TSTP Solution File: SWC270-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC270-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 11:56:42 EDT 2022
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 71
% Syntax : Number of formulae : 143 ( 50 unt; 15 typ; 0 def)
% Number of atoms : 1077 ( 113 equ)
% Maximal formula atoms : 36 ( 8 avg)
% Number of connectives : 1672 ( 802 ~; 781 |; 0 &)
% ( 89 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 79 ( 79 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 13 >; 4 *; 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 : 260 ( 235 !; 0 ?; 260 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssList_type,type,
ssList: $i > $o ).
tff(skaf66_type,type,
skaf66: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(skaf67_type,type,
skaf67: $i > $i ).
tff(skaf68_type,type,
skaf68: $i > $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(skaf65_type,type,
skaf65: $i > $i ).
tff(skaf64_type,type,
skaf64: $i > $i ).
tff(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(totalorderedP_type,type,
totalorderedP: $i > $o ).
tff(sk1_type,type,
sk1: $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(
( ssList(skaf66(U))
<=> ssList(skaf66(U)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [U: $i] : ssList(skaf66(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause29) ).
tff(5,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [U: $i] : ssList(skaf66(U)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [U: $i] : ssList(skaf66(U))
| ssList(skaf66(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
ssList(skaf66(sk3)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [U: $i] :
refl(
( ssList(skaf67(U))
<=> ssList(skaf67(U)) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [U: $i] : ssList(skaf67(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause28) ).
tff(14,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [U: $i] : ssList(skaf67(U)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [U: $i] : ssList(skaf67(U))
| ssList(skaf67(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
ssList(skaf67(sk3)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [U: $i] :
refl(
( ssList(skaf68(U))
<=> ssList(skaf68(U)) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [U: $i] : ssList(skaf68(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause27) ).
tff(23,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [U: $i] : ssList(skaf68(U)),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [U: $i] : ssList(skaf68(U))
| ssList(skaf68(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
ssList(skaf68(sk3)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [U: $i] :
refl(
( ssItem(skaf65(U))
<=> ssItem(skaf65(U)) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [U: $i] : ssItem(skaf65(U))
<=> ! [U: $i] : ssItem(skaf65(U)) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [U: $i] : ssItem(skaf65(U))
<=> ! [U: $i] : ssItem(skaf65(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
! [U: $i] : ssItem(skaf65(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause30) ).
tff(32,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [U: $i] : ssItem(skaf65(U))
| ssItem(skaf65(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
ssItem(skaf65(sk3)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
^ [U: $i] :
refl(
( ssItem(skaf64(U))
<=> ssItem(skaf64(U)) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [U: $i] : ssItem(skaf64(U))
<=> ! [U: $i] : ssItem(skaf64(U)) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [U: $i] : ssItem(skaf64(U))
<=> ! [U: $i] : ssItem(skaf64(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [U: $i] : ssItem(skaf64(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause31) ).
tff(41,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [U: $i] : ssItem(skaf64(U))
| ssItem(skaf64(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
ssItem(skaf64(sk3)),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
( ~ totalorderedP(sk1)
<=> ~ totalorderedP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ totalorderedP(sk1)
<=> ~ totalorderedP(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
~ totalorderedP(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(49,plain,
~ totalorderedP(sk1),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
~ totalorderedP(sk3),
inference(modus_ponens,[status(thm)],[49,46]) ).
tff(51,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(54,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[54,51]) ).
tff(56,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(57,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)],[56]) ).
tff(58,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(59,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(60,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)],[59]) ).
tff(61,axiom,
! [U: $i] :
( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause91) ).
tff(62,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| totalorderedP(sk3)
| ~ ssList(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| totalorderedP(sk3)
| ~ ssList(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) )
<=> ( totalorderedP(sk3)
| ~ ssList(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,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)) )
| totalorderedP(sk3)
| ~ ssList(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,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)) )
| totalorderedP(sk3)
| ~ ssList(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,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(71,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| totalorderedP(sk3)
| ~ ssList(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
~ leq(skaf64(sk3),skaf65(sk3)),
inference(unit_resolution,[status(thm)],[71,65,55,50]) ).
tff(73,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(74,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)],[73]) ).
