%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC261-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:30:43 AM UTC 2025
% Result : Unsatisfiable 112.83s 112.98s
% Output : Proof 113.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 102
% Syntax : Number of formulae : 276 ( 93 unt; 0 typ; 0 def)
% Number of atoms : 1503 ( 195 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 2178 (1024 ~;1015 |; 0 &)
% ( 139 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 73 ( 73 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 : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 490 ( 444 !; 0 ?; 490 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: $i ).
tff(skaf64_type,type,
skaf64: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(skaf68_type,type,
skaf68: $i > $i ).
tff(skaf65_type,type,
skaf65: $i > $i ).
tff(tl_type,type,
tl: $i > $i ).
tff(skaf67_type,type,
skaf67: $i > $i ).
tff(skaf66_type,type,
skaf66: $i > $i ).
tff(totalorderedP_type,type,
totalorderedP: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
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/sandbox2/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,
( totalorderedP(sk3)
<=> totalorderedP(sk1) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( totalorderedP(sk1)
<=> totalorderedP(sk3) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ~ totalorderedP(sk1)
<=> ~ totalorderedP(sk3) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ~ totalorderedP(sk1)
<=> ~ totalorderedP(sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
~ totalorderedP(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(10,plain,
~ totalorderedP(sk1),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
~ totalorderedP(sk3),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(14,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| totalorderedP(U) )
<=> ( ~ ssList(U)
| totalorderedP(U) ) )),
( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
rewrite(( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause164) ).
tff(21,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(unit_resolution,[status(thm)],[27,24,14]) ).
tff(29,plain,
app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3,
inference(unit_resolution,[status(thm)],[28,11]) ).
tff(30,plain,
^ [U: $i] :
refl(( ssItem(skaf65(U))
<=> ssItem(skaf65(U)) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [U: $i] : ssItem(skaf65(U))
<=> ! [U: $i] : ssItem(skaf65(U)) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [U: $i] : ssItem(skaf65(U))
<=> ! [U: $i] : ssItem(skaf65(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [U: $i] : ssItem(skaf65(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause30) ).
tff(34,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [U: $i] : ssItem(skaf65(U))
| ssItem(skaf65(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
ssItem(skaf65(sk3)),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
^ [U: $i] :
refl(( ssList(skaf68(U))
<=> ssList(skaf68(U)) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
! [U: $i] : ssList(skaf68(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause27) ).
tff(43,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [U: $i] : ssList(skaf68(U)),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [U: $i] : ssList(skaf68(U))
| ssList(skaf68(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
ssList(skaf68(sk3)),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(54,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ssList(cons(skaf65(sk3),skaf68(sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ssList(cons(skaf65(sk3),skaf68(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ssList(cons(skaf65(sk3),skaf68(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ssList(cons(skaf65(sk3),skaf68(sk3))) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ssList(cons(skaf65(sk3),skaf68(sk3))) ),
inference(unit_resolution,[status(thm)],[60,57]) ).
tff(62,plain,
ssList(cons(skaf65(sk3),skaf68(sk3))),
inference(unit_resolution,[status(thm)],[61,47,38]) ).
tff(63,plain,
^ [U: $i] :
refl(( ssList(skaf66(U))
<=> ssList(skaf66(U)) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
! [U: $i] : ssList(skaf66(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause29) ).
tff(67,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [U: $i] : ssList(skaf66(U)),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ~ ! [U: $i] : ssList(skaf66(U))
| ssList(skaf66(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
ssList(skaf66(sk3)),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
^ [U: $i] :
refl(( ssItem(skaf64(U))
<=> ssItem(skaf64(U)) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [U: $i] : ssItem(skaf64(U))
<=> ! [U: $i] : ssItem(skaf64(U)) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [U: $i] : ssItem(skaf64(U))
<=> ! [U: $i] : ssItem(skaf64(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
! [U: $i] : ssItem(skaf64(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause31) ).
tff(76,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ~ ! [U: $i] : ssItem(skaf64(U))
| ssItem(skaf64(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
ssItem(skaf64(sk3)),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
^ [U: $i] :
refl(( ssList(skaf67(U))
<=> ssList(skaf67(U)) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,axiom,
! [U: $i] : ssList(skaf67(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause28) ).
tff(85,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [U: $i] : ssList(skaf67(U)),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
( ~ ! [U: $i] : ssList(skaf67(U))
| ssList(skaf67(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
ssList(skaf67(sk3)),
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ssList(cons(skaf64(sk3),skaf67(sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ssList(cons(skaf64(sk3),skaf67(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ssList(cons(skaf64(sk3),skaf67(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ssList(cons(skaf64(sk3),skaf67(sk3))) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
( ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ssList(cons(skaf64(sk3),skaf67(sk3))) ),
inference(unit_resolution,[status(thm)],[92,57]) ).
