TSTP Solution File: SWC046-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC046-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 : Tue Sep 20 11:54:53 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 90
% Syntax : Number of formulae : 210 ( 58 unt; 12 typ; 0 def)
% Number of atoms : 1467 ( 436 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 2177 (1011 ~;1035 |; 0 &)
% ( 131 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 103 ( 103 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 8 >; 2 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 373 ( 332 !; 0 ?; 373 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(skaf83_type,type,
skaf83: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(tl_type,type,
tl: $i > $i ).
tff(hd_type,type,
hd: $i > $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(skaf82_type,type,
skaf82: $i > $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(nil_type,type,
nil: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
^ [U: $i] :
refl(
( ssList(skaf82(U))
<=> ssList(skaf82(U)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [U: $i] : ssList(skaf82(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
tff(5,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [U: $i] : ssList(skaf82(U)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [U: $i] : ssList(skaf82(U))
| ssList(skaf82(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
ssList(skaf82(sk3)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( nil != sk1 )
<=> ( sk4 != sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(13,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
sk4 != sk3,
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(18,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) )
<=> ( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
^ [U: $i] :
trans(
monotonicity(
rewrite(
( ( nil = U )
<=> ( sk4 = U ) )),
( ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ( sk4 = U )
| ssList(tl(U)) ) )),
rewrite(
( ( ~ ssList(U)
| ( sk4 = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) ) )),
( ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
tff(28,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) ),
inference(modus_ponens,[status(thm)],[29,23]) ).
tff(31,plain,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) ),
inference(modus_ponens,[status(thm)],[31,21]) ).
tff(33,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) )
| ~ ssList(sk3)
| ssList(tl(sk3))
| ( sk4 = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) )
| ~ ssList(sk3)
| ssList(tl(sk3))
| ( sk4 = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) )
| ~ ssList(sk3)
| ssList(tl(sk3))
| ( sk4 = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( sk4 = U ) )
| ~ ssList(sk3)
| ssList(tl(sk3))
| ( sk4 = sk3 ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
ssList(tl(sk3)),
inference(unit_resolution,[status(thm)],[35,32,19,14]) ).
tff(37,plain,
^ [U: $i] :
refl(
( ssItem(skaf83(U))
<=> ssItem(skaf83(U)) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [U: $i] : ssItem(skaf83(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
tff(41,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [U: $i] : ssItem(skaf83(U))
| ssItem(skaf83(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
ssItem(skaf83(sk3)),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,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(51,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(52,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)],[51]) ).
tff(53,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
tff(54,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[55,49]) ).
tff(57,plain,
! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[57,47]) ).
tff(59,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( sk4 = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( sk4 = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( sk4 = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( sk4 = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
cons(skaf83(sk3),skaf82(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[61,58,19,14]) ).
tff(63,plain,
sk3 = cons(skaf83(sk3),skaf82(sk3)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,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(69,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(70,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)],[69]) ).
tff(71,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
tff(72,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[73,67]) ).
tff(75,plain,
! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[75,65]) ).
tff(77,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( sk4 = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( sk4 = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( sk4 = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( sk4 = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( sk4 = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
cons(hd(sk3),tl(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[79,76,19,14]) ).
tff(81,plain,
cons(hd(sk3),tl(sk3)) = cons(skaf83(sk3),skaf82(sk3)),
inference(transitivity,[status(thm)],[80,63]) ).
tff(82,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) )
<=> ( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
^ [U: $i] :
trans(
monotonicity(
rewrite(
( ( nil = U )
<=> ( sk4 = U ) )),
( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( sk4 = U )
| ssItem(hd(U)) ) )),
rewrite(
( ( ~ ssList(U)
| ( sk4 = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) ) )),
( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(90,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) ),
inference(modus_ponens,[status(thm)],[91,85]) ).
tff(93,plain,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) ),
inference(modus_ponens,[status(thm)],[93,83]) ).
