%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN714-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 05:39:53 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 29
% Syntax : Number of formulae : 60 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 384 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 529 ( 229 ~; 265 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 127 ( 113 !; 0 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
tff(p51_type,type,
p51: ( $i * $i ) > $o ).
tff(f25_type,type,
f25: ( $i * $i ) > $i ).
tff(c67_type,type,
c67: $i ).
tff(f27_type,type,
f27: ( $i * $i ) > $i ).
tff(c68_type,type,
c68: $i ).
tff(c59_type,type,
c59: $i ).
tff(c66_type,type,
c66: $i ).
tff(p50_type,type,
p50: ( $i * $i * $i ) > $o ).
tff(c62_type,type,
c62: $i ).
tff(p53_type,type,
p53: ( $i * $i ) > $o ).
tff(f17_type,type,
f17: $i > $i ).
tff(c60_type,type,
c60: $i ).
tff(p52_type,type,
p52: ( $i * $i ) > $o ).
tff(f20_type,type,
f20: $i > $i ).
tff(f21_type,type,
f21: ( $i * $i ) > $i ).
tff(c64_type,type,
c64: $i ).
tff(p16_type,type,
p16: ( $i * $i ) > $o ).
tff(c65_type,type,
c65: $i ).
tff(1,plain,
^ [X160: $i] :
refl(( ( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) )
<=> ( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) )
<=> ! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) )
<=> ! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [X160: $i] :
rewrite(( ( p50(c66,f25(f27(c59,X160),c67),c62)
| ~ p53(X160,f17(c66)) )
<=> ( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X160: $i] :
( p50(c66,f25(f27(c59,X160),c67),c62)
| ~ p53(X160,f17(c66)) )
<=> ! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X160: $i] :
( p50(c66,f25(f27(c59,X160),c67),c62)
| ~ p53(X160,f17(c66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p50_64) ).
tff(7,plain,
! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( p53(c68,f17(c66))
<=> p53(c68,f17(c66)) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
p53(c68,f17(c66)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p53_23) ).
tff(13,plain,
p53(c68,f17(c66)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) )
| ~ p53(c68,f17(c66))
| p50(c66,f25(f27(c59,c68),c67),c62) )
<=> ( ~ ! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) )
| ~ p53(c68,f17(c66))
| p50(c66,f25(f27(c59,c68),c67),c62) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) )
| ~ p53(c68,f17(c66))
| p50(c66,f25(f27(c59,c68),c67),c62) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X160: $i] :
( ~ p53(X160,f17(c66))
| p50(c66,f25(f27(c59,X160),c67),c62) )
| ~ p53(c68,f17(c66))
| p50(c66,f25(f27(c59,c68),c67),c62) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
p50(c66,f25(f27(c59,c68),c67),c62),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [X16: $i,X15: $i] :
refl(( ( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) )
<=> ( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) )
<=> ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) )
<=> ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [X16: $i,X15: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( p16(f17(X15),c65)
| p50(X15,X16,c60)
| ~ p51(X15,X16) )
<=> ( p16(f17(X15),c65)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ) )),
( ( p16(f17(X15),c65)
| p50(X15,X16,c60)
| ~ p51(X15,X16)
| ~ p50(X15,X16,c62) )
<=> ( p16(f17(X15),c65)
| ~ p51(X15,X16)
| p50(X15,X16,c60)
| ~ p50(X15,X16,c62) ) )),
rewrite(( ( p16(f17(X15),c65)
| ~ p51(X15,X16)
| p50(X15,X16,c60)
| ~ p50(X15,X16,c62) )
<=> ( p16(f17(X15),c65)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ) )),
( ( p16(f17(X15),c65)
| p50(X15,X16,c60)
| ~ p51(X15,X16)
| ~ p50(X15,X16,c62) )
<=> ( p16(f17(X15),c65)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ) )),
( ( p16(f17(X15),c65)
| p50(X15,X16,c60)
| ~ p51(X15,X16)
| ~ p50(X15,X16,c62)
| ~ p52(f20(f21(c62,c64)),X15) )
<=> ( p16(f17(X15),c65)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60)
| ~ p52(f20(f21(c62,c64)),X15) ) )),
rewrite(( ( p16(f17(X15),c65)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60)
| ~ p52(f20(f21(c62,c64)),X15) )
<=> ( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ) )),
( ( p16(f17(X15),c65)
| p50(X15,X16,c60)
| ~ p51(X15,X16)
| ~ p50(X15,X16,c62)
| ~ p52(f20(f21(c62,c64)),X15) )
<=> ( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| p50(X15,X16,c60)
| ~ p51(X15,X16)
| ~ p50(X15,X16,c62)
| ~ p52(f20(f21(c62,c64)),X15) )
<=> ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| p50(X15,X16,c60)
| ~ p51(X15,X16)
| ~ p50(X15,X16,c62)
| ~ p52(f20(f21(c62,c64)),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_98) ).
