%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC258-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:42 AM UTC 2025
% Result : Unsatisfiable 3.98s 4.14s
% Output : Proof 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 135
% Syntax : Number of formulae : 341 ( 101 unt; 0 typ; 0 def)
% Number of atoms : 2086 ( 735 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 3026 (1394 ~;1442 |; 0 &)
% ( 190 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 113 ( 113 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 : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 552 ( 502 !; 0 ?; 552 :)
% Comments :
%------------------------------------------------------------------------------
tff(nil_type,type,
nil: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(skaf68_type,type,
skaf68: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(skaf65_type,type,
skaf65: $i > $i ).
tff(tl_type,type,
tl: $i > $i ).
tff(skaf67_type,type,
skaf67: $i > $i ).
tff(skaf64_type,type,
skaf64: $i > $i ).
tff(skaf66_type,type,
skaf66: $i > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(hd_type,type,
hd: $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,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(4,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( totalorderedP(sk3)
<=> totalorderedP(sk1) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( totalorderedP(sk1)
<=> totalorderedP(sk3) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( ~ totalorderedP(sk1)
<=> ~ totalorderedP(sk3) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ~ totalorderedP(sk1)
<=> ~ totalorderedP(sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
~ totalorderedP(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(11,plain,
~ totalorderedP(sk1),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
~ totalorderedP(sk3),
inference(modus_ponens,[status(thm)],[11,8]) ).
tff(13,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(15,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,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(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(quant_intro,[status(thm)],[16]) ).
tff(18,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(19,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(20,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)],[19]) ).
tff(21,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(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)],[21,20]) ).
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(modus_ponens,[status(thm)],[22,18]) ).
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(skolemize,[status(sab)],[23]) ).
tff(25,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)],[24,17]) ).
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 ) )
<=> ( ~ ! [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(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(quant_inst,[status(thm)],[]) ).
tff(28,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)],[27,26]) ).
tff(29,plain,
( totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(unit_resolution,[status(thm)],[28,25,15]) ).
tff(30,plain,
app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3,
inference(unit_resolution,[status(thm)],[29,12]) ).
tff(31,plain,
( ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = nil )
<=> ( sk3 = nil ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = nil )
<=> ( nil = sk3 ) ),
inference(transitivity,[status(thm)],[31,1]) ).
tff(33,plain,
( ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
^ [U: $i] :
refl(( ssList(skaf66(U))
<=> ssList(skaf66(U)) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [U: $i] : ssList(skaf66(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause29) ).
tff(38,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [U: $i] : ssList(skaf66(U)),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [U: $i] : ssList(skaf66(U))
| ssList(skaf66(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
ssList(skaf66(sk3)),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
^ [U: $i] :
refl(( ssItem(skaf64(U))
<=> ssItem(skaf64(U)) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [U: $i] : ssItem(skaf64(U))
<=> ! [U: $i] : ssItem(skaf64(U)) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [U: $i] : ssItem(skaf64(U))
<=> ! [U: $i] : ssItem(skaf64(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
! [U: $i] : ssItem(skaf64(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause31) ).
tff(47,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [U: $i] : ssItem(skaf64(U))
| ssItem(skaf64(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
ssItem(skaf64(sk3)),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
^ [U: $i] :
refl(( ssList(skaf67(U))
<=> ssList(skaf67(U)) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
! [U: $i] : ssList(skaf67(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause28) ).
tff(56,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [U: $i] : ssList(skaf67(U)),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [U: $i] : ssList(skaf67(U))
| ssList(skaf67(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
ssList(skaf67(sk3)),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,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(62,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)],[61]) ).
tff(63,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(64,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(65,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)],[64]) ).
tff(66,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(67,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,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(72,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(73,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)],[72,71]) ).
tff(74,plain,
( ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ssList(cons(skaf64(sk3),skaf67(sk3))) ),
inference(unit_resolution,[status(thm)],[73,70]) ).
