%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC181-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:30:26 AM UTC 2025
% Result : Unsatisfiable 0.47s 0.70s
% Output : Proof 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 49
% Syntax : Number of formulae : 120 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 959 ( 100 equ)
% Maximal formula atoms : 31 ( 7 avg)
% Number of connectives : 1522 ( 749 ~; 688 |; 0 &)
% ( 85 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 66 ( 66 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 277 ( 251 !; 0 ?; 277 :)
% Comments :
%------------------------------------------------------------------------------
tff(strictorderedP_type,type,
strictorderedP: $i > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(skaf77_type,type,
skaf77: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(skaf74_type,type,
skaf74: $i > $i ).
tff(skaf76_type,type,
skaf76: $i > $i ).
tff(skaf75_type,type,
skaf75: $i > $i ).
tff(duplicatefreeP_type,type,
duplicatefreeP: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( duplicatefreeP(sk3)
<=> duplicatefreeP(sk1) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( duplicatefreeP(sk1)
<=> duplicatefreeP(sk3) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ~ duplicatefreeP(sk1)
<=> ~ duplicatefreeP(sk3) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ~ duplicatefreeP(sk1)
<=> ~ duplicatefreeP(sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
~ duplicatefreeP(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(10,plain,
~ duplicatefreeP(sk1),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
~ duplicatefreeP(sk3),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(14,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
<=> ( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| duplicatefreeP(U) )
<=> ( ~ ssList(U)
| duplicatefreeP(U) ) )),
( ( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
<=> ( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ) )),
rewrite(( ( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
<=> ( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ) )),
( ( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
<=> ( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause162) ).
tff(21,plain,
! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
| ~ ssList(sk3)
| duplicatefreeP(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
| ~ ssList(sk3)
| duplicatefreeP(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
| ~ ssList(sk3)
| duplicatefreeP(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
| ~ ssList(sk3)
| duplicatefreeP(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( duplicatefreeP(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) ),
inference(unit_resolution,[status(thm)],[27,24,14]) ).
tff(29,plain,
app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3,
inference(unit_resolution,[status(thm)],[28,11]) ).
tff(30,plain,
( strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
<=> strictorderedP(sk3) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( strictorderedP(sk3)
<=> strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))) ),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( strictorderedP(sk3)
<=> strictorderedP(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(34,plain,
strictorderedP(sk3),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))),
inference(modus_ponens,[status(thm)],[34,31]) ).
tff(36,plain,
^ [U: $i] :
refl(( ssList(skaf75(U))
<=> ssList(skaf75(U)) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [U: $i] : ssList(skaf75(U))
<=> ! [U: $i] : ssList(skaf75(U)) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [U: $i] : ssList(skaf75(U))
<=> ! [U: $i] : ssList(skaf75(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
! [U: $i] : ssList(skaf75(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause20) ).
tff(40,plain,
! [U: $i] : ssList(skaf75(U)),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [U: $i] : ssList(skaf75(U)),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [U: $i] : ssList(skaf75(U)),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [U: $i] : ssList(skaf75(U))
| ssList(skaf75(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
ssList(skaf75(sk3)),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
^ [U: $i] :
refl(( ssItem(skaf74(U))
<=> ssItem(skaf74(U)) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [U: $i] : ssItem(skaf74(U))
<=> ! [U: $i] : ssItem(skaf74(U)) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [U: $i] : ssItem(skaf74(U))
<=> ! [U: $i] : ssItem(skaf74(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
! [U: $i] : ssItem(skaf74(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause21) ).
tff(49,plain,
! [U: $i] : ssItem(skaf74(U)),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [U: $i] : ssItem(skaf74(U)),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [U: $i] : ssItem(skaf74(U)),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [U: $i] : ssItem(skaf74(U))
| ssItem(skaf74(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
ssItem(skaf74(sk3)),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
^ [U: $i] :
refl(( ssList(skaf77(U))
<=> ssList(skaf77(U)) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [U: $i] : ssList(skaf77(U))
<=> ! [U: $i] : ssList(skaf77(U)) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [U: $i] : ssList(skaf77(U))
<=> ! [U: $i] : ssList(skaf77(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
! [U: $i] : ssList(skaf77(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause18) ).
