%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC008-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:29:54 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 37
% Syntax : Number of formulae : 83 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 504 ( 161 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 793 ( 402 ~; 347 |; 0 &)
% ( 44 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 30 ( 30 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 : 142 ( 129 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk2_type,type,
sk2: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(skaf45_type,type,
skaf45: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(3,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
tff(7,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
app(sk4,nil) = sk4,
inference(unit_resolution,[status(thm)],[17,14,7]) ).
tff(19,plain,
( frontsegP(sk4,sk3)
<=> frontsegP(sk4,sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
frontsegP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(21,plain,
frontsegP(sk4,sk3),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(24,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,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(26,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)],[25]) ).
tff(27,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(28,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(29,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)],[28]) ).
tff(30,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(31,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ~ ssList(sk4)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ~ ssList(sk4)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) )
<=> ( ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ~ ssList(sk4)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ~ ssList(sk4)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ~ ssList(sk4)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ~ ssList(sk4)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
app(sk3,skaf45(sk4,sk3)) = sk4,
inference(unit_resolution,[status(thm)],[40,34,24,7,21]) ).
tff(42,plain,
app(app(sk3,skaf45(sk4,sk3)),nil) = app(sk4,nil),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
app(app(sk3,skaf45(sk4,sk3)),nil) = sk2,
inference(transitivity,[status(thm)],[42,18,4]) ).
tff(44,plain,
^ [V: $i,U: $i] :
refl(( ssList(skaf45(U,V))
<=> ssList(skaf45(U,V)) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [V: $i,U: $i] : ssList(skaf45(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf45(U,V)) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [V: $i,U: $i] : ssList(skaf45(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf45(U,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
tff(48,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf45(U,V))
| ssList(skaf45(sk4,sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
ssList(skaf45(sk4,sk3)),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(55,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[59,14,24]) ).
tff(61,plain,
app(sk3,nil) = sk1,
inference(transitivity,[status(thm)],[60,56]) ).
tff(62,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,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) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ) )),
( ( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(68,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(74,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(sk3,nil) != sk1 )
| ( app(app(sk3,skaf45(sk4,sk3)),nil) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(sk3,nil) != sk1 )
| ( app(app(sk3,skaf45(sk4,sk3)),nil) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(sk3,skaf45(sk4,sk3)),nil) != sk2 )
| ( app(sk3,nil) != sk1 ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(sk3,nil) != sk1 )
| ( app(app(sk3,skaf45(sk4,sk3)),nil) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(sk3,skaf45(sk4,sk3)),nil) != sk2 )
| ( app(sk3,nil) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(sk3,nil) != sk1 )
| ( app(app(sk3,skaf45(sk4,sk3)),nil) != sk2 ) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(sk3,skaf45(sk4,sk3)),nil) != sk2 )
| ( app(sk3,nil) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(sk3,nil) != sk1 )
| ( app(app(sk3,skaf45(sk4,sk3)),nil) != sk2 ) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(sk3,skaf45(sk4,sk3)),nil) != sk2 )
| ( app(sk3,nil) != sk1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(app(A,B),C) != sk2 )
| ( app(A,C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(sk3,nil) != sk1 )
| ( app(app(sk3,skaf45(sk4,sk3)),nil) != sk2 ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( ~ ssList(skaf45(sk4,sk3))
| ( app(app(sk3,skaf45(sk4,sk3)),nil) != sk2 ) ),
inference(unit_resolution,[status(thm)],[80,74,24,71,61]) ).
tff(82,plain,
app(app(sk3,skaf45(sk4,sk3)),nil) != sk2,
inference(unit_resolution,[status(thm)],[81,52]) ).
tff(83,plain,
$false,
inference(unit_resolution,[status(thm)],[82,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC008-1 : TPTP v9.0.0. Released v2.4.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 07:59:20 EDT 2025
% 0.13/0.34 % 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
%------------------------------------------------------------------------------