%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC094-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:30:09 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 39
% Syntax : Number of formulae : 90 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 550 ( 172 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 849 ( 426 ~; 369 |; 0 &)
% ( 54 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 148 ( 134 !; 0 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(skaf45_type,type,
skaf45: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(7,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[17,14,7]) ).
tff(19,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ frontsegP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ~ frontsegP(U,V)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ~ frontsegP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
tff(25,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(31,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ( ~ ssList(nil)
| frontsegP(nil,nil) )
<=> ( ~ ssList(nil)
| frontsegP(nil,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( frontsegP(nil,nil)
| ~ ssList(nil) )
<=> ( ~ ssList(nil)
| frontsegP(nil,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ! [U: $i] :
( frontsegP(nil,nil)
| ~ ssList(nil) )
<=> ( frontsegP(nil,nil)
| ~ ssList(nil) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(35,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ! [U: $i] :
( frontsegP(nil,nil)
| ~ ssList(nil) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(36,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ( frontsegP(nil,nil)
| ~ ssList(nil) ) ),
inference(transitivity,[status(thm)],[35,34]) ).
tff(37,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ( ~ ssList(nil)
| frontsegP(nil,nil) ) ),
inference(transitivity,[status(thm)],[36,33]) ).
tff(38,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ( nil != U )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U ) ) )),
( ( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) )),
rewrite(( ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) )),
( ( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [U: $i] :
( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [U: $i] :
( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) )
<=> ( ~ ssList(nil)
| frontsegP(nil,nil) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,axiom,
! [U: $i] :
( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause83) ).
tff(42,plain,
( ~ ssList(nil)
| frontsegP(nil,nil) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
( ~ ssList(nil)
| frontsegP(nil,nil) ),
inference(modus_ponens,[status(thm)],[42,32]) ).
tff(44,plain,
frontsegP(nil,nil),
inference(unit_resolution,[status(thm)],[43,31]) ).
tff(45,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ( app(nil,skaf45(nil,nil)) = nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ( app(nil,skaf45(nil,nil)) = nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ ssList(nil)
| ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ( app(nil,skaf45(nil,nil)) = nil ) )
<=> ( ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ( app(nil,skaf45(nil,nil)) = nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(nil)
| ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ( app(nil,skaf45(nil,nil)) = nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ( app(nil,skaf45(nil,nil)) = nil ) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(nil)
| ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ( app(nil,skaf45(nil,nil)) = nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ( app(nil,skaf45(nil,nil)) = nil ) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(nil)
| ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ( app(nil,skaf45(nil,nil)) = nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ( app(nil,skaf45(nil,nil)) = nil ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
app(nil,skaf45(nil,nil)) = nil,
inference(unit_resolution,[status(thm)],[50,31,44,28]) ).
tff(52,plain,
app(app(nil,skaf45(nil,nil)),sk3) = app(nil,sk3),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
app(app(nil,skaf45(nil,nil)),sk3) = sk1,
inference(transitivity,[status(thm)],[52,18,4]) ).
tff(54,plain,
^ [V: $i,U: $i] :
refl(( ssList(skaf45(U,V))
<=> ssList(skaf45(U,V)) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [V: $i,U: $i] : ssList(skaf45(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf45(U,V)) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [V: $i,U: $i] : ssList(skaf45(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf45(U,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
tff(58,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf45(U,V))
| ssList(skaf45(nil,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
ssList(skaf45(nil,nil)),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(65,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ( sk4 = sk3 )
<=> ( sk4 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,axiom,
sk4 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(69,plain,
sk4 = sk3,
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
sk3 = sk4,
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
app(nil,sk3) = sk2,
inference(transitivity,[status(thm)],[18,70,66]) ).
tff(72,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk1 )
| ( app(A,C) != sk2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(78,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[80,73]) ).
tff(82,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(nil,nil))
| ( app(nil,sk3) != sk2 )
| ( app(app(nil,skaf45(nil,nil)),sk3) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(nil,nil))
| ( app(nil,sk3) != sk2 )
| ( app(app(nil,skaf45(nil,nil)),sk3) != sk1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(skaf45(nil,nil))
| ( app(nil,sk3) != sk2 )
| ( app(app(nil,skaf45(nil,nil)),sk3) != sk1 ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(nil,nil))
| ( app(nil,sk3) != sk2 )
| ( app(app(nil,skaf45(nil,nil)),sk3) != sk1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(skaf45(nil,nil))
| ( app(nil,sk3) != sk2 )
| ( app(app(nil,skaf45(nil,nil)),sk3) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(nil,nil))
| ( app(nil,sk3) != sk2 )
| ( app(app(nil,skaf45(nil,nil)),sk3) != sk1 ) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(skaf45(nil,nil))
| ( app(nil,sk3) != sk2 )
| ( app(app(nil,skaf45(nil,nil)),sk3) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(nil,nil))
| ( app(nil,sk3) != sk2 )
| ( app(app(nil,skaf45(nil,nil)),sk3) != sk1 ) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(skaf45(nil,nil))
| ( app(nil,sk3) != sk2 )
| ( app(app(nil,skaf45(nil,nil)),sk3) != sk1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk2 )
| ( app(app(A,B),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(nil,nil))
| ( app(nil,sk3) != sk2 )
| ( app(app(nil,skaf45(nil,nil)),sk3) != sk1 ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
( ~ ssList(skaf45(nil,nil))
| ( app(app(nil,skaf45(nil,nil)),sk3) != sk1 ) ),
inference(unit_resolution,[status(thm)],[87,31,7,81,71]) ).
tff(89,plain,
app(app(nil,skaf45(nil,nil)),sk3) != sk1,
inference(unit_resolution,[status(thm)],[88,62]) ).
tff(90,plain,
$false,
inference(unit_resolution,[status(thm)],[89,53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SWC094-1 : TPTP v9.0.0. Released v2.4.0.
% 0.10/0.13 % Command : run_E %s %d THM
% 0.12/0.35 % Computer : n007.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Jun 20 08:19:35 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% See solution above
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------