tff(94,plain,
ssList(cons(skaf64(sk3),skaf67(sk3))),
inference(unit_resolution,[status(thm)],[93,89,80]) ).
tff(95,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(96,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(99,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(101,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[103,96]) ).
tff(105,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = app(skaf66(sk3),app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = app(skaf66(sk3),app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = app(skaf66(sk3),app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = app(skaf66(sk3),app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
( ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = app(skaf66(sk3),app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(unit_resolution,[status(thm)],[107,104]) ).
tff(109,plain,
app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = app(skaf66(sk3),app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3)))),
inference(unit_resolution,[status(thm)],[108,94,71,62]) ).
tff(110,plain,
app(skaf66(sk3),app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3)))) = app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) )),
inference(bind,[status(th)],[]) ).
tff(112,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W) ) )),
( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) )),
( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) )),
inference(bind,[status(th)],[]) ).
tff(115,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause157) ).
tff(117,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( cons(skaf64(sk3),app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))) = app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( cons(skaf64(sk3),app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))) = app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( cons(skaf64(sk3),app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))) = app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( cons(skaf64(sk3),app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))) = app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3))) ) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
cons(skaf64(sk3),app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))) = app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3))),
inference(unit_resolution,[status(thm)],[123,120,62,80,89]) ).
tff(125,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
tff(131,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ( tl(cons(skaf64(sk3),skaf67(sk3))) = skaf67(sk3) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ( tl(cons(skaf64(sk3),skaf67(sk3))) = skaf67(sk3) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ( tl(cons(skaf64(sk3),skaf67(sk3))) = skaf67(sk3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ( tl(cons(skaf64(sk3),skaf67(sk3))) = skaf67(sk3) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ( tl(cons(skaf64(sk3),skaf67(sk3))) = skaf67(sk3) ) ),
inference(unit_resolution,[status(thm)],[137,134]) ).
tff(139,plain,
tl(cons(skaf64(sk3),skaf67(sk3))) = skaf67(sk3),
inference(unit_resolution,[status(thm)],[138,89,80]) ).
tff(140,plain,
skaf67(sk3) = tl(cons(skaf64(sk3),skaf67(sk3))),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3))) = app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3))),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) = cons(skaf64(sk3),app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) = app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3))),
inference(transitivity,[status(thm)],[143,124]) ).
tff(145,plain,
app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))) = app(skaf66(sk3),app(cons(skaf64(sk3),skaf67(sk3)),cons(skaf65(sk3),skaf68(sk3)))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))) = sk3,
inference(transitivity,[status(thm)],[145,110,29]) ).
tff(147,plain,
( memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3))
<=> memberP(sk3,skaf64(sk3)) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3))))
<=> ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(149,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(150,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(153,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(155,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[156]) ).
tff(158,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[157,150]) ).
tff(159,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(skaf67(sk3))
| ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(skaf67(sk3))
| ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,plain,
( ( ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(skaf67(sk3)) )
<=> ( ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(skaf67(sk3))
| ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(skaf67(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(skaf67(sk3))
| ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(skaf67(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(skaf67(sk3))
| ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(transitivity,[status(thm)],[161,159]) ).
tff(163,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(skaf67(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(skaf67(sk3))
| ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
ssList(app(skaf67(sk3),cons(skaf65(sk3),skaf68(sk3)))),
inference(unit_resolution,[status(thm)],[164,158,62,89]) ).
tff(166,plain,
ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))),
inference(modus_ponens,[status(thm)],[165,148]) ).
tff(167,plain,
( ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(168,plain,
( ssList(sk3)
<=> ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))))) ),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))))),
inference(modus_ponens,[status(thm)],[14,168]) ).
tff(170,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) )),
inference(bind,[status(th)],[]) ).
tff(171,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(quant_intro,[status(thm)],[170]) ).
tff(172,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,plain,
^ [W: $i,V: $i,U: $i] :
rewrite(( ( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) )),
inference(bind,[status(th)],[]) ).
tff(174,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(quant_intro,[status(thm)],[173]) ).
tff(175,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(176,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(177,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) ) ),
inference(transitivity,[status(thm)],[176,175]) ).
tff(178,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(transitivity,[status(thm)],[177,174]) ).
tff(179,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],[]) ).
tff(180,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[179]) ).
