%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC264-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:44 AM UTC 2025
% Result : Unsatisfiable 0.37s 0.53s
% Output : Proof 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 57
% Syntax : Number of formulae : 141 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 1128 ( 85 equ)
% Maximal formula atoms : 32 ( 8 avg)
% Number of connectives : 1748 ( 841 ~; 811 |; 0 &)
% ( 96 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 80 ( 80 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 306 ( 277 !; 0 ?; 306 :)
% Comments :
%------------------------------------------------------------------------------
tff(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(skaf65_type,type,
skaf65: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(skaf64_type,type,
skaf64: $i > $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(totalorderedP_type,type,
totalorderedP: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(skaf66_type,type,
skaf66: $i > $i ).
tff(skaf68_type,type,
skaf68: $i > $i ).
tff(skaf67_type,type,
skaf67: $i > $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(strictorderedP_type,type,
strictorderedP: $i > $o ).
tff(1,plain,
^ [U: $i] :
refl(( ssItem(skaf65(U))
<=> ssItem(skaf65(U)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [U: $i] : ssItem(skaf65(U))
<=> ! [U: $i] : ssItem(skaf65(U)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [U: $i] : ssItem(skaf65(U))
<=> ! [U: $i] : ssItem(skaf65(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [U: $i] : ssItem(skaf65(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause30) ).
tff(5,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [U: $i] : ssItem(skaf65(U))
| ssItem(skaf65(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ssItem(skaf65(sk3)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [U: $i] :
refl(( ssItem(skaf64(U))
<=> ssItem(skaf64(U)) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [U: $i] : ssItem(skaf64(U))
<=> ! [U: $i] : ssItem(skaf64(U)) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [U: $i] : ssItem(skaf64(U))
<=> ! [U: $i] : ssItem(skaf64(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [U: $i] : ssItem(skaf64(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause31) ).
tff(14,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [U: $i] : ssItem(skaf64(U))
| ssItem(skaf64(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ssItem(skaf64(sk3)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(21,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( totalorderedP(sk3)
<=> totalorderedP(sk1) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( totalorderedP(sk1)
<=> totalorderedP(sk3) ),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ~ totalorderedP(sk1)
<=> ~ totalorderedP(sk3) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ~ totalorderedP(sk1)
<=> ~ totalorderedP(sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
~ totalorderedP(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(28,plain,
~ totalorderedP(sk1),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ totalorderedP(sk3),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(32,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
( ( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) )
<=> ( ~ ssList(U)
| ~ leq(skaf64(U),skaf65(U))
| totalorderedP(U) ) )),
rewrite(( ( ~ ssList(U)
| ~ leq(skaf64(U),skaf65(U))
| totalorderedP(U) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
( ( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [U: $i] :
( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [U: $i] :
( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause91) ).
tff(39,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(unit_resolution,[status(thm)],[45,42,32]) ).
tff(47,plain,
~ leq(skaf64(sk3),skaf65(sk3)),
inference(unit_resolution,[status(thm)],[46,29]) ).
tff(48,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ lt(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ~ lt(U,V)
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(V)
| ~ lt(U,V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| leq(U,V) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause103) ).
tff(54,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| leq(skaf64(sk3),skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) )
<=> ( leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| leq(skaf64(sk3),skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| leq(skaf64(sk3),skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| leq(skaf64(sk3),skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ),
inference(unit_resolution,[status(thm)],[63,57,47]) ).
tff(65,plain,
~ lt(skaf64(sk3),skaf65(sk3)),
inference(unit_resolution,[status(thm)],[64,18,9]) ).
tff(66,plain,
^ [U: $i] :
refl(( ssList(skaf66(U))
<=> ssList(skaf66(U)) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
! [U: $i] : ssList(skaf66(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause29) ).
tff(70,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [U: $i] : ssList(skaf66(U)),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [U: $i] : ssList(skaf66(U))
| ssList(skaf66(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
ssList(skaf66(sk3)),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
^ [U: $i] :
refl(( ssList(skaf68(U))
<=> ssList(skaf68(U)) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
! [U: $i] : ssList(skaf68(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause27) ).
tff(79,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [U: $i] : ssList(skaf68(U)),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ~ ! [U: $i] : ssList(skaf68(U))
| ssList(skaf68(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
ssList(skaf68(sk3)),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
^ [U: $i] :
refl(( ssList(skaf67(U))
<=> ssList(skaf67(U)) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
! [U: $i] : ssList(skaf67(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause28) ).
tff(88,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [U: $i] : ssList(skaf67(U)),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
( ~ ! [U: $i] : ssList(skaf67(U))
| ssList(skaf67(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
ssList(skaf67(sk3)),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| totalorderedP(U) )
<=> ( ~ ssList(U)
| totalorderedP(U) ) )),
( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
rewrite(( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause164) ).
tff(99,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
( totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(unit_resolution,[status(thm)],[105,102,32]) ).
tff(107,plain,
app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3,
inference(unit_resolution,[status(thm)],[106,29]) ).
tff(108,plain,
( ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ssList(sk3)
<=> ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))),
inference(modus_ponens,[status(thm)],[32,109]) ).
tff(111,plain,
( strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
<=> strictorderedP(sk3) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(112,plain,
( strictorderedP(sk3)
<=> strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
( strictorderedP(sk3)
<=> strictorderedP(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,axiom,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(115,plain,
strictorderedP(sk3),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))),
inference(modus_ponens,[status(thm)],[115,112]) ).
tff(117,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) )),
inference(bind,[status(th)],[]) ).
tff(121,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(123,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(124,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) ) ),
inference(transitivity,[status(thm)],[123,122]) ).
tff(125,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) ),
inference(transitivity,[status(thm)],[124,121]) ).
tff(126,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y) )
<=> ( ~ ssList(Y)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W) )
<=> ( ~ ssList(Y)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(W) ) )),
rewrite(( ( ~ ssList(Y)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(W) )
<=> ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W) )
<=> ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X) )
<=> ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(X) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(V) ) )),
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(V) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ strictorderedP(Z) ) )),
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ strictorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Z) ) )),
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| lt(V,X) ) )),
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| lt(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) ),
inference(transitivity,[status(thm)],[127,125]) ).
tff(129,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause181) ).
tff(130,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ),
inference(modus_ponens,[status(thm)],[130,119]) ).
tff(132,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ),
inference(modus_ponens,[status(thm)],[132,118]) ).
tff(134,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(skaf66(sk3))
| ~ strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(skaf66(sk3))
| ~ strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ( ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| lt(skaf64(sk3),skaf65(sk3))
| ~ strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) )
<=> ( ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(skaf66(sk3))
| ~ strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| lt(skaf64(sk3),skaf65(sk3))
| ~ strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(skaf66(sk3))
| ~ strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| lt(skaf64(sk3),skaf65(sk3))
| ~ strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(skaf66(sk3))
| ~ strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| lt(skaf64(sk3),skaf65(sk3))
| ~ strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(skaf66(sk3))
| ~ strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ ssList(skaf66(sk3))
| ~ strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ),
inference(unit_resolution,[status(thm)],[139,133]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,116,110,18,92,9,83,74,65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWC264-1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 08:50:35 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.37/0.53 % SZS status Unsatisfiable
% 0.37/0.53 % SZS output start Proof
% See solution above
% 0.39/0.55 % E exiting
%------------------------------------------------------------------------------