tff(95,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) )
| ~ ssList(sk3)
| ssItem(hd(sk3))
| ( sk4 = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) )
| ~ ssList(sk3)
| ssItem(hd(sk3))
| ( sk4 = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) )
| ~ ssList(sk3)
| ssItem(hd(sk3))
| ( sk4 = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( sk4 = U ) )
| ~ ssList(sk3)
| ssItem(hd(sk3))
| ( sk4 = sk3 ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
ssItem(hd(sk3)),
inference(unit_resolution,[status(thm)],[97,94,19,14]) ).
tff(99,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(100,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)],[99]) ).
tff(101,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(102,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(103,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)],[102]) ).
tff(104,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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause170) ).
tff(105,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)],[104,103]) ).
tff(106,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)],[105,101]) ).
tff(107,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)],[106]) ).
tff(108,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)],[107,100]) ).
tff(109,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) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) )
| ( hd(sk3) = skaf83(sk3) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) )
| ( hd(sk3) = skaf83(sk3) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = skaf83(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) )
| ( hd(sk3) = skaf83(sk3) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,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(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = skaf83(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) )
| ( hd(sk3) = skaf83(sk3) ) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,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(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = skaf83(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) )
| ( hd(sk3) = skaf83(sk3) ) ) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,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(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = skaf83(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,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) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) )
| ( hd(sk3) = skaf83(sk3) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = skaf83(sk3) ) ),
inference(unit_resolution,[status(thm)],[114,108,98,81]) ).
tff(116,plain,
hd(sk3) = skaf83(sk3),
inference(unit_resolution,[status(thm)],[115,45,36,9]) ).
tff(117,plain,
skaf83(sk3) = hd(sk3),
inference(symmetry,[status(thm)],[116]) ).
tff(118,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(119,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)],[118]) ).
tff(120,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(121,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(122,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)],[121]) ).
tff(123,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(124,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)],[123,122]) ).
tff(125,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)],[124,120]) ).
tff(126,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)],[125]) ).
tff(127,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)],[126,119]) ).
tff(128,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) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(129,plain,
( ( ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,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(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,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(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(transitivity,[status(thm)],[130,128]) ).
tff(132,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(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,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) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) ) ),
inference(unit_resolution,[status(thm)],[133,127,98,81]) ).
tff(135,plain,
skaf82(sk3) = tl(sk3),
inference(unit_resolution,[status(thm)],[134,45,36,9]) ).
tff(136,plain,
tl(sk3) = skaf82(sk3),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
cons(skaf83(sk3),tl(sk3)) = cons(skaf83(sk3),skaf82(sk3)),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
cons(skaf83(sk3),tl(sk3)) = sk3,
inference(transitivity,[status(thm)],[137,62]) ).
tff(139,plain,
( memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3))
<=> memberP(sk3,hd(sk3)) ),
inference(monotonicity,[status(thm)],[138,117]) ).
tff(140,plain,
( memberP(sk3,hd(sk3))
<=> memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) ),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
( ~ memberP(sk3,hd(sk3))
<=> ~ memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) ),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ memberP(sk4,U) )
<=> ( ~ ssItem(U)
| ~ memberP(sk4,U) ) )),
inference(bind,[status(th)],]) ).
tff(143,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk4,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk4,U) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
^ [U: $i] :
rewrite(
( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(sk4,U) ) )),
inference(bind,[status(th)],]) ).
tff(145,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk4,U) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
^ [U: $i] :
rewrite(
( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(148,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(150,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk4,U) ),
inference(modus_ponens,[status(thm)],[151,145]) ).
tff(153,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk4,U) ),
inference(skolemize,[status(sab)],[152]) ).
tff(154,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk4,U) ),
inference(modus_ponens,[status(thm)],[153,143]) ).
tff(155,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk4,U) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk4,hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk4,U) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk4,hd(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk4,U) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk4,hd(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk4,U) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk4,hd(sk3)) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
~ memberP(sk4,hd(sk3)),
inference(unit_resolution,[status(thm)],[157,154,98]) ).