tff(181,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(transitivity,[status(thm)],[180,178]) ).
tff(182,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause175) ).
tff(183,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(modus_ponens,[status(thm)],[183,172]) ).
tff(185,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(skolemize,[status(sab)],[184]) ).
tff(186,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(modus_ponens,[status(thm)],[185,171]) ).
tff(187,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,plain,
( ( ~ ssList(skaf66(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)) )
<=> ( ~ ssItem(skaf64(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(189,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(skaf66(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)) ) ),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(skaf66(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)) ) ),
inference(transitivity,[status(thm)],[189,187]) ).
tff(191,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(skaf66(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)) ),
inference(modus_ponens,[status(thm)],[191,190]) ).
tff(193,plain,
( ~ ssList(app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)) ),
inference(unit_resolution,[status(thm)],[192,186,80,71]) ).
tff(194,plain,
memberP(app(skaf66(sk3),cons(skaf64(sk3),app(tl(cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))),skaf64(sk3)),
inference(unit_resolution,[status(thm)],[193,169,166]) ).
tff(195,plain,
memberP(sk3,skaf64(sk3)),
inference(modus_ponens,[status(thm)],[194,147]) ).
tff(196,plain,
^ [A: $i] :
refl(( ( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) )
<=> ( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) ) )),
inference(bind,[status(th)],[]) ).
tff(197,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) ) ),
inference(quant_intro,[status(thm)],[196]) ).
tff(198,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(199,plain,
^ [A: $i] :
rewrite(( ( ~ ssItem(A)
| ( sk5 = A )
| ~ memberP(sk3,A) )
<=> ( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) ) )),
inference(bind,[status(th)],[]) ).
tff(200,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ( sk5 = A )
| ~ memberP(sk3,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) ) ),
inference(quant_intro,[status(thm)],[199]) ).
tff(201,axiom,
! [A: $i] :
( ~ ssItem(A)
| ( sk5 = A )
| ~ memberP(sk3,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(202,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) ),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) ),
inference(modus_ponens,[status(thm)],[202,198]) ).
tff(204,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) ),
inference(skolemize,[status(sab)],[203]) ).
tff(205,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) ),
inference(modus_ponens,[status(thm)],[204,197]) ).
tff(206,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) )
| ~ ssItem(skaf64(sk3))
| ~ memberP(sk3,skaf64(sk3))
| ( sk5 = skaf64(sk3) ) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) )
| ~ ssItem(skaf64(sk3))
| ~ memberP(sk3,skaf64(sk3))
| ( sk5 = skaf64(sk3) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) )
| ~ ssItem(skaf64(sk3))
| ~ memberP(sk3,skaf64(sk3))
| ( sk5 = skaf64(sk3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(208,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) )
| ~ ssItem(skaf64(sk3))
| ~ memberP(sk3,skaf64(sk3))
| ( sk5 = skaf64(sk3) ) ),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
( ~ memberP(sk3,skaf64(sk3))
| ( sk5 = skaf64(sk3) ) ),
inference(unit_resolution,[status(thm)],[208,205,80]) ).
tff(210,plain,
sk5 = skaf64(sk3),
inference(unit_resolution,[status(thm)],[209,195]) ).
tff(211,plain,
skaf64(sk3) = sk5,
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
( leq(skaf64(sk3),sk5)
<=> leq(sk5,sk5) ),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
( leq(sk5,sk5)
<=> leq(skaf64(sk3),sk5) ),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(215,axiom,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(216,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
^ [U: $i] :
refl(( ( ~ ssItem(U)
| leq(U,U) )
<=> ( ~ ssItem(U)
| leq(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(218,plain,
( ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ) ),
inference(quant_intro,[status(thm)],[217]) ).
tff(219,plain,
( ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(220,axiom,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause62) ).
tff(221,plain,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
inference(skolemize,[status(sab)],[221]) ).
tff(223,plain,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
inference(modus_ponens,[status(thm)],[222,218]) ).
tff(224,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk5)
| leq(sk5,sk5) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk5)
| leq(sk5,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(225,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk5)
| leq(sk5,sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(226,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk5)
| leq(sk5,sk5) ),
inference(modus_ponens,[status(thm)],[225,224]) ).
tff(227,plain,
leq(sk5,sk5),
inference(unit_resolution,[status(thm)],[226,223,216]) ).
tff(228,plain,
leq(skaf64(sk3),sk5),
inference(modus_ponens,[status(thm)],[227,213]) ).
tff(229,plain,
sk3 = app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),
inference(symmetry,[status(thm)],[29]) ).
