TSTP Solution File: SYN598-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN598-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 23:56:35 EDT 2022
% Result : Unsatisfiable 7.74s 5.22s
% Output : Proof 7.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 78
% Syntax : Number of formulae : 152 ( 45 unt; 18 typ; 0 def)
% Number of atoms : 571 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 730 ( 334 ~; 330 |; 0 &)
% ( 66 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of FOOLs : 41 ( 41 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 15 >; 6 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 353 ( 312 !; 0 ?; 353 :)
% Comments :
%------------------------------------------------------------------------------
tff(p7_type,type,
p7: ( $i * $i ) > $o ).
tff(f10_type,type,
f10: ( $i * $i ) > $i ).
tff(f11_type,type,
f11: ( $i * $i ) > $i ).
tff(f12_type,type,
f12: $i > $i ).
tff(f13_type,type,
f13: $i > $i ).
tff(c23_type,type,
c23: $i ).
tff(f14_type,type,
f14: $i > $i ).
tff(f15_type,type,
f15: $i > $i ).
tff(c22_type,type,
c22: $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(f6_type,type,
f6: $i > $i ).
tff(c21_type,type,
c21: $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(f8_type,type,
f8: $i > $i ).
tff(f9_type,type,
f9: $i > $i ).
tff(p5_type,type,
p5: ( $i * $i ) > $o ).
tff(p19_type,type,
p19: ( $i * $i ) > $o ).
tff(p18_type,type,
p18: $i > $o ).
tff(1,plain,
^ [X18: $i] :
refl(
( p3(X18,X18)
<=> p3(X18,X18) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X18: $i] : p3(X18,X18)
<=> ! [X18: $i] : p3(X18,X18) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X18: $i] : p3(X18,X18)
<=> ! [X18: $i] : p3(X18,X18) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X18: $i] : p3(X18,X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_5) ).
tff(5,plain,
! [X18: $i] : p3(X18,X18),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X18: $i] : p3(X18,X18),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X18: $i] : p3(X18,X18),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X18: $i] : p3(X18,X18)
| p3(f12(f15(f13(c23))),f12(f15(f13(c23)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p3(f12(f15(f13(c23))),f12(f15(f13(c23)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X45: $i,X46: $i] :
refl(
( ( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) )
<=> ( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) )
<=> ! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) )
<=> ! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X45: $i,X46: $i] :
rewrite(
( ( p7(f14(X45),f14(X46))
| ~ p3(X45,X46) )
<=> ( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X45: $i,X46: $i] :
( p7(f14(X45),f14(X46))
| ~ p3(X45,X46) )
<=> ! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X45: $i,X46: $i] :
( p7(f14(X45),f14(X46))
| ~ p3(X45,X46) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_17) ).
tff(16,plain,
! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) )
| ~ p3(f12(f15(f13(c23))),f12(f15(f13(c23))))
| p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23))))) )
<=> ( ~ ! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) )
| ~ p3(f12(f15(f13(c23))),f12(f15(f13(c23))))
| p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) )
| ~ p3(f12(f15(f13(c23))),f12(f15(f13(c23))))
| p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [X45: $i,X46: $i] :
( ~ p3(X45,X46)
| p7(f14(X45),f14(X46)) )
| ~ p3(f12(f15(f13(c23))),f12(f15(f13(c23))))
| p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23))))) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23))))),
inference(unit_resolution,[status(thm)],[22,19,9]) ).
