%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC046-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:30:01 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 57
% Syntax : Number of formulae : 145 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 634 ( 154 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 842 ( 386 ~; 386 |; 0 &)
% ( 70 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 33 ( 33 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 192 ( 171 !; 0 ?; 192 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(hd_type,type,
hd: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(nil_type,type,
nil: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(skaf83_type,type,
skaf83: $i > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(skaf82_type,type,
skaf82: $i > $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_6) ).
tff(3,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( nil = sk2 )
<=> ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
nil = sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(6,plain,
nil = sk2,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
nil = sk4,
inference(transitivity,[status(thm)],[6,3]) ).
tff(8,plain,
( memberP(nil,hd(sk3))
<=> memberP(sk4,hd(sk3)) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ~ memberP(nil,hd(sk3))
<=> ~ memberP(sk4,hd(sk3)) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(12,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( ( nil = sk3 )
<=> ( nil = sk1 ) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(19,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(23,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(30,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(unit_resolution,[status(thm)],[36,33,23]) ).
tff(38,plain,
ssItem(hd(sk3)),
inference(unit_resolution,[status(thm)],[37,20]) ).
tff(39,plain,
^ [U: $i] :
refl(( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [U: $i] :
rewrite(( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(45,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(hd(sk3))
| ~ memberP(nil,hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(hd(sk3))
| ~ memberP(nil,hd(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(hd(sk3))
| ~ memberP(nil,hd(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(hd(sk3))
| ~ memberP(nil,hd(sk3)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
~ memberP(nil,hd(sk3)),
inference(unit_resolution,[status(thm)],[51,48,38]) ).
tff(53,plain,
~ memberP(sk4,hd(sk3)),
inference(modus_ponens,[status(thm)],[52,9]) ).
tff(54,plain,
^ [U: $i] :
refl(( ssList(skaf82(U))
<=> ssList(skaf82(U)) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
! [U: $i] : ssList(skaf82(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
tff(58,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [U: $i] : ssList(skaf82(U)),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ ! [U: $i] : ssList(skaf82(U))
| ssList(skaf82(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
ssList(skaf82(sk3)),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
^ [U: $i] :
refl(( ssItem(skaf83(U))
<=> ssItem(skaf83(U)) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
! [U: $i] : ssItem(skaf83(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
tff(67,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ~ ! [U: $i] : ssItem(skaf83(U))
| ssItem(skaf83(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
ssItem(skaf83(sk3)),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
tff(78,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[80,73]) ).
tff(82,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3) ) ),
inference(unit_resolution,[status(thm)],[84,81]) ).
tff(86,plain,
hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3),
inference(unit_resolution,[status(thm)],[85,71,62]) ).
tff(87,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(91,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
tff(93,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[95,88]) ).
tff(97,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(unit_resolution,[status(thm)],[99,96,23]) ).
tff(101,plain,
cons(skaf83(sk3),skaf82(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[100,20]) ).
tff(102,plain,
hd(cons(skaf83(sk3),skaf82(sk3))) = hd(sk3),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
hd(sk3) = hd(cons(skaf83(sk3),skaf82(sk3))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
hd(sk3) = skaf83(sk3),
inference(transitivity,[status(thm)],[103,86]) ).
tff(105,plain,
sk3 = cons(skaf83(sk3),skaf82(sk3)),
inference(symmetry,[status(thm)],[101]) ).
tff(106,plain,
( memberP(sk3,hd(sk3))
<=> memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) ),
inference(monotonicity,[status(thm)],[105,104]) ).
tff(107,plain,
( memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3))
<=> memberP(sk3,hd(sk3)) ),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
^ [W: $i,V: $i] :
refl(( ( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
<=> ( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) )),
inference(bind,[status(th)],[]) ).
tff(109,plain,
( ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
<=> ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,plain,
( ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
<=> ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
^ [W: $i,V: $i] :
rewrite(( ( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) )
<=> ( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) )),
inference(bind,[status(th)],[]) ).
tff(112,plain,
( ! [W: $i,V: $i] :
( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [W: $i,V: $i,U: $i] :
( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i] :
( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(114,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i,U: $i] :
( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(115,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i] :
( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) ) ),
inference(transitivity,[status(thm)],[114,113]) ).
tff(116,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) ),
inference(transitivity,[status(thm)],[115,112]) ).
tff(117,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( U != V )
| ~ ssList(W) )
<=> ( ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) ) )),
rewrite(( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,axiom,
! [W: $i,V: $i,U: $i] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause138) ).
tff(121,plain,
! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ),
inference(modus_ponens,[status(thm)],[121,110]) ).
tff(123,plain,
! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ),
inference(modus_ponens,[status(thm)],[123,109]) ).
tff(125,plain,
( ( ~ ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) )
<=> ( ~ ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) ),
inference(unit_resolution,[status(thm)],[127,124]) ).
tff(129,plain,
memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)),
inference(unit_resolution,[status(thm)],[128,71,62]) ).
tff(130,plain,
memberP(sk3,hd(sk3)),
inference(modus_ponens,[status(thm)],[129,107]) ).
tff(131,plain,
^ [A: $i] :
refl(( ( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
<=> ( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) )),
inference(bind,[status(th)],[]) ).
tff(132,plain,
( ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
^ [A: $i] :
rewrite(( ( ~ ssItem(A)
| ~ memberP(sk3,A)
| memberP(sk4,A) )
<=> ( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) )),
inference(bind,[status(th)],[]) ).
tff(135,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| memberP(sk4,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,axiom,
! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| memberP(sk4,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(137,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[139,132]) ).
tff(141,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| memberP(sk4,hd(sk3))
| ~ memberP(sk3,hd(sk3)) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| memberP(sk4,hd(sk3))
| ~ memberP(sk3,hd(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| memberP(sk4,hd(sk3))
| ~ memberP(sk3,hd(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| memberP(sk4,hd(sk3))
| ~ memberP(sk3,hd(sk3)) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
( memberP(sk4,hd(sk3))
| ~ memberP(sk3,hd(sk3)) ),
inference(unit_resolution,[status(thm)],[143,140,38]) ).
tff(145,plain,
$false,
inference(unit_resolution,[status(thm)],[144,130,53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC046-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.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 08:06:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% See solution above
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------