tff(230,plain,
( memberP(sk3,skaf65(sk3))
<=> memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) ),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
( memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3))
<=> memberP(sk3,skaf65(sk3)) ),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(233,plain,
( ( ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf66(sk3)) )
<=> ( ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(234,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf66(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ) ),
inference(monotonicity,[status(thm)],[233]) ).
tff(235,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf66(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ) ),
inference(transitivity,[status(thm)],[234,232]) ).
tff(236,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf66(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(237,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ),
inference(modus_ponens,[status(thm)],[236,235]) ).
tff(238,plain,
( ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ),
inference(unit_resolution,[status(thm)],[237,158]) ).
tff(239,plain,
ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),
inference(unit_resolution,[status(thm)],[238,94,71]) ).
tff(240,plain,
( ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(241,plain,
( ssList(sk3)
<=> ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))),
inference(modus_ponens,[status(thm)],[14,241]) ).
tff(243,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(244,plain,
( ( ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) )
<=> ( ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(245,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) ) ),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) ) ),
inference(transitivity,[status(thm)],[245,243]) ).
tff(247,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) ),
inference(modus_ponens,[status(thm)],[247,246]) ).
tff(249,plain,
( ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)) ),
inference(unit_resolution,[status(thm)],[248,186]) ).
tff(250,plain,
memberP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))),skaf65(sk3)),
inference(unit_resolution,[status(thm)],[249,242,38,47,239]) ).
tff(251,plain,
memberP(sk3,skaf65(sk3)),
inference(modus_ponens,[status(thm)],[250,231]) ).
tff(252,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) )
| ~ ssItem(skaf65(sk3))
| ~ memberP(sk3,skaf65(sk3))
| ( sk5 = skaf65(sk3) ) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) )
| ~ ssItem(skaf65(sk3))
| ~ memberP(sk3,skaf65(sk3))
| ( sk5 = skaf65(sk3) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(253,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) )
| ~ ssItem(skaf65(sk3))
| ~ memberP(sk3,skaf65(sk3))
| ( sk5 = skaf65(sk3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| ( sk5 = A ) )
| ~ ssItem(skaf65(sk3))
| ~ memberP(sk3,skaf65(sk3))
| ( sk5 = skaf65(sk3) ) ),
inference(modus_ponens,[status(thm)],[253,252]) ).
tff(255,plain,
( ~ memberP(sk3,skaf65(sk3))
| ( sk5 = skaf65(sk3) ) ),
inference(unit_resolution,[status(thm)],[254,205,38]) ).
tff(256,plain,
sk5 = skaf65(sk3),
inference(unit_resolution,[status(thm)],[255,251]) ).
tff(257,plain,
skaf65(sk3) = sk5,
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
( leq(skaf64(sk3),skaf65(sk3))
<=> leq(skaf64(sk3),sk5) ),
inference(monotonicity,[status(thm)],[257]) ).
tff(259,plain,
( ~ leq(skaf64(sk3),skaf65(sk3))
<=> ~ leq(skaf64(sk3),sk5) ),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(261,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) ),
inference(quant_intro,[status(thm)],[260]) ).
tff(262,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(263,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
( ( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) )
<=> ( ~ ssList(U)
| ~ leq(skaf64(U),skaf65(U))
| totalorderedP(U) ) )),
rewrite(( ( ~ ssList(U)
| ~ leq(skaf64(U),skaf65(U))
| totalorderedP(U) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
( ( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(264,plain,
( ! [U: $i] :
( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) ),
inference(quant_intro,[status(thm)],[263]) ).
tff(265,axiom,
! [U: $i] :
( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause91) ).
tff(266,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[265,264]) ).
tff(267,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[266,262]) ).
tff(268,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(skolemize,[status(sab)],[267]) ).
tff(269,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[268,261]) ).
tff(270,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(271,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(272,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(modus_ponens,[status(thm)],[271,270]) ).
tff(273,plain,
( totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(unit_resolution,[status(thm)],[272,269,14]) ).
tff(274,plain,
~ leq(skaf64(sk3),skaf65(sk3)),
inference(unit_resolution,[status(thm)],[273,11]) ).
tff(275,plain,
~ leq(skaf64(sk3),sk5),
inference(modus_ponens,[status(thm)],[274,259]) ).
tff(276,plain,
$false,
inference(unit_resolution,[status(thm)],[275,228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC261-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:46:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 112.83/112.98 % SZS status Unsatisfiable
% 112.83/112.98 % SZS output start Proof
% See solution above
% 113.15/113.35 % E exiting
%------------------------------------------------------------------------------