tff(24,plain,
^ [X43: $i,X42: $i,X41: $i,X44: $i] :
refl(
( ( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) )
<=> ( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) )
<=> ! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) )
<=> ! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [X43: $i,X42: $i,X41: $i,X44: $i] :
trans(
monotonicity(
rewrite(
( ( p7(f11(X41,X42),f11(X43,X44))
| ~ p3(X42,X44) )
<=> ( ~ p3(X42,X44)
| p7(f11(X41,X42),f11(X43,X44)) ) )),
( ( p7(f11(X41,X42),f11(X43,X44))
| ~ p3(X42,X44)
| ~ p7(X41,X43) )
<=> ( ~ p3(X42,X44)
| p7(f11(X41,X42),f11(X43,X44))
| ~ p7(X41,X43) ) )),
rewrite(
( ( ~ p3(X42,X44)
| p7(f11(X41,X42),f11(X43,X44))
| ~ p7(X41,X43) )
<=> ( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) ) )),
( ( p7(f11(X41,X42),f11(X43,X44))
| ~ p3(X42,X44)
| ~ p7(X41,X43) )
<=> ( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X43: $i,X42: $i,X41: $i,X44: $i] :
( p7(f11(X41,X42),f11(X43,X44))
| ~ p3(X42,X44)
| ~ p7(X41,X43) )
<=> ! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [X43: $i,X42: $i,X41: $i,X44: $i] :
( p7(f11(X41,X42),f11(X43,X44))
| ~ p3(X42,X44)
| ~ p7(X41,X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_25) ).
tff(30,plain,
! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( p3(f4(f6(c21)),c22)
<=> p3(f4(f6(c21)),c22) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
p3(f4(f6(c21)),c22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_7) ).
tff(36,plain,
p3(f4(f6(c21)),c22),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ( ~ ! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) )
| ~ p3(f4(f6(c21)),c22)
| ~ p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23)))))
| p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22)) )
<=> ( ~ ! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) )
| ~ p3(f4(f6(c21)),c22)
| ~ p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23)))))
| p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) )
| ~ p3(f4(f6(c21)),c22)
| ~ p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23)))))
| p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22)) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [X43: $i,X42: $i,X41: $i,X44: $i] :
( ~ p3(X42,X44)
| ~ p7(X41,X43)
| p7(f11(X41,X42),f11(X43,X44)) )
| ~ p3(f4(f6(c21)),c22)
| ~ p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23)))))
| p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22)),
inference(unit_resolution,[status(thm)],[39,36,33,23]) ).
tff(41,plain,
^ [X34: $i] :
refl(
( p7(X34,X34)
<=> p7(X34,X34) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [X34: $i] : p7(X34,X34)
<=> ! [X34: $i] : p7(X34,X34) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [X34: $i] : p7(X34,X34)
<=> ! [X34: $i] : p7(X34,X34) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
! [X34: $i] : p7(X34,X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_3) ).
tff(45,plain,
! [X34: $i] : p7(X34,X34),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [X34: $i] : p7(X34,X34),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X34: $i] : p7(X34,X34),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [X34: $i] : p7(X34,X34)
| p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
^ [X39: $i,X38: $i,X37: $i,X40: $i] :
refl(
( ( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) )
<=> ( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) )
<=> ! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) )
<=> ! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
^ [X39: $i,X38: $i,X37: $i,X40: $i] :
trans(
monotonicity(
rewrite(
( ( p7(f10(X37,X38),f10(X39,X40))
| ~ p7(X38,X40) )
<=> ( ~ p7(X38,X40)
| p7(f10(X37,X38),f10(X39,X40)) ) )),
( ( p7(f10(X37,X38),f10(X39,X40))
| ~ p7(X38,X40)
| ~ p7(X37,X39) )
<=> ( ~ p7(X38,X40)
| p7(f10(X37,X38),f10(X39,X40))
| ~ p7(X37,X39) ) )),
rewrite(
( ( ~ p7(X38,X40)
| p7(f10(X37,X38),f10(X39,X40))
| ~ p7(X37,X39) )
<=> ( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) ) )),
( ( p7(f10(X37,X38),f10(X39,X40))
| ~ p7(X38,X40)
| ~ p7(X37,X39) )
<=> ( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [X39: $i,X38: $i,X37: $i,X40: $i] :
( p7(f10(X37,X38),f10(X39,X40))
| ~ p7(X38,X40)
| ~ p7(X37,X39) )
<=> ! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [X39: $i,X38: $i,X37: $i,X40: $i] :
( p7(f10(X37,X38),f10(X39,X40))
| ~ p7(X38,X40)
| ~ p7(X37,X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_26) ).