tff(75,plain,
ssList(cons(skaf64(sk3),skaf67(sk3))),
inference(unit_resolution,[status(thm)],[74,60,51]) ).
tff(76,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(77,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)],[76]) ).
tff(78,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(79,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(80,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)],[79]) ).
tff(81,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(82,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[84,77]) ).
tff(86,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(87,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(88,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)],[87]) ).
tff(89,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)],[88,86]) ).
tff(90,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(91,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)],[90,89]) ).
tff(92,plain,
( ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ),
inference(unit_resolution,[status(thm)],[91,85]) ).
tff(93,plain,
ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),
inference(unit_resolution,[status(thm)],[92,75,42]) ).
tff(94,plain,
^ [U: $i] :
refl(( ssItem(skaf65(U))
<=> ssItem(skaf65(U)) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [U: $i] : ssItem(skaf65(U))
<=> ! [U: $i] : ssItem(skaf65(U)) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [U: $i] : ssItem(skaf65(U))
<=> ! [U: $i] : ssItem(skaf65(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
! [U: $i] : ssItem(skaf65(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause30) ).
tff(98,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [U: $i] : ssItem(skaf65(U))
| ssItem(skaf65(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
ssItem(skaf65(sk3)),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
^ [U: $i] :
refl(( ssList(skaf68(U))
<=> ssList(skaf68(U)) )),
inference(bind,[status(th)],[]) ).
tff(104,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,axiom,
! [U: $i] : ssList(skaf68(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause27) ).
tff(107,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [U: $i] : ssList(skaf68(U)),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
( ~ ! [U: $i] : ssList(skaf68(U))
| ssList(skaf68(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
ssList(skaf68(sk3)),
inference(unit_resolution,[status(thm)],[110,109]) ).
tff(112,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(113,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(114,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)],[113,112]) ).
tff(115,plain,
( ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ssList(cons(skaf65(sk3),skaf68(sk3))) ),
inference(unit_resolution,[status(thm)],[114,70]) ).
tff(116,plain,
ssList(cons(skaf65(sk3),skaf68(sk3))),
inference(unit_resolution,[status(thm)],[115,111,102]) ).
tff(117,plain,
( ( cons(skaf65(sk3),skaf68(sk3)) = nil )
<=> ( nil = cons(skaf65(sk3),skaf68(sk3)) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(118,plain,
( ( cons(skaf65(sk3),skaf68(sk3)) != nil )
<=> ( nil != cons(skaf65(sk3),skaf68(sk3)) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( cons(U,V) != nil )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != nil ) ) )),
( ( ( cons(U,V) != nil )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != nil )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssItem(U)
| ( cons(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) )),
( ( ( cons(U,V) != nil )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [V: $i,U: $i] :
( ( cons(U,V) != nil )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != nil )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
tff(125,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[127,120]) ).
tff(129,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ( cons(skaf65(sk3),skaf68(sk3)) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ( cons(skaf65(sk3),skaf68(sk3)) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ( cons(skaf65(sk3),skaf68(sk3)) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ( cons(skaf65(sk3),skaf68(sk3)) != nil ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
( ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ( cons(skaf65(sk3),skaf68(sk3)) != nil ) ),
inference(unit_resolution,[status(thm)],[131,128]) ).
tff(133,plain,
cons(skaf65(sk3),skaf68(sk3)) != nil,
inference(unit_resolution,[status(thm)],[132,111,102]) ).
tff(134,plain,
nil != cons(skaf65(sk3),skaf68(sk3)),
inference(modus_ponens,[status(thm)],[133,118]) ).
tff(135,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(136,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(139,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
tff(141,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[141,137]) ).
tff(143,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(skolemize,[status(sab)],[142]) ).
tff(144,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[143,136]) ).
tff(145,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,plain,
( ( ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) )
<=> ( ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) ) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) ) ),
inference(transitivity,[status(thm)],[147,145]) ).
tff(149,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
( ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) ),
inference(unit_resolution,[status(thm)],[150,144]) ).