tff(159,plain,
^ [A: $i] :
refl(
( ( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
<=> ( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(160,plain,
( ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,plain,
( ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,plain,
^ [A: $i] :
rewrite(
( ( ~ ssItem(A)
| ~ memberP(sk3,A)
| memberP(sk4,A) )
<=> ( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(163,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| memberP(sk4,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,axiom,
! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| memberP(sk4,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(165,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[165,161]) ).
tff(167,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(skolemize,[status(sab)],[166]) ).
tff(168,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[167,160]) ).
tff(169,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| memberP(sk4,hd(sk3))
| ~ memberP(sk3,hd(sk3)) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| memberP(sk4,hd(sk3))
| ~ memberP(sk3,hd(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| memberP(sk4,hd(sk3))
| ~ memberP(sk3,hd(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk4,A)
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| memberP(sk4,hd(sk3))
| ~ memberP(sk3,hd(sk3)) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
( memberP(sk4,hd(sk3))
| ~ memberP(sk3,hd(sk3)) ),
inference(unit_resolution,[status(thm)],[171,168,98]) ).
tff(173,plain,
~ memberP(sk3,hd(sk3)),
inference(unit_resolution,[status(thm)],[172,158]) ).
tff(174,plain,
~ memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)),
inference(modus_ponens,[status(thm)],[173,141]) ).
tff(175,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) )),
inference(bind,[status(th)],]) ).
tff(176,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) ),
inference(quant_intro,[status(thm)],[175]) ).
tff(177,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( U != V )
| ~ ssList(W) )
<=> ( ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) ) )),
rewrite(
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| ~ ssItem(U) ) )),
rewrite(
( ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) )),
inference(bind,[status(th)],]) ).
tff(179,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) ),
inference(quant_intro,[status(thm)],[178]) ).
tff(180,axiom,
! [W: $i,V: $i,U: $i] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause138) ).
tff(181,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ),
inference(modus_ponens,[status(thm)],[181,177]) ).
tff(183,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ),
inference(skolemize,[status(sab)],[182]) ).
tff(184,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ),
inference(modus_ponens,[status(thm)],[183,176]) ).
tff(185,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(186,plain,
( ( ~ ssItem(skaf83(sk3))
| ~ ssItem(skaf83(sk3))
| $false
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) )
<=> ( ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(188,plain,
( ( skaf83(sk3) = skaf83(sk3) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(189,plain,
( ( skaf83(sk3) != skaf83(sk3) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
( ( skaf83(sk3) != skaf83(sk3) )
<=> $false ),
inference(transitivity,[status(thm)],[189,187]) ).
tff(191,plain,
( ( ~ ssItem(skaf83(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf83(sk3) != skaf83(sk3) )
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) )
<=> ( ~ ssItem(skaf83(sk3))
| ~ ssItem(skaf83(sk3))
| $false
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) ) ),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
( ( ~ ssItem(skaf83(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf83(sk3) != skaf83(sk3) )
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) )
<=> ( ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) ) ),
inference(transitivity,[status(thm)],[191,186]) ).
tff(193,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
| ~ ssItem(skaf83(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf83(sk3) != skaf83(sk3) )
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) ) ),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
| ~ ssItem(skaf83(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf83(sk3) != skaf83(sk3) )
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) ) ),
inference(transitivity,[status(thm)],[193,185]) ).
tff(195,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
| ~ ssItem(skaf83(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf83(sk3) != skaf83(sk3) )
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(196,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)) ),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
memberP(cons(skaf83(sk3),tl(sk3)),skaf83(sk3)),
inference(unit_resolution,[status(thm)],[196,184,45,36]) ).
tff(198,plain,
$false,
inference(unit_resolution,[status(thm)],[197,174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC046-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 20:48:57 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.50 % SZS status Unsatisfiable
% 0.20/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------