tff(24,plain,
! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ~ p50(c66,f25(f27(c59,c68),c67),c60)
<=> ~ p50(c66,f25(f27(c59,c68),c67),c60) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
~ p50(c66,f25(f27(c59,c68),c67),c60),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p50_33) ).
tff(30,plain,
~ p50(c66,f25(f27(c59,c68),c67),c60),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( p52(f20(f21(c62,c64)),c66)
<=> p52(f20(f21(c62,c64)),c66) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
p52(f20(f21(c62,c64)),c66),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p52_28) ).
tff(33,plain,
p52(f20(f21(c62,c64)),c66),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( ~ p16(f17(c66),c65)
<=> ~ p16(f17(c66),c65) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
~ p16(f17(c66),c65),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p16_24) ).
tff(36,plain,
~ p16(f17(c66),c65),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ( ~ ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) )
| p16(f17(c66),c65)
| p50(c66,f25(f27(c59,c68),c67),c60)
| ~ p52(f20(f21(c62,c64)),c66)
| ~ p50(c66,f25(f27(c59,c68),c67),c62)
| ~ p51(c66,f25(f27(c59,c68),c67)) )
<=> ( ~ ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) )
| p16(f17(c66),c65)
| p50(c66,f25(f27(c59,c68),c67),c60)
| ~ p52(f20(f21(c62,c64)),c66)
| ~ p50(c66,f25(f27(c59,c68),c67),c62)
| ~ p51(c66,f25(f27(c59,c68),c67)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( p16(f17(c66),c65)
| ~ p52(f20(f21(c62,c64)),c66)
| ~ p50(c66,f25(f27(c59,c68),c67),c62)
| ~ p51(c66,f25(f27(c59,c68),c67))
| p50(c66,f25(f27(c59,c68),c67),c60) )
<=> ( p16(f17(c66),c65)
| p50(c66,f25(f27(c59,c68),c67),c60)
| ~ p52(f20(f21(c62,c64)),c66)
| ~ p50(c66,f25(f27(c59,c68),c67),c62)
| ~ p51(c66,f25(f27(c59,c68),c67)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) )
| p16(f17(c66),c65)
| ~ p52(f20(f21(c62,c64)),c66)
| ~ p50(c66,f25(f27(c59,c68),c67),c62)
| ~ p51(c66,f25(f27(c59,c68),c67))
| p50(c66,f25(f27(c59,c68),c67),c60) )
<=> ( ~ ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) )
| p16(f17(c66),c65)
| p50(c66,f25(f27(c59,c68),c67),c60)
| ~ p52(f20(f21(c62,c64)),c66)
| ~ p50(c66,f25(f27(c59,c68),c67),c62)
| ~ p51(c66,f25(f27(c59,c68),c67)) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) )
| p16(f17(c66),c65)
| ~ p52(f20(f21(c62,c64)),c66)
| ~ p50(c66,f25(f27(c59,c68),c67),c62)
| ~ p51(c66,f25(f27(c59,c68),c67))
| p50(c66,f25(f27(c59,c68),c67),c60) )
<=> ( ~ ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) )
| p16(f17(c66),c65)
| p50(c66,f25(f27(c59,c68),c67),c60)
| ~ p52(f20(f21(c62,c64)),c66)
| ~ p50(c66,f25(f27(c59,c68),c67),c62)
| ~ p51(c66,f25(f27(c59,c68),c67)) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) )
| p16(f17(c66),c65)
| ~ p52(f20(f21(c62,c64)),c66)
| ~ p50(c66,f25(f27(c59,c68),c67),c62)
| ~ p51(c66,f25(f27(c59,c68),c67))
| p50(c66,f25(f27(c59,c68),c67),c60) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [X16: $i,X15: $i] :
( p16(f17(X15),c65)
| ~ p52(f20(f21(c62,c64)),X15)
