TSTP Solution File: SWC180-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC180-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 11:55:54 EDT 2022
% Result : Unsatisfiable 198.51s 127.86s
% Output : Proof 198.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 107
% Syntax : Number of formulae : 247 ( 72 unt; 14 typ; 0 def)
% Number of atoms : 1665 ( 281 equ)
% Maximal formula atoms : 27 ( 7 avg)
% Number of connectives : 2602 (1250 ~;1217 |; 0 &)
% ( 135 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 80 ( 80 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 11 >; 4 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 507 ( 465 !; 0 ?; 507 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(skaf74_type,type,
skaf74: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(skaf77_type,type,
skaf77: $i > $i ).
tff(skaf76_type,type,
skaf76: $i > $i ).
tff(nil_type,type,
nil: $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,
( ~ duplicatefreeP(sk1)
<=> ~ duplicatefreeP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ duplicatefreeP(sk1)
<=> ~ duplicatefreeP(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ duplicatefreeP(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(4,plain,
~ duplicatefreeP(sk1),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ duplicatefreeP(sk3),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(9,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,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(12,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)],[11]) ).
tff(13,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(14,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(15,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)],[14]) ).
tff(16,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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause162) ).
tff(17,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)],[16,15]) ).
tff(18,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)],[17,13]) ).
tff(19,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)],[18]) ).
tff(20,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)],[19,12]) ).
tff(21,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| duplicatefreeP(U)
| ( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) )
| duplicatefreeP(sk3)
| ~ ssList(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 ) )
| duplicatefreeP(sk3)
| ~ ssList(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ ssList(sk3)
| duplicatefreeP(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) )
<=> ( duplicatefreeP(sk3)
| ~ ssList(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,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 ) )
| duplicatefreeP(sk3)
| ~ ssList(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) ) ),
inference(monotonicity,[status(thm)],[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 ) )
| ~ 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 ) )
| duplicatefreeP(sk3)
| ~ ssList(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
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 ) ),
inference(quant_inst,[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 ) )
| duplicatefreeP(sk3)
| ~ ssList(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3,
inference(unit_resolution,[status(thm)],[26,20,10,5]) ).
tff(28,plain,
^ [U: $i] :
refl(
( ssList(skaf77(U))
<=> ssList(skaf77(U)) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [U: $i] : ssList(skaf77(U))
<=> ! [U: $i] : ssList(skaf77(U)) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [U: $i] : ssList(skaf77(U))
<=> ! [U: $i] : ssList(skaf77(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
! [U: $i] : ssList(skaf77(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause18) ).
tff(32,plain,
! [U: $i] : ssList(skaf77(U)),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [U: $i] : ssList(skaf77(U)),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [U: $i] : ssList(skaf77(U)),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [U: $i] : ssList(skaf77(U))
| ssList(skaf77(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
ssList(skaf77(sk3)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
^ [U: $i] :
refl(
( ssItem(skaf74(U))
<=> ssItem(skaf74(U)) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [U: $i] : ssItem(skaf74(U))
<=> ! [U: $i] : ssItem(skaf74(U)) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [U: $i] : ssItem(skaf74(U))
<=> ! [U: $i] : ssItem(skaf74(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [U: $i] : ssItem(skaf74(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause21) ).
tff(41,plain,
! [U: $i] : ssItem(skaf74(U)),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [U: $i] : ssItem(skaf74(U)),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [U: $i] : ssItem(skaf74(U)),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [U: $i] : ssItem(skaf74(U))
| ssItem(skaf74(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
ssItem(skaf74(sk3)),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(52,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf77(sk3))
| ssList(cons(skaf74(sk3),skaf77(sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf77(sk3))
| ssList(cons(skaf74(sk3),skaf77(sk3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf77(sk3))
| ssList(cons(skaf74(sk3),skaf77(sk3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf77(sk3))
| ssList(cons(skaf74(sk3),skaf77(sk3))) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( ~ ssItem(skaf74(sk3))
| ~ ssList(skaf77(sk3))
| ssList(cons(skaf74(sk3),skaf77(sk3))) ),
inference(unit_resolution,[status(thm)],[58,55]) ).
tff(60,plain,
ssList(cons(skaf74(sk3),skaf77(sk3))),
inference(unit_resolution,[status(thm)],[59,45,36]) ).
tff(61,plain,
^ [U: $i] :
refl(
( ssList(skaf75(U))
<=> ssList(skaf75(U)) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [U: $i] : ssList(skaf75(U))
<=> ! [U: $i] : ssList(skaf75(U)) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [U: $i] : ssList(skaf75(U))
<=> ! [U: $i] : ssList(skaf75(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
! [U: $i] : ssList(skaf75(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause20) ).
