f11(f4(c46),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
<=> ~ p2(f11(f4(c46),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
~ p2(f11(f4(c46),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p2_53) ).
tff(12,plain,
~ p2(f11(f4(c46),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X43: $i,X45: $i,X44: $i] :
refl(
( ( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
<=> ( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
<=> ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
<=> ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [X43: $i,X45: $i,X44: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X44,X45)
| ~ p2(X43,X44) )
<=> ( p2(X44,X45)
| ~ p2(X43,X44) ) )),
( ( p2(X44,X45)
| ~ p2(X43,X44)
| ~ p2(X43,X45) )
<=> ( p2(X44,X45)
| ~ p2(X43,X44)
| ~ p2(X43,X45) ) )),
rewrite(
( ( p2(X44,X45)
| ~ p2(X43,X44)
| ~ p2(X43,X45) )
<=> ( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) ) )),
( ( p2(X44,X45)
| ~ p2(X43,X44)
| ~ p2(X43,X45) )
<=> ( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X44)
| ~ p2(X43,X45) )
<=> ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X44)
| ~ p2(X43,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_40) ).
tff(19,plain,
! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(c46),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43)) )
<=> ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(c46),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(c46),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43)) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(c46),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43)),
inference(unit_resolution,[status(thm)],[25,22,12,9]) ).
tff(27,plain,
^ [X5: $i] :
refl(
( p10(X5,X5)
<=> p10(X5,X5) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X5: $i] : p10(X5,X5)
<=> ! [X5: $i] : p10(X5,X5) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [X5: $i] : p10(X5,X5)
<=> ! [X5: $i] : p10(X5,X5) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [X5: $i] : p10(X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_7) ).
tff(31,plain,
! [X5: $i] : p10(X5,X5),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [X5: $i] : p10(X5,X5),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X5: $i] : p10(X5,X5),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [X5: $i] : p10(X5,X5)
| p10(c43,c43) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
p10(c43,c43),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
^ [X90: $i,X91: $i] :
refl(
( ( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) )
<=> ( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) )
<=> ! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) )
<=> ! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [X90: $i,X91: $i] :
rewrite(
( ( p3(f4(X90),f4(X91))
| ~ p2(X90,X91) )
<=> ( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X90: $i,X91: $i] :
( p3(f4(X90),f4(X91))
| ~ p2(X90,X91) )
<=> ! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X90: $i,X91: $i] :
( p3(f4(X90),f4(X91))
| ~ p2(X90,X91) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_34) ).
tff(42,plain,
! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( p2(c44,c46)
<=> p2(c44,c46) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
p2(c44,c46),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_16) ).
tff(48,plain,
p2(c44,c46),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( ( ~ ! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) )
| ~ p2(c44,c46)
| p3(f4(c44),f4(c46)) )
<=> ( ~ ! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) )
| ~ p2(c44,c46)
| p3(f4(c44),f4(c46)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ ! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) )
| ~ p2(c44,c46)
| p3(f4(c44),f4(c46)) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [X90: $i,X91: $i] :
( ~ p2(X90,X91)
| p3(f4(X90),f4(X91)) )
| ~ p2(c44,c46)
| p3(f4(c44),f4(c46)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
p3(f4(c44),f4(c46)),
inference(unit_resolution,[status(thm)],[51,48,45]) ).
tff(53,plain,
^ [X47: $i,X49: $i,X46: $i,X48: $i] :
refl(
( ( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) )
<=> ( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) )
<=> ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) )
<=> ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
^ [X47: $i,X49: $i,X46: $i,X48: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f11(X46,X47),f11(X48,X49))
| ~ p10(X47,X49) )
<=> ( ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ) )),
( ( p2(f11(X46,X47),f11(X48,X49))
| ~ p10(X47,X49)
| ~ p3(X46,X48) )
<=> ( ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49))
| ~ p3(X46,X48) ) )),
rewrite(
( ( ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49))
| ~ p3(X46,X48) )
<=> ( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ) )),
( ( p2(f11(X46,X47),f11(X48,X49))
| ~ p10(X47,X49)
| ~ p3(X46,X48) )
<=> ( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( p2(f11(X46,X47),f11(X48,X49))
| ~ p10(X47,X49)
| ~ p3(X46,X48) )
<=> ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,axiom,
! [X47: $i,X49: $i,X46: $i,X48: $i] :
( p2(f11(X46,X47),f11(X48,X49))
| ~ p10(X47,X49)
| ~ p3(X46,X48) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_58) ).