tff(56,plain,
! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) )
| ~ p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))
| ~ p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22))
| p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))) )
<=> ( ~ ! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) )
| ~ p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))
| ~ p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22))
| p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) )
| ~ p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))
| ~ p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22))
| p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [X39: $i,X38: $i,X37: $i,X40: $i] :
( ~ p7(X38,X40)
| ~ p7(X37,X39)
| p7(f10(X37,X38),f10(X39,X40)) )
| ~ p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))
| ~ p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22))
| p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))),
inference(unit_resolution,[status(thm)],[62,59,49,40]) ).
tff(64,plain,
^ [X31: $i] :
refl(
( p5(X31,X31)
<=> p5(X31,X31) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [X31: $i] : p5(X31,X31)
<=> ! [X31: $i] : p5(X31,X31) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [X31: $i] : p5(X31,X31)
<=> ! [X31: $i] : p5(X31,X31) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
! [X31: $i] : p5(X31,X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_6) ).
tff(68,plain,
! [X31: $i] : p5(X31,X31),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [X31: $i] : p5(X31,X31),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [X31: $i] : p5(X31,X31),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [X31: $i] : p5(X31,X31)
| p5(c21,c21) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
p5(c21,c21),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
^ [X49: $i,X50: $i] :
refl(
( ( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) )
<=> ( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) )
<=> ! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) )
<=> ! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
^ [X49: $i,X50: $i] :
rewrite(
( ( p7(f9(X49),f9(X50))
| ~ p5(X49,X50) )
<=> ( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [X49: $i,X50: $i] :
( p7(f9(X49),f9(X50))
| ~ p5(X49,X50) )
<=> ! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,axiom,
! [X49: $i,X50: $i] :
( p7(f9(X49),f9(X50))
| ~ p5(X49,X50) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_10) ).
tff(79,plain,
! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) ),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
( ( ~ ! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) )
| ~ p5(c21,c21)
| p7(f9(c21),f9(c21)) )
<=> ( ~ ! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) )
| ~ p5(c21,c21)
| p7(f9(c21),f9(c21)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ~ ! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) )
| ~ p5(c21,c21)
| p7(f9(c21),f9(c21)) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
( ~ ! [X49: $i,X50: $i] :
( ~ p5(X49,X50)
| p7(f9(X49),f9(X50)) )
| ~ p5(c21,c21)
| p7(f9(c21),f9(c21)) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
p7(f9(c21),f9(c21)),
inference(unit_resolution,[status(thm)],[85,82,72]) ).
tff(87,plain,
^ [X47: $i,X48: $i] :
refl(
( ( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) )
<=> ( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) )
<=> ! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) )
<=> ! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
^ [X47: $i,X48: $i] :
rewrite(
( ( p7(f8(X47),f8(X48))
| ~ p7(X47,X48) )
<=> ( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [X47: $i,X48: $i] :
( p7(f8(X47),f8(X48))
| ~ p7(X47,X48) )
<=> ! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,axiom,
! [X47: $i,X48: $i] :
( p7(f8(X47),f8(X48))
| ~ p7(X47,X48) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_18) ).
tff(93,plain,
! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) ),
inference(modus_ponens,[status(thm)],[95,88]) ).
tff(97,plain,
( ( ~ ! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) )
| ~ p7(f9(c21),f9(c21))
| p7(f8(f9(c21)),f8(f9(c21))) )
<=> ( ~ ! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) )
| ~ p7(f9(c21),f9(c21))
| p7(f8(f9(c21)),f8(f9(c21))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) )
| ~ p7(f9(c21),f9(c21))
| p7(f8(f9(c21)),f8(f9(c21))) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [X47: $i,X48: $i] :
( ~ p7(X47,X48)
| p7(f8(X47),f8(X48)) )
| ~ p7(f9(c21),f9(c21))
| p7(f8(f9(c21)),f8(f9(c21))) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
p7(f8(f9(c21)),f8(f9(c21))),
inference(unit_resolution,[status(thm)],[99,96,86]) ).
tff(101,plain,
^ [X8: $i] :
refl(
( ( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
<=> ( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
<=> ! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
<=> ! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
^ [X8: $i] :
rewrite(
( ( p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8)))
| ~ p18(X8) )
<=> ( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [X8: $i] :
( p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8)))
| ~ p18(X8) )
<=> ! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [X8: $i] :
( p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8)))
| ~ p18(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19_28) ).