tff(58,plain,
! [U: $i] : ssList(skaf77(U)),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [U: $i] : ssList(skaf77(U)),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [U: $i] : ssList(skaf77(U)),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ ! [U: $i] : ssList(skaf77(U))
| ssList(skaf77(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
ssList(skaf77(sk3)),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
^ [U: $i] :
refl(( ssList(skaf76(U))
<=> ssList(skaf76(U)) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [U: $i] : ssList(skaf76(U))
<=> ! [U: $i] : ssList(skaf76(U)) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [U: $i] : ssList(skaf76(U))
<=> ! [U: $i] : ssList(skaf76(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
! [U: $i] : ssList(skaf76(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause19) ).
tff(67,plain,
! [U: $i] : ssList(skaf76(U)),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [U: $i] : ssList(skaf76(U)),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [U: $i] : ssList(skaf76(U)),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ~ ! [U: $i] : ssList(skaf76(U))
| ssList(skaf76(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
ssList(skaf76(sk3)),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
( ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(73,plain,
( ssList(sk3)
<=> ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))) ),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))),
inference(modus_ponens,[status(thm)],[14,73]) ).
tff(75,plain,
^ [V: $i] :
refl(( ( ~ ssItem(V)
| ~ lt(V,V) )
<=> ( ~ ssItem(V)
| ~ lt(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
^ [V: $i] :
rewrite(( ( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) )
<=> ( ~ ssItem(V)
| ~ lt(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(81,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(82,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(transitivity,[status(thm)],[81,80]) ).
tff(83,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(transitivity,[status(thm)],[82,79]) ).
tff(84,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) )),
( ( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ~ lt(U,V)
| ( U != V )
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(V)
| ~ lt(U,V)
| ( U != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) )),
( ( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(transitivity,[status(thm)],[85,83]) ).
tff(87,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause111) ).
tff(88,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[88,77]) ).
tff(90,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[90,76]) ).
tff(92,plain,
( ( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(skaf74(sk3))
| ~ lt(skaf74(sk3),skaf74(sk3)) )
<=> ( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(skaf74(sk3))
| ~ lt(skaf74(sk3),skaf74(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(skaf74(sk3))
| ~ lt(skaf74(sk3),skaf74(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(skaf74(sk3))
| ~ lt(skaf74(sk3),skaf74(sk3)) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
~ lt(skaf74(sk3),skaf74(sk3)),
inference(unit_resolution,[status(thm)],[94,91,53]) ).
tff(96,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(97,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)],[96]) ).
tff(98,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(99,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(100,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)],[99]) ).
tff(101,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(102,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(103,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)],[102,101]) ).
tff(104,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)],[103,100]) ).
tff(105,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(106,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)],[105]) ).
tff(107,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)],[106,104]) ).
tff(108,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(109,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)],[108,107]) ).
tff(110,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)],[109,98]) ).
tff(111,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)],[110]) ).
tff(112,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)],[111,97]) ).
tff(113,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(skaf77(sk3))
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf75(sk3))
| ~ strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(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(skaf77(sk3))
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf75(sk3))
| ~ strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ( ~ ssItem(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))) )
<=> ( ~ ssList(skaf77(sk3))
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf75(sk3))
| ~ strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,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(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(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(skaf77(sk3))
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf75(sk3))
| ~ strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,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(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(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(skaf77(sk3))
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf75(sk3))
| ~ strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(transitivity,[status(thm)],[115,113]) ).
tff(117,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(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))) ),
inference(quant_inst,[status(thm)],[]) ).
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))) )
| ~ ssList(skaf77(sk3))
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf75(sk3))
| ~ strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
( ~ ssList(skaf77(sk3))
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf75(sk3))
| ~ strictorderedP(app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))) ),
inference(unit_resolution,[status(thm)],[118,112]) ).
tff(120,plain,
$false,
inference(unit_resolution,[status(thm)],[119,95,74,71,62,53,44,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWC181-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 08:32:32 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.47/0.70 % SZS status Unsatisfiable
% 0.47/0.70 % SZS output start Proof
% See solution above
% 0.54/0.72 % E exiting
%------------------------------------------------------------------------------