%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC392-1 : 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 05:31:06 AM UTC 2025
% Result : Unsatisfiable 57.03s 57.23s
% Output : Proof 57.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 120
% Syntax : Number of formulae : 314 ( 97 unt; 0 typ; 0 def)
% Number of atoms : 2129 ( 628 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 3155 (1470 ~;1500 |; 0 &)
% ( 185 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 130 ( 130 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 : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 560 ( 506 !; 0 ?; 560 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(hd_type,type,
hd: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(skaf83_type,type,
skaf83: $i > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(skaf82_type,type,
skaf82: $i > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(nil_type,type,
nil: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(skaf43_type,type,
skaf43: ( $i * $i ) > $i ).
tff(skaf42_type,type,
skaf42: ( $i * $i ) > $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk6_type,type,
sk6: $i ).
tff(tl_type,type,
tl: $i > $i ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(6,plain,
( memberP(sk3,sk5)
<=> memberP(sk1,sk5) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(7,plain,
( memberP(sk1,sk5)
<=> memberP(sk3,sk5) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( memberP(sk1,sk5)
<=> memberP(sk1,sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
memberP(sk1,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(10,plain,
memberP(sk1,sk5),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
memberP(sk3,sk5),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(14,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(17,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
tff(24,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) )
<=> ( ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ),
inference(unit_resolution,[status(thm)],[33,27,17,14]) ).
tff(35,plain,
app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3,
inference(unit_resolution,[status(thm)],[34,11]) ).
tff(36,plain,
( ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = nil )
<=> ( sk3 = nil ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = nil )
<=> ( nil = sk3 ) ),
inference(transitivity,[status(thm)],[36,5]) ).
tff(38,plain,
( ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
^ [V: $i,U: $i] :
refl(( ssList(skaf43(U,V))
<=> ssList(skaf43(U,V)) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).
tff(43,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf43(U,V))
| ssList(skaf43(sk5,sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
ssList(skaf43(sk5,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/sandbox/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(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ),
inference(unit_resolution,[status(thm)],[60,57,14]) ).
tff(62,plain,
ssList(cons(sk5,skaf43(sk5,sk3))),
inference(unit_resolution,[status(thm)],[61,47]) ).
tff(63,plain,
^ [V: $i,U: $i] :
refl(( ssList(skaf42(U,V))
<=> ssList(skaf42(U,V)) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).
tff(67,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf42(U,V))
| ssList(skaf42(sk3,sk5)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
ssList(skaf42(sk3,sk5)),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
( ( cons(sk5,skaf43(sk5,sk3)) = nil )
<=> ( nil = cons(sk5,skaf43(sk5,sk3)) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(73,plain,
( ( cons(sk5,skaf43(sk5,sk3)) != nil )
<=> ( nil != cons(sk5,skaf43(sk5,sk3)) ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,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(75,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)],[74]) ).
tff(76,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(77,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(78,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)],[77]) ).
tff(79,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != nil )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
tff(80,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( cons(sk5,skaf43(sk5,sk3)) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( cons(sk5,skaf43(sk5,sk3)) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( cons(sk5,skaf43(sk5,sk3)) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( cons(sk5,skaf43(sk5,sk3)) != nil ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ ssList(skaf43(sk5,sk3))
| ( cons(sk5,skaf43(sk5,sk3)) != nil ) ),
inference(unit_resolution,[status(thm)],[86,83,14]) ).
tff(88,plain,
cons(sk5,skaf43(sk5,sk3)) != nil,
inference(unit_resolution,[status(thm)],[87,47]) ).
tff(89,plain,
nil != cons(sk5,skaf43(sk5,sk3)),
inference(modus_ponens,[status(thm)],[88,73]) ).
tff(90,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(91,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)],[90]) ).
tff(92,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(93,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(94,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)],[93]) ).
tff(95,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).
tff(96,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[98,91]) ).
tff(100,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil )
| ( nil = cons(sk5,skaf43(sk5,sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil )
| ( nil = cons(sk5,skaf43(sk5,sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil )
| ( nil = cons(sk5,skaf43(sk5,sk3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil )
| ( nil = cons(sk5,skaf43(sk5,sk3)) ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
( ~ ssList(skaf42(sk3,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil )
| ( nil = cons(sk5,skaf43(sk5,sk3)) ) ),
inference(unit_resolution,[status(thm)],[102,99]) ).
tff(104,plain,
app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil,
inference(unit_resolution,[status(thm)],[103,89,71,62]) ).
tff(105,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[104,38]) ).
tff(106,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(110,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
tff(112,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[114,107]) ).
tff(116,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
( ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(unit_resolution,[status(thm)],[118,115,17]) ).
