TSTP Solution File: SWC179-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC179-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 11:55:53 EDT 2022
% Result : Unsatisfiable 0.51s 0.60s
% Output : Proof 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 82
% Syntax : Number of formulae : 183 ( 54 unt; 15 typ; 0 def)
% Number of atoms : 1448 ( 259 equ)
% Maximal formula atoms : 35 ( 8 avg)
% Number of connectives : 2330 (1154 ~;1056 |; 0 &)
% ( 120 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 104 ( 104 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 11 >; 3 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 351 ( 317 !; 0 ?; 351 :)
% Comments :
%------------------------------------------------------------------------------
tff(strictorderedP_type,type,
strictorderedP: $i > $o ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(skaf77_type,type,
skaf77: $i > $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,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ~ duplicatefreeP(sk1)
<=> ~ duplicatefreeP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ~ duplicatefreeP(sk1)
<=> ~ duplicatefreeP(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
~ duplicatefreeP(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(5,plain,
~ duplicatefreeP(sk1),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
~ duplicatefreeP(sk3),
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(10,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,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(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(quant_intro,[status(thm)],[12]) ).
tff(14,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(15,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(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,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(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)],[17,16]) ).
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(modus_ponens,[status(thm)],[18,14]) ).
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(skolemize,[status(sab)],[19]) ).
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)],[20,13]) ).
tff(22,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(23,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(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(monotonicity,[status(thm)],[23]) ).
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 ) )
| duplicatefreeP(sk3)
| ~ ssList(sk3)
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3 ) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
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 ) )
| duplicatefreeP(sk3)
| ~ ssList(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,
app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = sk3,
inference(unit_resolution,[status(thm)],[27,21,11,6]) ).
tff(29,plain,
( ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = nil )
<=> ( sk3 = nil ) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) = nil )
<=> ( nil = sk3 ) ),
inference(transitivity,[status(thm)],[29,1]) ).
tff(31,plain,
( ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
^ [U: $i] :
refl(
( ssItem(skaf74(U))
<=> ssItem(skaf74(U)) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [U: $i] : ssItem(skaf74(U))
<=> ! [U: $i] : ssItem(skaf74(U)) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [U: $i] : ssItem(skaf74(U))
<=> ! [U: $i] : ssItem(skaf74(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [U: $i] : ssItem(skaf74(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause21) ).
tff(36,plain,
! [U: $i] : ssItem(skaf74(U)),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [U: $i] : ssItem(skaf74(U)),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [U: $i] : ssItem(skaf74(U)),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [U: $i] : ssItem(skaf74(U))
| ssItem(skaf74(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
ssItem(skaf74(sk3)),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
^ [U: $i] :
refl(
( ssList(skaf75(U))
<=> ssList(skaf75(U)) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [U: $i] : ssList(skaf75(U))
<=> ! [U: $i] : ssList(skaf75(U)) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [U: $i] : ssList(skaf75(U))
<=> ! [U: $i] : ssList(skaf75(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
! [U: $i] : ssList(skaf75(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause20) ).
tff(45,plain,
! [U: $i] : ssList(skaf75(U)),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [U: $i] : ssList(skaf75(U)),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [U: $i] : ssList(skaf75(U)),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [U: $i] : ssList(skaf75(U))
| ssList(skaf75(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
ssList(skaf75(sk3)),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
^ [U: $i] :
refl(
( ssList(skaf77(U))
<=> ssList(skaf77(U)) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [U: $i] : ssList(skaf77(U))
<=> ! [U: $i] : ssList(skaf77(U)) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [U: $i] : ssList(skaf77(U))
<=> ! [U: $i] : ssList(skaf77(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
! [U: $i] : ssList(skaf77(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause18) ).
tff(54,plain,
! [U: $i] : ssList(skaf77(U)),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [U: $i] : ssList(skaf77(U)),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [U: $i] : ssList(skaf77(U)),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [U: $i] : ssList(skaf77(U))
| ssList(skaf77(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
ssList(skaf77(sk3)),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
^ [U: $i] :
refl(
( ssList(skaf76(U))
<=> ssList(skaf76(U)) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [U: $i] : ssList(skaf76(U))
<=> ! [U: $i] : ssList(skaf76(U)) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [U: $i] : ssList(skaf76(U))
<=> ! [U: $i] : ssList(skaf76(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
! [U: $i] : ssList(skaf76(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause19) ).
tff(63,plain,
! [U: $i] : ssList(skaf76(U)),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [U: $i] : ssList(skaf76(U)),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [U: $i] : ssList(skaf76(U)),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ~ ! [U: $i] : ssList(skaf76(U))
| ssList(skaf76(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
ssList(skaf76(sk3)),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
( ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W) )
<=> ( ~ ssList(X)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(W) ) )),
rewrite(
( ( ~ ssList(X)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(W) )
<=> ( ~ ssList(X)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
( ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W) )
<=> ( ~ ssList(X)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
( ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
( ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
( ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
( ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
( ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ duplicatefreeP(Y) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ duplicatefreeP(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
( ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
( ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(Y) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
( ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(Y) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).
tff(74,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(80,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( duplicatefreeP(nil)
<=> duplicatefreeP(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(82,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause2) ).
tff(83,plain,
duplicatefreeP(nil),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil )
| ~ duplicatefreeP(nil) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil )
| ~ duplicatefreeP(nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ( ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ~ duplicatefreeP(nil)
| ~ ssList(skaf76(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil ) )
<=> ( ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil )
| ~ duplicatefreeP(nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) )
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ~ duplicatefreeP(nil)
| ~ ssList(skaf76(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil ) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil )
| ~ duplicatefreeP(nil) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) )
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ~ duplicatefreeP(nil)
| ~ ssList(skaf76(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil ) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil )
| ~ duplicatefreeP(nil) ) ),
inference(transitivity,[status(thm)],[86,84]) ).