tff(65,plain,
! [U: $i] : ssList(skaf75(U)),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [U: $i] : ssList(skaf75(U)),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [U: $i] : ssList(skaf75(U)),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
( ~ ! [U: $i] : ssList(skaf75(U))
| ssList(skaf75(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
ssList(skaf75(sk3)),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
^ [U: $i] :
refl(
( ssList(skaf76(U))
<=> ssList(skaf76(U)) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [U: $i] : ssList(skaf76(U))
<=> ! [U: $i] : ssList(skaf76(U)) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [U: $i] : ssList(skaf76(U))
<=> ! [U: $i] : ssList(skaf76(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
! [U: $i] : ssList(skaf76(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause19) ).
tff(74,plain,
! [U: $i] : ssList(skaf76(U)),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [U: $i] : ssList(skaf76(U)),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [U: $i] : ssList(skaf76(U)),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [U: $i] : ssList(skaf76(U))
| ssList(skaf76(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
ssList(skaf76(sk3)),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ssList(cons(skaf74(sk3),skaf76(sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ssList(cons(skaf74(sk3),skaf76(sk3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ssList(cons(skaf74(sk3),skaf76(sk3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ssList(cons(skaf74(sk3),skaf76(sk3))) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
( ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ssList(cons(skaf74(sk3),skaf76(sk3))) ),
inference(unit_resolution,[status(thm)],[81,55]) ).
tff(83,plain,
ssList(cons(skaf74(sk3),skaf76(sk3))),
inference(unit_resolution,[status(thm)],[82,78,45]) ).
tff(84,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(90,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
tff(94,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf75(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),skaf76(sk3)))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf75(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),skaf76(sk3)))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),skaf76(sk3)))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) ) )
<=> ( ~ ssList(skaf75(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),skaf76(sk3)))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),skaf76(sk3)))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf75(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),skaf76(sk3)))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) ) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),skaf76(sk3)))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf75(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),skaf76(sk3)))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) ) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),skaf76(sk3)))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf75(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),skaf76(sk3)))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ~ ssList(skaf75(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),skaf76(sk3)))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(unit_resolution,[status(thm)],[99,93]) ).
tff(101,plain,
app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))),
inference(unit_resolution,[status(thm)],[100,83,69,60]) ).
tff(102,plain,
app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))) = app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(109,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[111,104]) ).
tff(113,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ( app(cons(skaf74(sk3),nil),skaf76(sk3)) = cons(skaf74(sk3),skaf76(sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ( app(cons(skaf74(sk3),nil),skaf76(sk3)) = cons(skaf74(sk3),skaf76(sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ( app(cons(skaf74(sk3),nil),skaf76(sk3)) = cons(skaf74(sk3),skaf76(sk3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ( app(cons(skaf74(sk3),nil),skaf76(sk3)) = cons(skaf74(sk3),skaf76(sk3)) ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ( app(cons(skaf74(sk3),nil),skaf76(sk3)) = cons(skaf74(sk3),skaf76(sk3)) ) ),
inference(unit_resolution,[status(thm)],[115,112]) ).
tff(117,plain,
app(cons(skaf74(sk3),nil),skaf76(sk3)) = cons(skaf74(sk3),skaf76(sk3)),
inference(unit_resolution,[status(thm)],[116,78,45]) ).
tff(118,plain,
app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(120,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(121,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ssList(cons(skaf74(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ssList(cons(skaf74(sk3),nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ( ~ ssItem(skaf74(sk3))
| ~ ssList(nil)
| ssList(cons(skaf74(sk3),nil)) )
<=> ( ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ssList(cons(skaf74(sk3),nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(nil)
| ssList(cons(skaf74(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ssList(cons(skaf74(sk3),nil)) ) ),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(nil)
| ssList(cons(skaf74(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ssList(cons(skaf74(sk3),nil)) ) ),
inference(transitivity,[status(thm)],[124,122]) ).
tff(126,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(nil)
| ssList(cons(skaf74(sk3),nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ssList(cons(skaf74(sk3),nil)) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
ssList(cons(skaf74(sk3),nil)),
inference(unit_resolution,[status(thm)],[127,121,55,45]) ).
tff(129,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),nil))
| ( app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),nil))
| ( app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ( ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),nil))
| ( app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) )
<=> ( ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),nil))
| ( app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),nil))
| ( app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),nil))
| ( app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) ) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),nil))
| ( app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),nil))
| ( app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) ) ),
inference(transitivity,[status(thm)],[131,129]) ).
tff(133,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),nil))
| ( app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ~ ssList(cons(skaf74(sk3),nil))
| ( app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( ~ ssList(cons(skaf74(sk3),nil))
| ( app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(unit_resolution,[status(thm)],[134,93,78,60]) ).