| ~ p50(X15,X16,c62)
| ~ p51(X15,X16)
| p50(X15,X16,c60) )
| p16(f17(c66),c65)
| p50(c66,f25(f27(c59,c68),c67),c60)
| ~ p52(f20(f21(c62,c64)),c66)
| ~ p50(c66,f25(f27(c59,c68),c67),c62)
| ~ p51(c66,f25(f27(c59,c68),c67)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
~ p51(c66,f25(f27(c59,c68),c67)),
inference(unit_resolution,[status(thm)],[42,36,33,30,27,17]) ).
tff(44,plain,
^ [X166: $i,X168: $i,X167: $i,X165: $i] :
refl(( ( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) )
<=> ( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) )
<=> ! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) )
<=> ! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
^ [X166: $i,X168: $i,X167: $i,X165: $i] :
trans(monotonicity(rewrite(( ( p51(X165,f25(f27(X166,X167),X168))
| ~ p51(X165,X168) )
<=> ( ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) ) )),
( ( p51(X165,f25(f27(X166,X167),X168))
| ~ p51(X165,X168)
| ~ p53(X167,f17(X165)) )
<=> ( ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168))
| ~ p53(X167,f17(X165)) ) )),
rewrite(( ( ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168))
| ~ p53(X167,f17(X165)) )
<=> ( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) ) )),
( ( p51(X165,f25(f27(X166,X167),X168))
| ~ p51(X165,X168)
| ~ p53(X167,f17(X165)) )
<=> ( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [X166: $i,X168: $i,X167: $i,X165: $i] :
( p51(X165,f25(f27(X166,X167),X168))
| ~ p51(X165,X168)
| ~ p53(X167,f17(X165)) )
<=> ! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [X166: $i,X168: $i,X167: $i,X165: $i] :
( p51(X165,f25(f27(X166,X167),X168))
| ~ p51(X165,X168)
| ~ p53(X167,f17(X165)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p51_87) ).
tff(50,plain,
! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( p51(c66,c67)
<=> p51(c66,c67) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
p51(c66,c67),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p51_22) ).
tff(56,plain,
p51(c66,c67),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ( ~ ! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) )
| ~ p53(c68,f17(c66))
| ~ p51(c66,c67)
| p51(c66,f25(f27(c59,c68),c67)) )
<=> ( ~ ! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) )
| ~ p53(c68,f17(c66))
| ~ p51(c66,c67)
| p51(c66,f25(f27(c59,c68),c67)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) )
| ~ p53(c68,f17(c66))
| ~ p51(c66,c67)
| p51(c66,f25(f27(c59,c68),c67)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [X166: $i,X168: $i,X167: $i,X165: $i] :
( ~ p53(X167,f17(X165))
| ~ p51(X165,X168)
| p51(X165,f25(f27(X166,X167),X168)) )
| ~ p53(c68,f17(c66))
| ~ p51(c66,c67)
| p51(c66,f25(f27(c59,c68),c67)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
$false,
inference(unit_resolution,[status(thm)],[59,56,13,53,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN714-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 : Fri Jun 20 12:40:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% See solution above
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------