tff(59,plain,
! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) ),
inference(modus_ponens,[status(thm)],[61,54]) ).
tff(63,plain,
( ( ~ ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) )
| ~ p10(c43,c43)
| ~ p3(f4(c44),f4(c46))
| p2(f11(f4(c44),c43),f11(f4(c46),c43)) )
<=> ( ~ ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) )
| ~ p10(c43,c43)
| ~ p3(f4(c44),f4(c46))
| p2(f11(f4(c44),c43),f11(f4(c46),c43)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( ~ p3(f4(c44),f4(c46))
| ~ p10(c43,c43)
| p2(f11(f4(c44),c43),f11(f4(c46),c43)) )
<=> ( ~ p10(c43,c43)
| ~ p3(f4(c44),f4(c46))
| p2(f11(f4(c44),c43),f11(f4(c46),c43)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ~ ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) )
| ~ p3(f4(c44),f4(c46))
| ~ p10(c43,c43)
| p2(f11(f4(c44),c43),f11(f4(c46),c43)) )
<=> ( ~ ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) )
| ~ p10(c43,c43)
| ~ p3(f4(c44),f4(c46))
| p2(f11(f4(c44),c43),f11(f4(c46),c43)) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) )
| ~ p3(f4(c44),f4(c46))
| ~ p10(c43,c43)
| p2(f11(f4(c44),c43),f11(f4(c46),c43)) )
<=> ( ~ ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) )
| ~ p10(c43,c43)
| ~ p3(f4(c44),f4(c46))
| p2(f11(f4(c44),c43),f11(f4(c46),c43)) ) ),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,plain,
( ~ ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) )
| ~ p3(f4(c44),f4(c46))
| ~ p10(c43,c43)
| p2(f11(f4(c44),c43),f11(f4(c46),c43)) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [X47: $i,X49: $i,X46: $i,X48: $i] :
( ~ p3(X46,X48)
| ~ p10(X47,X49)
| p2(f11(X46,X47),f11(X48,X49)) )
| ~ p10(c43,c43)
| ~ p3(f4(c44),f4(c46))
| p2(f11(f4(c44),c43),f11(f4(c46),c43)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
p2(f11(f4(c44),c43),f11(f4(c46),c43)),
inference(unit_resolution,[status(thm)],[68,62,52,35]) ).
tff(70,plain,
( ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(c46),c43)) )
<=> ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(c46),c43)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) )
<=> ( p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(c46),c43)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) )
<=> ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(c46),c43)) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) )
<=> ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(c46),c43)) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c46),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(c44),c43),f11(f4(c46),c43)) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
~ p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)),
inference(unit_resolution,[status(thm)],[75,22,69,26]) ).
tff(77,plain,
( p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43))
<=> p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_52) ).
tff(79,plain,
p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) )
<=> ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ( p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)) )
<=> ( ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)) )
<=> ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) ) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)) )
<=> ( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) ) ),
inference(transitivity,[status(thm)],[82,80]) ).
tff(84,plain,
( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43)) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
( ~ ! [X43: $i,X45: $i,X44: $i] :
( p2(X44,X45)
| ~ p2(X43,X45)
| ~ p2(X43,X44) )
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(c44),c43))
| ~ p2(f11(f4(f23(c44,f9(f20(c37)))),c43),f11(f4(f23(c44,f9(f20(c37)))),c43))
| p2(f11(f4(c44),c43),f11(f4(f23(c44,f9(f20(c37)))),c43)) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
$false,
inference(unit_resolution,[status(thm)],[85,22,79,9,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN693-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 06:44:46 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.02/0.87 % SZS status Unsatisfiable
% 1.02/0.87 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------