%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC127-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:30:14 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 40
% Syntax : Number of formulae : 100 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 404 ( 116 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 544 ( 259 ~; 235 |; 0 &)
% ( 50 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 103 ( 92 !; 0 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(skaf44_type,type,
skaf44: $i > $i ).
tff(singletonP_type,type,
singletonP: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/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,
( neq(sk3,nil)
<=> neq(sk1,nil) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( neq(sk1,nil)
<=> neq(sk3,nil) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk3,nil) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(10,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( segmentP(sk2,sk1)
<=> segmentP(sk4,sk3) ),
inference(monotonicity,[status(thm)],[10,3]) ).
tff(12,plain,
( segmentP(sk4,sk3)
<=> segmentP(sk2,sk1) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( segmentP(sk4,sk3)
<=> segmentP(sk4,sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
segmentP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(15,plain,
segmentP(sk4,sk3),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
segmentP(sk2,sk1),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
( ( ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) )
<=> ( ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
( ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(19,plain,
( ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ neq(sk1,nil),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
~ neq(sk3,nil),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(23,plain,
( ( nil = sk3 )
<=> ( sk3 = nil ) ),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(25,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(27,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
( ( singletonP(sk3)
| ~ neq(sk4,nil) )
<=> ( singletonP(sk3)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
( singletonP(sk3)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(31,plain,
( singletonP(sk3)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
singletonP(sk3),
inference(unit_resolution,[status(thm)],[31,28]) ).
tff(33,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(35,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
<=> ( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [U: $i] :
rewrite(( ( ~ singletonP(U)
| ~ ssList(U)
| ( cons(skaf44(U),nil) = U ) )
<=> ( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [U: $i] :
( ~ singletonP(U)
| ~ ssList(U)
| ( cons(skaf44(U),nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [U: $i] :
( ~ singletonP(U)
| ~ ssList(U)
| ( cons(skaf44(U),nil) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
tff(42,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
| ~ ssList(sk3)
| ( cons(skaf44(sk3),nil) = sk3 )
| ~ singletonP(sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
| ~ ssList(sk3)
| ( cons(skaf44(sk3),nil) = sk3 )
| ~ singletonP(sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
| ~ ssList(sk3)
| ( cons(skaf44(sk3),nil) = sk3 )
| ~ singletonP(sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
| ~ ssList(sk3)
| ( cons(skaf44(sk3),nil) = sk3 )
| ~ singletonP(sk3) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( ( cons(skaf44(sk3),nil) = sk3 )
| ~ singletonP(sk3) ),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
cons(skaf44(sk3),nil) = sk3,
inference(unit_resolution,[status(thm)],[49,32]) ).
tff(51,plain,
( ( cons(skaf44(sk3),nil) = nil )
<=> ( sk3 = nil ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( cons(skaf44(sk3),nil) = nil )
<=> ( nil = sk3 ) ),
inference(transitivity,[status(thm)],[51,22]) ).
tff(53,plain,
( ( cons(skaf44(sk3),nil) = nil )
<=> ( sk3 = nil ) ),
inference(transitivity,[status(thm)],[52,23]) ).
tff(54,plain,
( ( cons(skaf44(sk3),nil) != nil )
<=> ( sk3 != nil ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
^ [U: $i] :
refl(( ssItem(skaf44(U))
<=> ssItem(skaf44(U)) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [U: $i] : ssItem(skaf44(U))
<=> ! [U: $i] : ssItem(skaf44(U)) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [U: $i] : ssItem(skaf44(U))
<=> ! [U: $i] : ssItem(skaf44(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
! [U: $i] : ssItem(skaf44(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).
tff(59,plain,
! [U: $i] : ssItem(skaf44(U)),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [U: $i] : ssItem(skaf44(U)),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [U: $i] : ssItem(skaf44(U)),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [U: $i] : ssItem(skaf44(U))
| ssItem(skaf44(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
ssItem(skaf44(sk3)),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( cons(U,V) != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
tff(70,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(76,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ( cons(skaf44(sk3),nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ( cons(skaf44(sk3),nil) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ( ~ ssItem(skaf44(sk3))
| ~ ssList(nil)
| ( cons(skaf44(sk3),nil) != nil ) )
<=> ( ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ( cons(skaf44(sk3),nil) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(skaf44(sk3))
| ~ ssList(nil)
| ( cons(skaf44(sk3),nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ( cons(skaf44(sk3),nil) != nil ) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(skaf44(sk3))
| ~ ssList(nil)
| ( cons(skaf44(sk3),nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ( cons(skaf44(sk3),nil) != nil ) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(skaf44(sk3))
| ~ ssList(nil)
| ( cons(skaf44(sk3),nil) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ( cons(skaf44(sk3),nil) != nil ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ~ ssItem(skaf44(sk3))
| ( cons(skaf44(sk3),nil) != nil ) ),
inference(unit_resolution,[status(thm)],[82,76,73]) ).
tff(84,plain,
cons(skaf44(sk3),nil) != nil,
inference(unit_resolution,[status(thm)],[83,63]) ).
tff(85,plain,
sk3 != nil,
inference(modus_ponens,[status(thm)],[84,54]) ).
tff(86,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(92,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[94,87]) ).
tff(96,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
( ( sk3 = nil )
| neq(sk3,nil) ),
inference(unit_resolution,[status(thm)],[98,76,95,35]) ).
tff(100,plain,
$false,
inference(unit_resolution,[status(thm)],[99,85,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC127-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 08:29:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------