tff(152,plain,
app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != nil,
inference(unit_resolution,[status(thm)],[151,134,116,93]) ).
tff(153,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[152,33]) ).
tff(154,plain,
( ( ( nil = sk3 )
| ( cons(sk5,nil) = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,axiom,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(157,plain,
( ( nil = sk3 )
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
( ( nil = sk3 )
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[157,154]) ).
tff(159,plain,
cons(sk5,nil) = sk3,
inference(unit_resolution,[status(thm)],[158,153]) ).
tff(160,plain,
sk3 = cons(sk5,nil),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(162,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(165,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[164]) ).
tff(166,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
tff(167,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[167,163]) ).
tff(169,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[169,162]) ).
tff(171,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
( ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(unit_resolution,[status(thm)],[173,170,15]) ).
tff(175,plain,
cons(hd(sk3),tl(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[174,153]) ).
tff(176,plain,
cons(hd(sk3),tl(sk3)) = cons(sk5,nil),
inference(transitivity,[status(thm)],[175,160]) ).
tff(177,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(178,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[177]) ).
tff(179,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(181,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[180]) ).
tff(182,axiom,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
tff(183,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[183,179]) ).
tff(185,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(skolemize,[status(sab)],[184]) ).
tff(186,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[185,178]) ).
tff(187,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(189,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(transitivity,[status(thm)],[189,187]) ).
tff(191,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ),
inference(modus_ponens,[status(thm)],[191,190]) ).
tff(193,plain,
ssList(tl(sk3)),
inference(unit_resolution,[status(thm)],[192,186,15,153]) ).
tff(194,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(195,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[194]) ).
tff(196,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(198,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[197]) ).
tff(199,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(200,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[200,196]) ).
tff(202,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(skolemize,[status(sab)],[201]) ).
tff(203,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[202,195]) ).
tff(204,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(206,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)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,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)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(transitivity,[status(thm)],[206,204]) ).
tff(208,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
( ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(unit_resolution,[status(thm)],[209,203,15]) ).
tff(211,plain,
ssItem(hd(sk3)),
inference(unit_resolution,[status(thm)],[210,153]) ).
tff(212,plain,
( ( ssItem(sk5)
| ( nil = sk3 ) )
<=> ( ssItem(sk5)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,axiom,
( ssItem(sk5)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(214,plain,
( ssItem(sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[213,212]) ).
tff(215,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[214,153]) ).
tff(216,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(217,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[216]) ).
tff(218,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(219,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W) )
<=> ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(X) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( X = V ) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( X = V ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(220,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[219]) ).
tff(221,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause171) ).
tff(222,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[222,218]) ).
tff(224,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(skolemize,[status(sab)],[223]) ).
tff(225,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[224,217]) ).
tff(226,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(227,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(228,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[227,226]) ).
tff(229,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk5)
| ( nil = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(sk5,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk5)
| ( nil = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(sk5,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(230,plain,
( ( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( nil = tl(sk3) )
| ~ ssItem(sk5)
| ( cons(hd(sk3),tl(sk3)) != cons(sk5,nil) ) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk5)
| ( nil = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(sk5,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(231,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( nil = tl(sk3) )
| ~ ssItem(sk5)
| ( cons(hd(sk3),tl(sk3)) != cons(sk5,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk5)
| ( nil = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(sk5,nil) ) ) ),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( nil = tl(sk3) )
| ~ ssItem(sk5)
| ( cons(hd(sk3),tl(sk3)) != cons(sk5,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk5)
| ( nil = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(sk5,nil) ) ) ),
inference(transitivity,[status(thm)],[231,229]) ).
tff(233,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( nil = tl(sk3) )
| ~ ssItem(sk5)
| ( cons(hd(sk3),tl(sk3)) != cons(sk5,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk5)
| ( nil = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(sk5,nil) ) ),
inference(modus_ponens,[status(thm)],[233,232]) ).
