%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC007-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 33
% Syntax : Number of formulae : 73 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 452 ( 204 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 711 ( 361 ~; 307 |; 0 &)
% ( 43 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 109 ( 99 !; 0 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk2_type,type,
sk2: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(1,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
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/sandbox/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/sandbox/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,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(23,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
app(nil,sk4) = sk4,
inference(unit_resolution,[status(thm)],[28,25,7]) ).
tff(30,plain,
app(app(nil,sk4),nil) = app(sk4,nil),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
app(app(nil,sk4),nil) = sk2,
inference(transitivity,[status(thm)],[30,18,4]) ).
tff(32,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(34,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ( nil = sk3 )
<=> ( nil = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
nil = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(38,plain,
nil = sk3,
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(41,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( ~ ssList(nil)
| ( app(nil,nil) = nil ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ! [V: $i,U: $i] :
( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) )
<=> ( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(45,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(46,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) )
<=> ( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(transitivity,[status(thm)],[45,44]) ).
tff(47,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(transitivity,[status(thm)],[46,43]) ).
tff(48,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( nil != U )
| ( nil != V )
| ~ ssList(V) )
<=> ( ( nil != U )
| ~ ssList(V)
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ~ ssList(U) ) )),
rewrite(( ( ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ( app(U,V) = nil ) ) )),
rewrite(( ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ( app(U,V) = nil ) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [V: $i,U: $i] :
( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [V: $i,U: $i] :
( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(transitivity,[status(thm)],[49,47]) ).
tff(51,axiom,
! [V: $i,U: $i] :
( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause145) ).
tff(52,plain,
( ~ ssList(nil)
| ( app(nil,nil) = nil ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ~ ssList(nil)
| ( app(nil,nil) = nil ) ),
inference(modus_ponens,[status(thm)],[52,42]) ).
tff(54,plain,
app(nil,nil) = nil,
inference(unit_resolution,[status(thm)],[53,41]) ).
tff(55,plain,
app(nil,nil) = sk1,
inference(transitivity,[status(thm)],[54,38,35]) ).
tff(56,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,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(A,C) != sk1 )
| ( 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(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,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(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,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/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(62,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( app(nil,nil) != sk1 )
| ( app(app(nil,sk4),nil) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( app(nil,nil) != sk1 )
| ( app(app(nil,sk4),nil) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ( ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( app(nil,nil) != sk1 )
| ( app(app(nil,sk4),nil) != sk2 ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk4)
| ( app(nil,nil) != sk1 )
| ( app(app(nil,sk4),nil) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( app(nil,nil) != sk1 )
| ( app(app(nil,sk4),nil) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( app(nil,nil) != sk1 )
| ( app(app(nil,sk4),nil) != sk2 ) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( app(nil,nil) != sk1 )
| ( app(app(nil,sk4),nil) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( app(nil,nil) != sk1 )
| ( app(app(nil,sk4),nil) != sk2 ) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( app(nil,nil) != sk1 )
| ( app(app(nil,sk4),nil) != sk2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(A,C) != sk1 )
| ( app(app(A,B),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( app(nil,nil) != sk1 )
| ( app(app(nil,sk4),nil) != sk2 ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
app(app(nil,sk4),nil) != sk2,
inference(unit_resolution,[status(thm)],[71,41,7,65,55]) ).
tff(73,plain,
$false,
inference(unit_resolution,[status(thm)],[72,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWC007-1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 08:01:16 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45 % SZS output start Proof
% See solution above
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------