%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC200-1 : 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 05:30:29 AM UTC 2025
% Result : Unsatisfiable 0.60s 0.76s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 47
% Syntax : Number of formulae : 109 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 595 ( 94 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 869 ( 417 ~; 395 |; 0 &)
% ( 57 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 34 ( 34 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 146 ( 132 !; 0 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: $i > $i ).
tff(skaf44_type,type,
skaf44: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk1_type,type,
sk1: $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,
( singletonP(sk3)
<=> singletonP(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
singletonP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(7,plain,
singletonP(sk3),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(10,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,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(12,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)],[11]) ).
tff(13,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(14,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(15,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)],[14]) ).
tff(16,axiom,
! [U: $i] :
( ~ singletonP(U)
| ~ ssList(U)
| ( cons(skaf44(U),nil) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
tff(17,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,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(22,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(23,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)],[22,21]) ).
tff(24,plain,
cons(skaf44(sk3),nil) = sk3,
inference(unit_resolution,[status(thm)],[23,20,10,7]) ).
tff(25,plain,
cons(skaf44(sk3),nil) = sk1,
inference(transitivity,[status(thm)],[24,4]) ).
tff(26,plain,
( memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3)))
<=> memberP(sk1,sk5(skaf44(sk3))) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( memberP(sk1,sk5(skaf44(sk3)))
<=> memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) ),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
^ [U: $i] :
refl(( ssItem(skaf44(U))
<=> ssItem(skaf44(U)) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [U: $i] : ssItem(skaf44(U))
<=> ! [U: $i] : ssItem(skaf44(U)) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [U: $i] : ssItem(skaf44(U))
<=> ! [U: $i] : ssItem(skaf44(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [U: $i] : ssItem(skaf44(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).
tff(32,plain,
! [U: $i] : ssItem(skaf44(U)),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [U: $i] : ssItem(skaf44(U)),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [U: $i] : ssItem(skaf44(U)),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [U: $i] : ssItem(skaf44(U))
| ssItem(skaf44(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
ssItem(skaf44(sk3)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
^ [A: $i] :
refl(( ( ~ ssItem(A)
| memberP(sk1,sk5(A)) )
<=> ( ~ ssItem(A)
| memberP(sk1,sk5(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(41,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) )
| ~ ssItem(skaf44(sk3))
| memberP(sk1,sk5(skaf44(sk3))) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) )
| ~ ssItem(skaf44(sk3))
| memberP(sk1,sk5(skaf44(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) )
| ~ ssItem(skaf44(sk3))
| memberP(sk1,sk5(skaf44(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) )
| ~ ssItem(skaf44(sk3))
| memberP(sk1,sk5(skaf44(sk3))) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
memberP(sk1,sk5(skaf44(sk3))),
inference(unit_resolution,[status(thm)],[46,43,36]) ).
tff(48,plain,
memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))),
inference(modus_ponens,[status(thm)],[47,27]) ).
tff(49,plain,
( ( sk5(skaf44(sk3)) = skaf44(sk3) )
<=> ( skaf44(sk3) = sk5(skaf44(sk3)) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(50,plain,
( ( skaf44(sk3) = sk5(skaf44(sk3)) )
<=> ( sk5(skaf44(sk3)) = skaf44(sk3) ) ),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
( ( skaf44(sk3) != sk5(skaf44(sk3)) )
<=> ( sk5(skaf44(sk3)) != skaf44(sk3) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
^ [A: $i] :
refl(( ( ~ ssItem(A)
| ( A != sk5(A) ) )
<=> ( ~ ssItem(A)
| ( A != sk5(A) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(56,plain,
! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
| ~ ssItem(skaf44(sk3))
| ( skaf44(sk3) != sk5(skaf44(sk3)) ) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
| ~ ssItem(skaf44(sk3))
| ( skaf44(sk3) != sk5(skaf44(sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
| ~ ssItem(skaf44(sk3))
| ( skaf44(sk3) != sk5(skaf44(sk3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
| ~ ssItem(skaf44(sk3))
| ( skaf44(sk3) != sk5(skaf44(sk3)) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
skaf44(sk3) != sk5(skaf44(sk3)),
inference(unit_resolution,[status(thm)],[61,58,36]) ).
tff(63,plain,
sk5(skaf44(sk3)) != skaf44(sk3),
inference(modus_ponens,[status(thm)],[62,51]) ).