tff(235,plain,
nil = tl(sk3),
inference(unit_resolution,[status(thm)],[234,228,225,215,211,193,176]) ).
tff(236,plain,
tl(sk3) = nil,
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
tl(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) = tl(sk3),
inference(monotonicity,[status(thm)],[30]) ).
tff(238,plain,
( ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
<=> ( nil = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(239,plain,
( ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) != nil )
<=> ( nil != app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) ) ),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
( ( cons(skaf64(sk3),skaf67(sk3)) = nil )
<=> ( nil = cons(skaf64(sk3),skaf67(sk3)) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(241,plain,
( ( cons(skaf64(sk3),skaf67(sk3)) != nil )
<=> ( nil != cons(skaf64(sk3),skaf67(sk3)) ) ),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ( cons(skaf64(sk3),skaf67(sk3)) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ( cons(skaf64(sk3),skaf67(sk3)) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(243,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ( cons(skaf64(sk3),skaf67(sk3)) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(244,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ( cons(skaf64(sk3),skaf67(sk3)) != nil ) ),
inference(modus_ponens,[status(thm)],[243,242]) ).
tff(245,plain,
( ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ( cons(skaf64(sk3),skaf67(sk3)) != nil ) ),
inference(unit_resolution,[status(thm)],[244,128]) ).
tff(246,plain,
cons(skaf64(sk3),skaf67(sk3)) != nil,
inference(unit_resolution,[status(thm)],[245,60,51]) ).
tff(247,plain,
nil != cons(skaf64(sk3),skaf67(sk3)),
inference(modus_ponens,[status(thm)],[246,241]) ).
tff(248,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf66(sk3))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) != nil )
| ( nil = cons(skaf64(sk3),skaf67(sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf66(sk3))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) != nil )
| ( nil = cons(skaf64(sk3),skaf67(sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(249,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf66(sk3))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) != nil )
| ( nil = cons(skaf64(sk3),skaf67(sk3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf66(sk3))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) != nil )
| ( nil = cons(skaf64(sk3),skaf67(sk3)) ) ),
inference(modus_ponens,[status(thm)],[249,248]) ).
tff(251,plain,
( ~ ssList(skaf66(sk3))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) != nil )
| ( nil = cons(skaf64(sk3),skaf67(sk3)) ) ),
inference(unit_resolution,[status(thm)],[250,144]) ).
tff(252,plain,
app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) != nil,
inference(unit_resolution,[status(thm)],[251,247,42,75]) ).
tff(253,plain,
nil != app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),
inference(modus_ponens,[status(thm)],[252,239]) ).
tff(254,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
inference(bind,[status(th)],[]) ).
tff(255,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) ),
inference(quant_intro,[status(thm)],[254]) ).
tff(256,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(257,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
inference(bind,[status(th)],[]) ).
tff(258,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) ),
inference(quant_intro,[status(thm)],[257]) ).
tff(259,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause133) ).
tff(260,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[259,258]) ).
tff(261,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[260,256]) ).
tff(262,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(skolemize,[status(sab)],[261]) ).
tff(263,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[262,255]) ).
tff(264,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( nil = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) )
| ( tl(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) = app(tl(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( nil = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) )
| ( tl(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) = app(tl(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(265,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( nil = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) )
| ( tl(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) = app(tl(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(266,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( nil = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) )
| ( tl(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) = app(tl(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) ) ),
inference(modus_ponens,[status(thm)],[265,264]) ).
tff(267,plain,
( ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( nil = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) )
| ( tl(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) = app(tl(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) ) ),
inference(unit_resolution,[status(thm)],[266,263]) ).
tff(268,plain,
tl(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) = app(tl(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))),
inference(unit_resolution,[status(thm)],[267,253,116,93]) ).
tff(269,plain,
app(tl(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = tl(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))),
inference(symmetry,[status(thm)],[268]) ).
tff(270,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(271,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[270]) ).
tff(272,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(273,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(274,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[273,272]) ).
tff(275,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[274]) ).
