%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC340-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:30:56 AM UTC 2025
% Result : Unsatisfiable 0.39s 0.56s
% Output : Proof 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 61
% Syntax : Number of formulae : 155 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 1154 ( 89 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 1773 ( 854 ~; 819 |; 0 &)
% ( 100 <=>; 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 : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 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(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $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,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(28,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( segmentP(sk2,sk1)
<=> segmentP(sk4,sk3) ),
inference(monotonicity,[status(thm)],[28,21]) ).
tff(30,plain,
( segmentP(sk4,sk3)
<=> segmentP(sk2,sk1) ),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( segmentP(sk4,sk3)
<=> segmentP(sk4,sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
segmentP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(33,plain,
segmentP(sk4,sk3),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
segmentP(sk2,sk1),
inference(modus_ponens,[status(thm)],[33,30]) ).
tff(35,plain,
( ( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(37,plain,
( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
inference(modus_ponens,[status(thm)],[37,35]) ).
tff(39,plain,
( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
inference(modus_ponens,[status(thm)],[38,35]) ).
tff(40,plain,
( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
inference(modus_ponens,[status(thm)],[40,35]) ).
tff(42,plain,
~ totalorderedP(sk1),
inference(unit_resolution,[status(thm)],[41,34]) ).
tff(43,plain,
~ totalorderedP(sk3),
inference(modus_ponens,[status(thm)],[42,25]) ).
tff(44,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(46,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,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(48,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)],[47]) ).
tff(49,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(50,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(51,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)],[50]) ).
tff(52,axiom,
! [U: $i] :
( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause91) ).
tff(53,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,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(58,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(59,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)],[58,57]) ).
tff(60,plain,
( totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(unit_resolution,[status(thm)],[59,56,46]) ).
tff(61,plain,
~ leq(skaf64(sk3),skaf65(sk3)),
inference(unit_resolution,[status(thm)],[60,43]) ).
tff(62,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(63,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)],[62]) ).
tff(64,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(65,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(66,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)],[65]) ).
tff(67,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(68,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,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(73,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(74,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)],[73]) ).
tff(75,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)],[74,72]) ).
tff(76,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(77,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)],[76,75]) ).
tff(78,plain,
( ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ),
inference(unit_resolution,[status(thm)],[77,71,61]) ).
tff(79,plain,
~ lt(skaf64(sk3),skaf65(sk3)),
inference(unit_resolution,[status(thm)],[78,18,9]) ).
tff(80,plain,
^ [U: $i] :
refl(( ssList(skaf66(U))
<=> ssList(skaf66(U)) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
! [U: $i] : ssList(skaf66(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause29) ).
tff(84,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [U: $i] : ssList(skaf66(U)),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ~ ! [U: $i] : ssList(skaf66(U))
| ssList(skaf66(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
ssList(skaf66(sk3)),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
^ [U: $i] :
refl(( ssList(skaf68(U))
<=> ssList(skaf68(U)) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
! [U: $i] : ssList(skaf68(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause27) ).
tff(93,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [U: $i] : ssList(skaf68(U)),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ~ ! [U: $i] : ssList(skaf68(U))
| ssList(skaf68(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
ssList(skaf68(sk3)),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
^ [U: $i] :
refl(( ssList(skaf67(U))
<=> ssList(skaf67(U)) )),
inference(bind,[status(th)],[]) ).
tff(99,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,axiom,
! [U: $i] : ssList(skaf67(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause28) ).
tff(102,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [U: $i] : ssList(skaf67(U)),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
( ~ ! [U: $i] : ssList(skaf67(U))
| ssList(skaf67(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
ssList(skaf67(sk3)),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,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(108,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)],[107]) ).
tff(109,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(110,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(111,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)],[110]) ).
tff(112,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(113,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)],[112,111]) ).
tff(114,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)],[113,109]) ).
tff(115,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)],[114]) ).
tff(116,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)],[115,108]) ).
tff(117,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(118,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(119,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)],[118,117]) ).
tff(120,plain,
( totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(unit_resolution,[status(thm)],[119,116,46]) ).
tff(121,plain,
app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3,
inference(unit_resolution,[status(thm)],[120,43]) ).
tff(122,plain,
( ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ssList(sk3)
<=> ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))),
inference(modus_ponens,[status(thm)],[46,123]) ).
tff(125,plain,
( strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
<=> strictorderedP(sk3) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(126,plain,
( strictorderedP(sk3)
<=> strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( strictorderedP(sk3)
<=> strictorderedP(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,axiom,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(129,plain,
strictorderedP(sk3),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
strictorderedP(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))),
inference(modus_ponens,[status(thm)],[129,126]) ).
tff(131,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(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))) )
<=> ! [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)],[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))) )
<=> ! [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(134,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(135,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)],[134]) ).
tff(136,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(137,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(138,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)],[137,136]) ).
tff(139,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)],[138,135]) ).
tff(140,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(141,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)],[140]) ).
tff(142,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)],[141,139]) ).
tff(143,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(144,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)],[143,142]) ).
tff(145,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)],[144,133]) ).
tff(146,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)],[145]) ).
tff(147,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)],[146,132]) ).
tff(148,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(149,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(150,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)],[149]) ).
tff(151,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)],[150,148]) ).
tff(152,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(153,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)],[152,151]) ).
tff(154,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)],[153,147]) ).
tff(155,plain,
$false,
inference(unit_resolution,[status(thm)],[154,130,124,18,106,9,97,88,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC340-1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.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 09:04:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.39/0.56 % SZS status Unsatisfiable
% 0.39/0.56 % SZS output start Proof
% See solution above
% 0.39/0.60 % E exiting
%------------------------------------------------------------------------------