tff(64,plain,
^ [A: $i] :
refl(( ( ~ ssItem(A)
| ssItem(sk5(A)) )
<=> ( ~ ssItem(A)
| ssItem(sk5(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(68,plain,
! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(skaf44(sk3))
| ssItem(sk5(skaf44(sk3))) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(skaf44(sk3))
| ssItem(sk5(skaf44(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(skaf44(sk3))
| ssItem(sk5(skaf44(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(skaf44(sk3))
| ssItem(sk5(skaf44(sk3))) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
ssItem(sk5(skaf44(sk3))),
inference(unit_resolution,[status(thm)],[73,70,36]) ).
tff(75,plain,
^ [U: $i] :
refl(( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
^ [U: $i] :
rewrite(( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(81,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf44(sk3)))
| ~ memberP(nil,sk5(skaf44(sk3))) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf44(sk3)))
| ~ memberP(nil,sk5(skaf44(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf44(sk3)))
| ~ memberP(nil,sk5(skaf44(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf44(sk3)))
| ~ memberP(nil,sk5(skaf44(sk3))) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
~ memberP(nil,sk5(skaf44(sk3))),
inference(unit_resolution,[status(thm)],[87,84,74]) ).
tff(89,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ memberP(cons(U,V),W)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U) )
<=> ( ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(W) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W)
| memberP(V,W) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W)
| memberP(V,W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W)
| ( W = U ) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W)
| ( W = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause161) ).
tff(95,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(101,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ~ ssItem(sk5(skaf44(sk3)))
| memberP(nil,sk5(skaf44(sk3)))
| ( sk5(skaf44(sk3)) = skaf44(sk3) )
| ~ memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ~ ssItem(sk5(skaf44(sk3)))
| memberP(nil,sk5(skaf44(sk3)))
| ( sk5(skaf44(sk3)) = skaf44(sk3) )
| ~ memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
( ( ~ ssItem(skaf44(sk3))
| ~ ssList(nil)
| ~ ssItem(sk5(skaf44(sk3)))
| memberP(nil,sk5(skaf44(sk3)))
| ( sk5(skaf44(sk3)) = skaf44(sk3) )
| ~ memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) )
<=> ( ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ~ ssItem(sk5(skaf44(sk3)))
| memberP(nil,sk5(skaf44(sk3)))
| ( sk5(skaf44(sk3)) = skaf44(sk3) )
| ~ memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(skaf44(sk3))
| ~ ssList(nil)
| ~ ssItem(sk5(skaf44(sk3)))
| memberP(nil,sk5(skaf44(sk3)))
| ( sk5(skaf44(sk3)) = skaf44(sk3) )
| ~ memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ~ ssItem(sk5(skaf44(sk3)))
| memberP(nil,sk5(skaf44(sk3)))
| ( sk5(skaf44(sk3)) = skaf44(sk3) )
| ~ memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(skaf44(sk3))
| ~ ssList(nil)
| ~ ssItem(sk5(skaf44(sk3)))
| memberP(nil,sk5(skaf44(sk3)))
| ( sk5(skaf44(sk3)) = skaf44(sk3) )
| ~ memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ~ ssItem(sk5(skaf44(sk3)))
| memberP(nil,sk5(skaf44(sk3)))
| ( sk5(skaf44(sk3)) = skaf44(sk3) )
| ~ memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) ) ),
inference(transitivity,[status(thm)],[104,102]) ).
tff(106,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(skaf44(sk3))
| ~ ssList(nil)
| ~ ssItem(sk5(skaf44(sk3)))
| memberP(nil,sk5(skaf44(sk3)))
| ( sk5(skaf44(sk3)) = skaf44(sk3) )
| ~ memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(skaf44(sk3))
| ~ ssItem(sk5(skaf44(sk3)))
| memberP(nil,sk5(skaf44(sk3)))
| ( sk5(skaf44(sk3)) = skaf44(sk3) )
| ~ memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
( memberP(nil,sk5(skaf44(sk3)))
| ( sk5(skaf44(sk3)) = skaf44(sk3) )
| ~ memberP(cons(skaf44(sk3),nil),sk5(skaf44(sk3))) ),
inference(unit_resolution,[status(thm)],[107,101,98,36,74]) ).
tff(109,plain,
$false,
inference(unit_resolution,[status(thm)],[108,88,63,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC200-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 08:41:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.60/0.76 % SZS status Unsatisfiable
% 0.60/0.76 % SZS output start Proof
% See solution above
% 0.61/0.77 % E exiting
%------------------------------------------------------------------------------