tff(120,plain,
cons(skaf83(sk3),skaf82(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[119,105]) ).
tff(121,plain,
cons(skaf83(sk3),skaf82(sk3)) = sk1,
inference(transitivity,[status(thm)],[120,4]) ).
tff(122,plain,
( memberP(cons(skaf83(sk3),skaf82(sk3)),sk5)
<=> memberP(sk1,sk5) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( memberP(sk1,sk5)
<=> memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) ),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
memberP(cons(skaf83(sk3),skaf82(sk3)),sk5),
inference(modus_ponens,[status(thm)],[10,123]) ).
tff(125,plain,
^ [U: $i] :
refl(( ssList(skaf82(U))
<=> ssList(skaf82(U)) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,axiom,
! [U: $i] : ssList(skaf82(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
tff(129,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [U: $i] : ssList(skaf82(U)),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
( ~ ! [U: $i] : ssList(skaf82(U))
| ssList(skaf82(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
ssList(skaf82(sk3)),
inference(unit_resolution,[status(thm)],[132,131]) ).
tff(134,plain,
^ [U: $i] :
refl(( ssItem(skaf83(U))
<=> ssItem(skaf83(U)) )),
inference(bind,[status(th)],[]) ).
tff(135,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,axiom,
! [U: $i] : ssItem(skaf83(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
tff(138,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[139,135]) ).
tff(141,plain,
( ~ ! [U: $i] : ssItem(skaf83(U))
| ssItem(skaf83(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
ssItem(skaf83(sk3)),
inference(unit_resolution,[status(thm)],[141,140]) ).
tff(143,plain,
( ( ( nil = sk3 )
| ( cons(sk6,nil) = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk6,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
( ( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk6,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,axiom,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
tff(146,plain,
( ( nil = sk3 )
| ( cons(sk6,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( ( nil = sk3 )
| ( cons(sk6,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[146,143]) ).
tff(148,plain,
cons(sk6,nil) = sk3,
inference(unit_resolution,[status(thm)],[147,105]) ).
tff(149,plain,
sk3 = cons(sk6,nil),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
cons(skaf83(sk3),skaf82(sk3)) = cons(sk6,nil),
inference(transitivity,[status(thm)],[120,149]) ).
tff(151,plain,
( ( ssItem(sk6)
| ( nil = sk3 ) )
<=> ( ssItem(sk6)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,axiom,
( ssItem(sk6)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(153,plain,
( ssItem(sk6)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
ssItem(sk6),
inference(unit_resolution,[status(thm)],[153,105]) ).
tff(155,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(156,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)],[155]) ).
tff(157,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(158,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(159,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)],[158]) ).
tff(160,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/sandbox/benchmark/Axioms/SWC001-0.ax',clause171) ).
tff(161,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)],[160,159]) ).
tff(162,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)],[161,157]) ).
tff(163,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)],[162]) ).
tff(164,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)],[163,156]) ).
tff(165,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(167,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,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(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( nil = skaf82(sk3) )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,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(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( nil = skaf82(sk3) )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ( ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( nil = skaf82(sk3) )
| ~ ssItem(sk6)
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( nil = skaf82(sk3) )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,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(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( nil = skaf82(sk3) )
| ~ ssItem(sk6)
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,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(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( nil = skaf82(sk3) )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ) ),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,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(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( nil = skaf82(sk3) )
| ~ ssItem(sk6)
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,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(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( nil = skaf82(sk3) )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ) ),
inference(transitivity,[status(thm)],[170,168]) ).
tff(172,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(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( nil = skaf82(sk3) )
| ~ ssItem(sk6)
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,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(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( nil = skaf82(sk3) )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( nil = skaf82(sk3) ) ),
inference(unit_resolution,[status(thm)],[173,167,164,154,150]) ).
tff(175,plain,
nil = skaf82(sk3),
inference(unit_resolution,[status(thm)],[174,142,133]) ).
tff(176,plain,
skaf82(sk3) = nil,
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
( memberP(skaf82(sk3),sk5)
<=> memberP(nil,sk5) ),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( memberP(nil,sk5)
<=> memberP(skaf82(sk3),sk5) ),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( ~ memberP(nil,sk5)
<=> ~ memberP(skaf82(sk3),sk5) ),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
^ [U: $i] :
refl(( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(181,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[180]) ).
tff(182,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(183,plain,
^ [U: $i] :
rewrite(( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(184,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[183]) ).
tff(185,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(186,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[186,182]) ).
tff(188,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[187]) ).
tff(189,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[188,181]) ).
tff(190,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(191,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(modus_ponens,[status(thm)],[191,190]) ).
tff(193,plain,
~ memberP(nil,sk5),
inference(unit_resolution,[status(thm)],[192,189,14]) ).