tff(136,plain,
app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))),
inference(unit_resolution,[status(thm)],[135,128]) ).
tff(137,plain,
app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(app(cons(skaf74(sk3),nil),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ( app(cons(skaf74(sk3),nil),nil) = cons(skaf74(sk3),nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ( app(cons(skaf74(sk3),nil),nil) = cons(skaf74(sk3),nil) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ( ~ ssItem(skaf74(sk3))
| ~ ssList(nil)
| ( app(cons(skaf74(sk3),nil),nil) = cons(skaf74(sk3),nil) ) )
<=> ( ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ( app(cons(skaf74(sk3),nil),nil) = cons(skaf74(sk3),nil) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(nil)
| ( app(cons(skaf74(sk3),nil),nil) = cons(skaf74(sk3),nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ( app(cons(skaf74(sk3),nil),nil) = cons(skaf74(sk3),nil) ) ) ),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(nil)
| ( app(cons(skaf74(sk3),nil),nil) = cons(skaf74(sk3),nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ( app(cons(skaf74(sk3),nil),nil) = cons(skaf74(sk3),nil) ) ) ),
inference(transitivity,[status(thm)],[140,138]) ).
tff(142,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(nil)
| ( app(cons(skaf74(sk3),nil),nil) = cons(skaf74(sk3),nil) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ( app(cons(skaf74(sk3),nil),nil) = cons(skaf74(sk3),nil) ) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
app(cons(skaf74(sk3),nil),nil) = cons(skaf74(sk3),nil),
inference(unit_resolution,[status(thm)],[143,121,112,45]) ).
tff(145,plain,
app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(cons(skaf74(sk3),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3))),
inference(transitivity,[status(thm)],[145,137,118]) ).
tff(147,plain,
app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) = app(skaf75(sk3),app(cons(skaf74(sk3),skaf76(sk3)),cons(skaf74(sk3),skaf77(sk3)))),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ssList(app(cons(skaf74(sk3),nil),nil))
<=> ssList(cons(skaf74(sk3),nil)) ),
inference(monotonicity,[status(thm)],[144]) ).
tff(149,plain,
( ssList(cons(skaf74(sk3),nil))
<=> ssList(app(cons(skaf74(sk3),nil),nil)) ),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
ssList(app(cons(skaf74(sk3),nil),nil)),
inference(modus_ponens,[status(thm)],[128,149]) ).
tff(151,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],]) ).
tff(152,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[151]) ).
tff(153,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(154,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],]) ).
tff(155,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(157,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[157,153]) ).
tff(159,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[158]) ).
tff(160,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[159,152]) ).
tff(161,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,plain,
( ( ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf76(sk3)) )
<=> ( ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(163,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf76(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf76(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ) ),
inference(transitivity,[status(thm)],[163,161]) ).
tff(165,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf76(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf76(sk3))
| ~ ssList(cons(skaf74(sk3),skaf77(sk3)))
| ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))),
inference(unit_resolution,[status(thm)],[166,160,78,60]) ).
tff(168,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf75(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(app(cons(skaf74(sk3),nil),nil))
| ( app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf75(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(app(cons(skaf74(sk3),nil),nil))
| ( app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
( ( ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(app(cons(skaf74(sk3),nil),nil))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) ) )
<=> ( ~ ssList(skaf75(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(app(cons(skaf74(sk3),nil),nil))
| ( app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(app(cons(skaf74(sk3),nil),nil))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf75(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(app(cons(skaf74(sk3),nil),nil))
| ( app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) ) ) ),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(app(cons(skaf74(sk3),nil),nil))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf75(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(app(cons(skaf74(sk3),nil),nil))
| ( app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) ) ) ),
inference(transitivity,[status(thm)],[170,168]) ).
tff(172,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(app(cons(skaf74(sk3),nil),nil))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(173,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf75(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(app(cons(skaf74(sk3),nil),nil))
| ( app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) ) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
( ~ ssList(app(cons(skaf74(sk3),nil),nil))
| ( app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))) ) ),
inference(unit_resolution,[status(thm)],[173,93,69,167]) ).
tff(175,plain,
app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(skaf75(sk3),app(app(cons(skaf74(sk3),nil),nil),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))),
inference(unit_resolution,[status(thm)],[174,150]) ).
tff(176,plain,
app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)) = app(skaf75(sk3),cons(skaf74(sk3),nil)),
inference(monotonicity,[status(thm)],[144]) ).
tff(177,plain,
app(skaf75(sk3),cons(skaf74(sk3),nil)) = app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = app(app(skaf75(sk3),app(cons(skaf74(sk3),nil),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) = sk3,
inference(transitivity,[status(thm)],[178,175,147,102,27]) ).