tff(75,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(76,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(77,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)],[76]) ).
tff(78,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(79,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssItem(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(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| leq(skaf64(sk3),skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) )
<=> ( leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,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(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,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(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(transitivity,[status(thm)],[85,83]) ).
tff(87,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(88,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ),
inference(unit_resolution,[status(thm)],[88,82,72]) ).
tff(90,plain,
~ lt(skaf64(sk3),skaf65(sk3)),
inference(unit_resolution,[status(thm)],[89,45,36]) ).
tff(91,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(92,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)],[91]) ).
tff(93,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(94,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(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(quant_intro,[status(thm)],[94]) ).
tff(96,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(97,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)],[96,95]) ).
tff(98,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)],[97,93]) ).
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(skolemize,[status(sab)],[98]) ).
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)],[99,92]) ).
tff(101,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| totalorderedP(sk3)
| ~ ssList(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 ) )
| totalorderedP(sk3)
| ~ ssList(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) )
<=> ( totalorderedP(sk3)
| ~ ssList(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
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 ) )
| totalorderedP(sk3)
| ~ ssList(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ) ),
inference(monotonicity,[status(thm)],[102]) ).
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 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| totalorderedP(sk3)
| ~ ssList(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ) ),
inference(transitivity,[status(thm)],[103,101]) ).
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(quant_inst,[status(thm)],]) ).
tff(106,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| totalorderedP(sk3)
| ~ ssList(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3,
inference(unit_resolution,[status(thm)],[106,100,55,50]) ).
tff(108,plain,
( strictorderedP(sk3)
<=> strictorderedP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(110,plain,
strictorderedP(sk3),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ 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 ) )
<=> ( ~ 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(112,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(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)],[111]) ).
tff(113,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(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,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(115,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)],[114]) ).
tff(116,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(117,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 ) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,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 ) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,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 ) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,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 ) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,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 ) )
| ~ ssList(sk3)
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != sk3 )
| ~ strictorderedP(sk3) )
<=> ( ~ ! [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 ) )
| ~ ssList(sk3)
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != sk3 )
| ~ strictorderedP(sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ( ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssList(sk3)
| ~ ssItem(skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ strictorderedP(sk3)
| ~ ssList(skaf67(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != sk3 ) )
<=> ( ~ ssList(sk3)
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != sk3 )
| ~ strictorderedP(sk3) ) ),
inference(rewrite,[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 ) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssList(sk3)
| ~ ssItem(skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ strictorderedP(sk3)
| ~ ssList(skaf67(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != sk3 ) )
<=> ( ~ ! [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 ) )
| ~ ssList(sk3)
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != sk3 )
| ~ strictorderedP(sk3) ) ),
inference(monotonicity,[status(thm)],[122]) ).
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 ) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssList(sk3)
| ~ ssItem(skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ strictorderedP(sk3)
| ~ ssList(skaf67(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != sk3 ) )
<=> ( ~ ! [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 ) )
| ~ ssList(sk3)
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != sk3 )
| ~ strictorderedP(sk3) ) ),
inference(transitivity,[status(thm)],[123,121]) ).
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 ) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(skaf68(sk3))
| ~ ssList(sk3)
| ~ ssItem(skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ strictorderedP(sk3)
| ~ ssList(skaf67(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,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 ) )
| ~ ssList(sk3)
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) != sk3 )
| ~ strictorderedP(sk3) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
( ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(skaf66(sk3)) ),
inference(unit_resolution,[status(thm)],[126,120,55,110,107]) ).
tff(128,plain,
$false,
inference(unit_resolution,[status(thm)],[127,90,45,36,27,18,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWC270-1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n022.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sat Sep 3 23:23:09 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.29 Usage: tptp [options] [-file:]file
% 0.09/0.29 -h, -? prints this message.
% 0.09/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.29 -m, -model generate model.
% 0.09/0.29 -p, -proof generate proof.
% 0.09/0.29 -c, -core generate unsat core of named formulas.
% 0.09/0.29 -st, -statistics display statistics.
% 0.09/0.29 -t:timeout set timeout (in second).
% 0.09/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.29 -<param>:<value> configuration parameter and value.
% 0.09/0.29 -o:<output-file> file to place output in.
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------