tff(276,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[275,271]) ).
tff(277,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(278,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(279,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) ) ),
inference(modus_ponens,[status(thm)],[278,277]) ).
tff(280,plain,
app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),
inference(unit_resolution,[status(thm)],[279,276,93]) ).
tff(281,plain,
app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),
inference(symmetry,[status(thm)],[280]) ).
tff(282,plain,
tl(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),
inference(monotonicity,[status(thm)],[281]) ).
tff(283,plain,
tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) = tl(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) = app(tl(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))),
inference(monotonicity,[status(thm)],[283]) ).
tff(285,plain,
app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) = nil,
inference(transitivity,[status(thm)],[284,269,237,236]) ).
tff(286,plain,
( ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = nil )
<=> ( nil = app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(287,plain,
( ( ~ ssList(nil)
| ( app(nil,nil) = nil ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(288,plain,
( ( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(289,plain,
( ! [V: $i,U: $i] :
( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) )
<=> ( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(290,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(291,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) )
<=> ( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(transitivity,[status(thm)],[290,289]) ).
tff(292,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(transitivity,[status(thm)],[291,288]) ).
tff(293,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( nil != U )
| ( nil != V )
| ~ ssList(V) )
<=> ( ( nil != U )
| ~ ssList(V)
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ~ ssList(U) ) )),
rewrite(( ( ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ( app(U,V) = nil ) ) )),
rewrite(( ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ( app(U,V) = nil ) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(294,plain,
( ! [V: $i,U: $i] :
( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) ) ),
inference(quant_intro,[status(thm)],[293]) ).
tff(295,plain,
( ! [V: $i,U: $i] :
( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(transitivity,[status(thm)],[294,292]) ).
tff(296,axiom,
! [V: $i,U: $i] :
( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause145) ).
tff(297,plain,
( ~ ssList(nil)
| ( app(nil,nil) = nil ) ),
inference(modus_ponens,[status(thm)],[296,295]) ).
tff(298,plain,
( ~ ssList(nil)
| ( app(nil,nil) = nil ) ),
inference(modus_ponens,[status(thm)],[297,287]) ).
tff(299,plain,
app(nil,nil) = nil,
inference(unit_resolution,[status(thm)],[298,228]) ).
tff(300,plain,
( ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(nil,nil) )
<=> ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = nil ) ),
inference(monotonicity,[status(thm)],[299]) ).
tff(301,plain,
( ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(nil,nil) )
<=> ( nil = app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) ) ),
inference(transitivity,[status(thm)],[300,286]) ).
tff(302,plain,
( ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) )
<=> ( nil != app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) ) ),
inference(monotonicity,[status(thm)],[301]) ).
tff(303,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) ) )),
inference(bind,[status(th)],[]) ).
tff(304,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) ) ),
inference(quant_intro,[status(thm)],[303]) ).
tff(305,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(306,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != app(U,W) )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != app(U,W) ) ) )),
( ( ( app(U,V) != app(U,W) )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != app(U,W) )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != app(U,W) )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != app(U,W) ) ) )),
( ( ( app(U,V) != app(U,W) )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != app(U,W) ) ) )),
( ( ( app(U,V) != app(U,W) )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != app(U,W) )
| ~ ssList(W) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != app(U,W) )
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != app(U,W) ) ) )),
( ( ( app(U,V) != app(U,W) )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != app(U,W) ) ) )),
( ( ( app(U,V) != app(U,W) )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| ( V = W ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != app(U,W) )
| ( V = W ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != app(U,W) )
| ( V = W ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) ) )),
( ( ( app(U,V) != app(U,W) )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| ( V = W ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) ) )),
inference(bind,[status(th)],[]) ).
tff(307,plain,
( ! [W: $i,V: $i,U: $i] :
( ( app(U,V) != app(U,W) )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| ( V = W ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) ) ),
inference(quant_intro,[status(thm)],[306]) ).