tff(180,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ lt(U,U) )
<=> ( ~ ssItem(U)
| ~ lt(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(181,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(quant_intro,[status(thm)],[180]) ).
tff(182,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(183,plain,
^ [U: $i] :
rewrite(
( ( ~ lt(U,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ lt(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(184,plain,
( ! [U: $i] :
( ~ lt(U,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(quant_intro,[status(thm)],[183]) ).
tff(185,axiom,
! [U: $i] :
( ~ lt(U,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause63) ).
tff(186,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[186,182]) ).
tff(188,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(skolemize,[status(sab)],[187]) ).
tff(189,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[188,181]) ).
tff(190,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(skaf74(sk3))
| ~ lt(skaf74(sk3),skaf74(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(skaf74(sk3))
| ~ lt(skaf74(sk3),skaf74(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(191,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(skaf74(sk3))
| ~ lt(skaf74(sk3),skaf74(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(192,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(skaf74(sk3))
| ~ lt(skaf74(sk3),skaf74(sk3)) ),
inference(modus_ponens,[status(thm)],[191,190]) ).
tff(193,plain,
~ lt(skaf74(sk3),skaf74(sk3)),
inference(unit_resolution,[status(thm)],[192,189,45]) ).
tff(194,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(195,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[194]) ).
tff(196,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(197,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(A,D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| lt(A,D) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| lt(A,D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(A,D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(C,D) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(C,D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(198,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[197]) ).
tff(199,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(200,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[200,196]) ).
tff(202,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(skolemize,[status(sab)],[201]) ).
tff(203,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[202,195]) ).
tff(204,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) != sk3 ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(205,plain,
( ( ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssItem(skaf74(sk3))
| ~ ssItem(skaf74(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) != sk3 ) )
<=> ( ~ ssItem(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(206,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssItem(skaf74(sk3))
| ~ ssItem(skaf74(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) != sk3 ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) != sk3 ) ) ),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssItem(skaf74(sk3))
| ~ ssItem(skaf74(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) != sk3 ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) != sk3 ) ) ),
inference(transitivity,[status(thm)],[206,204]) ).
tff(208,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssItem(skaf74(sk3))
| ~ ssItem(skaf74(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(209,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| lt(A,D)
| ~ memberP(C,D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),nil)),app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3)))) != sk3 ) ),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
~ memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3)),
inference(unit_resolution,[status(thm)],[209,203,45,69,193,167,179]) ).
tff(211,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(212,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[211]) ).
tff(213,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(214,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(215,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[214]) ).
tff(216,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause175) ).
tff(217,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[217,213]) ).
tff(219,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(skolemize,[status(sab)],[218]) ).
tff(220,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[219,212]) ).
tff(221,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(222,plain,
( ( ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf76(sk3))
| ~ ssItem(skaf74(sk3))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ~ ssList(skaf77(sk3))
| $false )
<=> ( ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(223,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(224,plain,
( ( app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) = app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(225,plain,
( ( app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) != app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
( ( app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) != app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) )
<=> $false ),
inference(transitivity,[status(thm)],[225,223]) ).
tff(227,plain,
( ( ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf76(sk3))
| ~ ssItem(skaf74(sk3))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ~ ssList(skaf77(sk3))
| ( app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) != app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) ) )
<=> ( ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf76(sk3))
| ~ ssItem(skaf74(sk3))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ~ ssList(skaf77(sk3))
| $false ) ),
inference(monotonicity,[status(thm)],[226]) ).
tff(228,plain,
( ( ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf76(sk3))
| ~ ssItem(skaf74(sk3))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ~ ssList(skaf77(sk3))
| ( app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) != app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) ) )
<=> ( ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3)) ) ),
inference(transitivity,[status(thm)],[227,222]) ).
tff(229,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf76(sk3))
| ~ ssItem(skaf74(sk3))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ~ ssList(skaf77(sk3))
| ( app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) != app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3)) ) ),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf76(sk3))
| ~ ssItem(skaf74(sk3))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ~ ssList(skaf77(sk3))
| ( app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) != app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3)) ) ),
inference(transitivity,[status(thm)],[229,221]) ).
tff(231,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| ~ ssList(skaf76(sk3))
| ~ ssItem(skaf74(sk3))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3))
| ~ ssList(skaf77(sk3))
| ( app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) != app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(232,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))))
| memberP(app(skaf76(sk3),cons(skaf74(sk3),skaf77(sk3))),skaf74(sk3)) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
$false,
inference(unit_resolution,[status(thm)],[232,220,45,78,36,167,210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC180-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 22:16:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 198.51/127.86 % SZS status Unsatisfiable
% 198.51/127.86 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------