tff(88,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) )
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ~ duplicatefreeP(nil)
| ~ ssList(skaf76(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(V,X)) != Y ) )
| ~ ssList(nil)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil )
| ~ duplicatefreeP(nil) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
( ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil ) ),
inference(unit_resolution,[status(thm)],[89,83,80,77]) ).
tff(91,plain,
app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != nil,
inference(unit_resolution,[status(thm)],[90,67,58,49,40]) ).
tff(92,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[91,31]) ).
tff(93,plain,
( ( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,axiom,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
tff(95,plain,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[95,93]) ).
tff(97,plain,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[96,93]) ).
tff(98,plain,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[98,93]) ).
tff(100,plain,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[99,93]) ).
tff(101,plain,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[101,93]) ).
tff(103,plain,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[102,93]) ).
tff(104,plain,
cons(sk5,nil) = sk3,
inference(unit_resolution,[status(thm)],[103,92]) ).
tff(105,plain,
( strictorderedP(cons(sk5,nil))
<=> strictorderedP(sk3) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( strictorderedP(sk3)
<=> strictorderedP(cons(sk5,nil)) ),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ~ strictorderedP(sk3)
<=> ~ strictorderedP(cons(sk5,nil)) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ lt(U,U) )
<=> ( ~ ssItem(U)
| ~ lt(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
^ [U: $i] :
rewrite(
( ( ~ lt(U,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ lt(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [U: $i] :
( ~ lt(U,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,axiom,
! [U: $i] :
( ~ lt(U,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause63) ).
tff(114,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[116,109]) ).
tff(118,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(119,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(skaf74(sk3))
| ~ lt(skaf74(sk3),skaf74(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(skaf74(sk3))
| ~ lt(skaf74(sk3),skaf74(sk3)) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
~ lt(skaf74(sk3),skaf74(sk3)),
inference(unit_resolution,[status(thm)],[120,117,40]) ).
tff(122,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(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)],[122]) ).
tff(124,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,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(126,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)],[125]) ).
tff(127,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(128,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ),
inference(modus_ponens,[status(thm)],[130,123]) ).
tff(132,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssList(sk3)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != sk3 )
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(sk3) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssList(sk3)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != sk3 )
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ( ~ ssItem(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(sk3)
| ~ ssItem(skaf74(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(sk3)
| ~ ssList(skaf76(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != sk3 ) )
<=> ( ~ ssList(sk3)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != sk3 )
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(sk3)
| ~ ssItem(skaf74(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(sk3)
| ~ ssList(skaf76(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != sk3 ) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssList(sk3)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != sk3 )
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(sk3) ) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(sk3)
| ~ ssItem(skaf74(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(sk3)
| ~ ssList(skaf76(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != sk3 ) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssList(sk3)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != sk3 )
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(sk3) ) ),
inference(transitivity,[status(thm)],[134,132]) ).
tff(136,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf75(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(sk3)
| ~ ssItem(skaf74(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(sk3)
| ~ ssList(skaf76(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssList(sk3)
| ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| ( app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) != sk3 )
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(sk3) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ ssItem(skaf74(sk3))
| ~ ssList(skaf76(sk3))
| ~ ssList(skaf77(sk3))
| ~ ssList(skaf75(sk3))
| lt(skaf74(sk3),skaf74(sk3))
| ~ strictorderedP(sk3) ),
inference(unit_resolution,[status(thm)],[137,131,11,28]) ).
tff(139,plain,
~ strictorderedP(sk3),
inference(unit_resolution,[status(thm)],[138,121,67,58,49,40]) ).
tff(140,plain,
~ strictorderedP(cons(sk5,nil)),
inference(modus_ponens,[status(thm)],[139,107]) ).
tff(141,plain,
( ( ssItem(sk5)
| ( nil = sk3 ) )
<=> ( ssItem(sk5)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,axiom,
( ssItem(sk5)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(143,plain,
( ssItem(sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[143,92]) ).
tff(145,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) )),
inference(bind,[status(th)],]) ).
tff(146,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( nil != U )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U ) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) )),
rewrite(
( ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) )),
inference(bind,[status(th)],]) ).
tff(149,plain,
( ! [V: $i,U: $i] :
( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,axiom,
! [V: $i,U: $i] :
( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause112) ).
tff(151,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ),
inference(skolemize,[status(sab)],[152]) ).
tff(154,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ),
inference(modus_ponens,[status(thm)],[153,146]) ).
tff(155,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( ( ~ ssList(nil)
| $false
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ( nil = nil )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
( ( nil != nil )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
( ( nil != nil )
<=> $false ),
inference(transitivity,[status(thm)],[159,157]) ).
tff(161,plain,
( ( ~ ssList(nil)
| ( nil != nil )
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) )
<=> ( ~ ssList(nil)
| $false
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ssList(nil)
| ( nil != nil )
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) ) ),
inference(transitivity,[status(thm)],[161,156]) ).
tff(163,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ( nil != nil )
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) ) ),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ( nil != nil )
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) ) ),
inference(transitivity,[status(thm)],[163,155]) ).
tff(165,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ( nil != nil )
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| strictorderedP(cons(sk5,nil)) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
strictorderedP(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[166,80,154,144]) ).
tff(168,plain,
$false,
inference(unit_resolution,[status(thm)],[167,140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC179-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n026.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 22:30:39 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.
% 0.51/0.60 % SZS status Unsatisfiable
% 0.51/0.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------