tff(194,plain,
~ memberP(skaf82(sk3),sk5),
inference(modus_ponens,[status(thm)],[193,179]) ).
tff(195,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) )),
inference(bind,[status(th)],[]) ).
tff(196,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) ),
inference(quant_intro,[status(thm)],[195]) ).
tff(197,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ memberP(cons(U,V),W)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U) )
<=> ( ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(W) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W)
| memberP(V,W) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W)
| memberP(V,W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W)
| ( W = U ) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W)
| ( W = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) )),
inference(bind,[status(th)],[]) ).
tff(199,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) ),
inference(quant_intro,[status(thm)],[198]) ).
tff(200,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause161) ).
tff(201,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(modus_ponens,[status(thm)],[200,199]) ).
tff(202,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(modus_ponens,[status(thm)],[201,197]) ).
tff(203,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(skolemize,[status(sab)],[202]) ).
tff(204,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(modus_ponens,[status(thm)],[203,196]) ).
tff(205,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(sk5)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( sk5 = skaf83(sk3) )
| memberP(skaf82(sk3),sk5)
| ~ memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(sk5)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( sk5 = skaf83(sk3) )
| memberP(skaf82(sk3),sk5)
| ~ memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(206,plain,
( ( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk5)
| memberP(skaf82(sk3),sk5)
| ( sk5 = skaf83(sk3) )
| ~ memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) )
<=> ( ~ ssItem(sk5)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( sk5 = skaf83(sk3) )
| memberP(skaf82(sk3),sk5)
| ~ memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk5)
| memberP(skaf82(sk3),sk5)
| ( sk5 = skaf83(sk3) )
| ~ memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(sk5)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( sk5 = skaf83(sk3) )
| memberP(skaf82(sk3),sk5)
| ~ memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) ) ),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk5)
| memberP(skaf82(sk3),sk5)
| ( sk5 = skaf83(sk3) )
| ~ memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(sk5)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( sk5 = skaf83(sk3) )
| memberP(skaf82(sk3),sk5)
| ~ memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) ) ),
inference(transitivity,[status(thm)],[207,205]) ).
tff(209,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk5)
| memberP(skaf82(sk3),sk5)
| ( sk5 = skaf83(sk3) )
| ~ memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(sk5)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( sk5 = skaf83(sk3) )
| memberP(skaf82(sk3),sk5)
| ~ memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
( ( sk5 = skaf83(sk3) )
| memberP(skaf82(sk3),sk5)
| ~ memberP(cons(skaf83(sk3),skaf82(sk3)),sk5) ),
inference(unit_resolution,[status(thm)],[210,204,14,142,133]) ).
tff(212,plain,
sk5 = skaf83(sk3),
inference(unit_resolution,[status(thm)],[211,194,124]) ).
tff(213,plain,
skaf83(sk3) = sk5,
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(215,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[214]) ).
tff(216,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(217,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)
| ( U = W ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( U = W ) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( U = W ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( U = W ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(218,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( U = W ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[217]) ).
tff(219,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( U = W ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause170) ).
tff(220,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[220,216]) ).
tff(222,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(skolemize,[status(sab)],[221]) ).
tff(223,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[222,215]) ).
tff(224,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( skaf83(sk3) = sk6 )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( skaf83(sk3) = sk6 )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(225,plain,
( ( ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( skaf83(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( skaf83(sk3) = sk6 )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(226,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( skaf83(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( skaf83(sk3) = sk6 )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ) ),
inference(monotonicity,[status(thm)],[225]) ).
tff(227,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( skaf83(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( skaf83(sk3) = sk6 )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ) ),
inference(transitivity,[status(thm)],[226,224]) ).
tff(228,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( skaf83(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(229,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(sk6)
| ( skaf83(sk3) = sk6 )
| ( cons(skaf83(sk3),skaf82(sk3)) != cons(sk6,nil) ) ),
inference(modus_ponens,[status(thm)],[228,227]) ).
tff(230,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( skaf83(sk3) = sk6 ) ),
inference(unit_resolution,[status(thm)],[229,167,223,154,150]) ).
tff(231,plain,
skaf83(sk3) = sk6,
inference(unit_resolution,[status(thm)],[230,142,133]) ).
tff(232,plain,
sk6 = skaf83(sk3),
inference(symmetry,[status(thm)],[231]) ).
tff(233,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(234,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)],[233]) ).
tff(235,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(236,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(237,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)],[236]) ).
tff(238,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
tff(239,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[238,237]) ).
tff(240,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[239,235]) ).
tff(241,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(skolemize,[status(sab)],[240]) ).
tff(242,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[241,234]) ).
tff(243,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(244,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(245,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)],[244,243]) ).