tff(308,axiom,
! [W: $i,V: $i,U: $i] :
( ( app(U,V) != app(U,W) )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| ( V = W ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause150) ).
tff(309,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) ),
inference(modus_ponens,[status(thm)],[308,307]) ).
tff(310,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) ),
inference(modus_ponens,[status(thm)],[309,305]) ).
tff(311,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) ),
inference(skolemize,[status(sab)],[310]) ).
tff(312,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) ),
inference(modus_ponens,[status(thm)],[311,304]) ).
tff(313,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(314,plain,
( ( ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(nil)
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) ) )
<=> ( ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(315,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(nil)
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) ) ) ),
inference(monotonicity,[status(thm)],[314]) ).
tff(316,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(nil)
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) ) ) ),
inference(transitivity,[status(thm)],[315,313]) ).
tff(317,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(nil)
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(318,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( V = W )
| ( app(U,V) != app(U,W) ) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) ) ),
inference(modus_ponens,[status(thm)],[317,316]) ).
tff(319,plain,
( ( app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) = nil )
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil) ) ),
inference(unit_resolution,[status(thm)],[318,228,312,93]) ).
tff(320,plain,
app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) != app(nil,nil),
inference(unit_resolution,[status(thm)],[319,252]) ).
tff(321,plain,
nil != app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),
inference(modus_ponens,[status(thm)],[320,302]) ).
tff(322,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(323,plain,
( ( ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ~ ssList(nil) )
<=> ( ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(324,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ~ ssList(nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) ) ),
inference(monotonicity,[status(thm)],[323]) ).
tff(325,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ~ ssList(nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) ) ),
inference(transitivity,[status(thm)],[324,322]) ).
tff(326,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ~ ssList(nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(327,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) ),
inference(modus_ponens,[status(thm)],[326,325]) ).
tff(328,plain,
ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),
inference(unit_resolution,[status(thm)],[327,228,85,93]) ).
tff(329,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( nil = app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) )
| ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( nil = app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) )
| ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(330,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( nil = app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) )
| ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(331,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( nil = app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) )
| ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))) ),
inference(modus_ponens,[status(thm)],[330,329]) ).
tff(332,plain,
ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))),
inference(unit_resolution,[status(thm)],[331,186,328,321]) ).
tff(333,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( nil = cons(skaf65(sk3),skaf68(sk3)) )
| ~ ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))))
| ( app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( nil = cons(skaf65(sk3),skaf68(sk3)) )
| ~ ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))))
| ( app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(334,plain,
( ( ~ ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) )
<=> ( ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( nil = cons(skaf65(sk3),skaf68(sk3)) )
| ~ ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))))
| ( app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(335,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( nil = cons(skaf65(sk3),skaf68(sk3)) )
| ~ ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))))
| ( app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil ) ) ),
inference(monotonicity,[status(thm)],[334]) ).
tff(336,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( nil = cons(skaf65(sk3),skaf68(sk3)) )
| ~ ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))))
| ( app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil ) ) ),
inference(transitivity,[status(thm)],[335,333]) ).
tff(337,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))))
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil )
| ( nil = cons(skaf65(sk3),skaf68(sk3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(338,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ( nil = cons(skaf65(sk3),skaf68(sk3)) )
| ~ ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))))
| ( app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil ) ),
inference(modus_ponens,[status(thm)],[337,336]) ).
tff(339,plain,
( ~ ssList(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))))
| ( app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil ) ),
inference(unit_resolution,[status(thm)],[338,144,116,134]) ).
tff(340,plain,
app(tl(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),cons(skaf65(sk3),skaf68(sk3))) != nil,
inference(unit_resolution,[status(thm)],[339,332]) ).
tff(341,plain,
$false,
inference(unit_resolution,[status(thm)],[340,285]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC258-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 08:50:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.98/4.14 % SZS status Unsatisfiable
% 3.98/4.14 % SZS output start Proof
% See solution above
% 4.02/4.19 % E exiting
%------------------------------------------------------------------------------