tff(107,plain,
! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
( p18(c21)
<=> p18(c21) ),
inference(rewrite,[status(thm)],]) ).
tff(112,axiom,
p18(c21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c21_is_p18_2) ).
tff(113,plain,
p18(c21),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
( ( ~ ! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
| ~ p18(c21)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) )
<=> ( ~ ! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
| ~ p18(c21)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ~ ! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
| ~ p18(c21)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [X8: $i] :
( ~ p18(X8)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
| ~ p18(c21)
| p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))),
inference(unit_resolution,[status(thm)],[116,113,110]) ).
tff(118,plain,
( ~ p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21)))
<=> ~ p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ),
inference(rewrite,[status(thm)],]) ).
tff(119,axiom,
~ p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p19_27) ).
tff(120,plain,
~ p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
^ [X6: $i,X4: $i,X7: $i,X5: $i] :
refl(
( ( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) )
<=> ( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) )
<=> ! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) )
<=> ! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
^ [X6: $i,X4: $i,X7: $i,X5: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p19(X4,X5)
| ~ p7(X6,X4) )
<=> ( ~ p7(X6,X4)
| p19(X4,X5) ) )),
( ( p19(X4,X5)
| ~ p7(X6,X4)
| ~ p7(X7,X5) )
<=> ( ~ p7(X6,X4)
| p19(X4,X5)
| ~ p7(X7,X5) ) )),
rewrite(
( ( ~ p7(X6,X4)
| p19(X4,X5)
| ~ p7(X7,X5) )
<=> ( ~ p7(X7,X5)
| ~ p7(X6,X4)
| p19(X4,X5) ) )),
( ( p19(X4,X5)
| ~ p7(X6,X4)
| ~ p7(X7,X5) )
<=> ( ~ p7(X7,X5)
| ~ p7(X6,X4)
| p19(X4,X5) ) )),
( ( p19(X4,X5)
| ~ p7(X6,X4)
| ~ p7(X7,X5)
| ~ p19(X6,X7) )
<=> ( ~ p7(X7,X5)
| ~ p7(X6,X4)
| p19(X4,X5)
| ~ p19(X6,X7) ) )),
rewrite(
( ( ~ p7(X7,X5)
| ~ p7(X6,X4)
| p19(X4,X5)
| ~ p19(X6,X7) )
<=> ( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) ) )),
( ( p19(X4,X5)
| ~ p7(X6,X4)
| ~ p7(X7,X5)
| ~ p19(X6,X7) )
<=> ( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [X6: $i,X4: $i,X7: $i,X5: $i] :
( p19(X4,X5)
| ~ p7(X6,X4)
| ~ p7(X7,X5)
| ~ p19(X6,X7) )
<=> ! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,axiom,
! [X6: $i,X4: $i,X7: $i,X5: $i] :
( p19(X4,X5)
| ~ p7(X6,X4)
| ~ p7(X7,X5)
| ~ p19(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19_23) ).
tff(127,plain,
! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) ),
inference(modus_ponens,[status(thm)],[129,122]) ).
tff(131,plain,
( ( ~ ! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) )
| ~ p7(f8(f9(c21)),f8(f9(c21)))
| ~ p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21)))
| ~ p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))))
| p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) )
<=> ( ~ ! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) )
| ~ p7(f8(f9(c21)),f8(f9(c21)))
| ~ p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21)))
| ~ p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))))
| p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
( ~ ! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) )
| ~ p7(f8(f9(c21)),f8(f9(c21)))
| ~ p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21)))
| ~ p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))))
| p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
( ~ ! [X6: $i,X4: $i,X7: $i,X5: $i] :
( ~ p7(X7,X5)
| ~ p19(X6,X7)
| ~ p7(X6,X4)
| p19(X4,X5) )
| ~ p7(f8(f9(c21)),f8(f9(c21)))
| ~ p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21)))
| ~ p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))))
| p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
$false,
inference(unit_resolution,[status(thm)],[133,130,120,117,100,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN598-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n007.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 05:43:35 EDT 2022
% 0.12/0.34 % 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.
% 7.74/5.22 % SZS status Unsatisfiable
% 7.74/5.22 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------