tff(246,plain,
( ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(unit_resolution,[status(thm)],[245,242,17]) ).
tff(247,plain,
cons(hd(sk3),tl(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[246,105]) ).
tff(248,plain,
cons(hd(sk3),tl(sk3)) = cons(sk6,nil),
inference(transitivity,[status(thm)],[247,149]) ).
tff(249,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(250,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[249]) ).
tff(251,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(252,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(253,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[252]) ).
tff(254,axiom,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
tff(255,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[254,253]) ).
tff(256,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[255,251]) ).
tff(257,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(skolemize,[status(sab)],[256]) ).
tff(258,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[257,250]) ).
tff(259,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(260,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(261,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)],[260]) ).
tff(262,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)],[261,259]) ).
tff(263,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(264,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ),
inference(modus_ponens,[status(thm)],[263,262]) ).
tff(265,plain,
ssList(tl(sk3)),
inference(unit_resolution,[status(thm)],[264,258,17,105]) ).
tff(266,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(267,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[266]) ).
tff(268,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(269,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(270,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[269]) ).
tff(271,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(272,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[271,270]) ).
tff(273,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[272,268]) ).
tff(274,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(skolemize,[status(sab)],[273]) ).
tff(275,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[274,267]) ).
tff(276,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(277,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(278,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)],[277]) ).
tff(279,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)],[278,276]) ).
tff(280,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(281,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ),
inference(modus_ponens,[status(thm)],[280,279]) ).
tff(282,plain,
( ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(unit_resolution,[status(thm)],[281,275,17]) ).
tff(283,plain,
ssItem(hd(sk3)),
inference(unit_resolution,[status(thm)],[282,105]) ).
tff(284,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( hd(sk3) = sk6 )
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( hd(sk3) = sk6 )
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(285,plain,
( ( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( hd(sk3) = sk6 )
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(286,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( hd(sk3) = sk6 )
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) ) ),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( hd(sk3) = sk6 )
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) ) ),
inference(transitivity,[status(thm)],[286,284]) ).
tff(288,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(289,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( hd(sk3) = sk6 )
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) ),
inference(modus_ponens,[status(thm)],[288,287]) ).
tff(290,plain,
hd(sk3) = sk6,
inference(unit_resolution,[status(thm)],[289,167,223,154,283,265,248]) ).
tff(291,plain,
hd(sk3) = sk5,
inference(transitivity,[status(thm)],[290,232,213]) ).
tff(292,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(293,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(294,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[293,292]) ).
tff(295,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
( memberP(sk4,hd(sk3))
<=> memberP(sk2,sk5) ),
inference(monotonicity,[status(thm)],[295,291]) ).
tff(297,plain,
( memberP(sk2,sk5)
<=> memberP(sk4,hd(sk3)) ),
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
( ~ memberP(sk2,sk5)
<=> ~ memberP(sk4,hd(sk3)) ),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
( ~ memberP(sk2,sk5)
<=> ~ memberP(sk2,sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(300,axiom,
~ memberP(sk2,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(301,plain,
~ memberP(sk2,sk5),
inference(modus_ponens,[status(thm)],[300,299]) ).
tff(302,plain,
~ memberP(sk4,hd(sk3)),
inference(modus_ponens,[status(thm)],[301,298]) ).
tff(303,plain,
sk6 = hd(sk3),
inference(symmetry,[status(thm)],[290]) ).
tff(304,plain,
( memberP(sk4,sk6)
<=> memberP(sk4,hd(sk3)) ),
inference(monotonicity,[status(thm)],[303]) ).
tff(305,plain,
( ( memberP(sk4,sk6)
| ( nil = sk3 ) )
<=> ( memberP(sk4,sk6)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(306,axiom,
( memberP(sk4,sk6)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(307,plain,
( memberP(sk4,sk6)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[306,305]) ).
tff(308,plain,
( memberP(sk4,sk6)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[307,305]) ).
tff(309,plain,
( memberP(sk4,sk6)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[308,305]) ).
tff(310,plain,
( memberP(sk4,sk6)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[309,305]) ).
tff(311,plain,
( memberP(sk4,sk6)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[310,305]) ).
tff(312,plain,
memberP(sk4,sk6),
inference(unit_resolution,[status(thm)],[311,105]) ).
tff(313,plain,
memberP(sk4,hd(sk3)),
inference(modus_ponens,[status(thm)],[312,304]) ).
tff(314,plain,
$false,
inference(unit_resolution,[status(thm)],[313,302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC392-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % 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 09:17:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 57.03/57.23 % SZS status Unsatisfiable
% 57.03/57.23 % SZS output start Proof
% See solution above
% 57.25/57.45 % E exiting
%------------------------------------------------------------------------------