TSTP Solution File: SWC198-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC198-1 : 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 11:56:03 EDT 2022
% Result : Unsatisfiable 36.26s 23.57s
% Output : Proof 36.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 126
% Syntax : Number of formulae : 292 ( 75 unt; 15 typ; 0 def)
% Number of atoms : 1795 ( 455 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 2656 (1242 ~;1259 |; 0 &)
% ( 155 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 104 ( 104 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 10 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 478 ( 432 !; 0 ?; 478 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk5_type,type,
sk5: $i > $i ).
tff(hd_type,type,
hd: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(skac3_type,type,
skac3: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(skaf43_type,type,
skaf43: ( $i * $i ) > $i ).
tff(skaf42_type,type,
skaf42: ( $i * $i ) > $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(tl_type,type,
tl: $i > $i ).
tff(1,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
^ [A: $i] :
refl(
( ( ~ ssItem(A)
| ssItem(sk5(A)) )
<=> ( ~ ssItem(A)
| ssItem(sk5(A)) ) )),
inference(bind,[status(th)],]) ).
tff(3,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ) ),
inference(quant_intro,[status(thm)],[2]) ).
tff(4,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(6,plain,
! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ),
inference(skolemize,[status(sab)],[6]) ).
tff(8,plain,
! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
( ssItem(skac3)
<=> ssItem(skac3) ),
inference(rewrite,[status(thm)],]) ).
tff(10,axiom,
ssItem(skac3),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause9) ).
tff(11,plain,
ssItem(skac3),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(skac3)
| ssItem(sk5(skac3)) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(skac3)
| ssItem(sk5(skac3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(skac3)
| ssItem(sk5(skac3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(14,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(skac3)
| ssItem(sk5(skac3)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
ssItem(sk5(skac3)),
inference(unit_resolution,[status(thm)],[14,11,8]) ).
tff(16,plain,
^ [A: $i] :
refl(
( ( ~ ssItem(A)
| memberP(sk3,sk5(A)) )
<=> ( ~ ssItem(A)
| memberP(sk3,sk5(A)) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [A: $i] :
rewrite(
( ( ~ ssItem(A)
| memberP(sk1,sk5(A)) )
<=> ( ~ ssItem(A)
| memberP(sk3,sk5(A)) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) )
<=> ! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(22,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk1,sk5(A)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) ),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) )
| ~ ssItem(skac3)
| memberP(sk3,sk5(skac3)) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) )
| ~ ssItem(skac3)
| memberP(sk3,sk5(skac3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) )
| ~ ssItem(skac3)
| memberP(sk3,sk5(skac3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) )
| ~ ssItem(skac3)
| memberP(sk3,sk5(skac3)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
memberP(sk3,sk5(skac3)),
inference(unit_resolution,[status(thm)],[28,11,25]) ).
tff(30,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(33,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[33,30]) ).
tff(35,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause169) ).
tff(41,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk3)
| ~ ssItem(sk5(skac3))
| ~ memberP(sk3,sk5(skac3))
| ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) = sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk3)
| ~ ssItem(sk5(skac3))
| ~ memberP(sk3,sk5(skac3))
| ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk3)
| ~ ssItem(sk5(skac3))
| ~ memberP(sk3,sk5(skac3))
| ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk3)
| ~ ssItem(sk5(skac3))
| ~ memberP(sk3,sk5(skac3))
| ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) = sk3 ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) = sk3,
inference(unit_resolution,[status(thm)],[47,44,34,29,15]) ).
tff(49,plain,
( ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) = nil )
<=> ( sk3 = nil ) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) = nil )
<=> ( nil = sk3 ) ),
inference(transitivity,[status(thm)],[49,1]) ).
tff(51,plain,
( ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) != nil )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf43(U,V))
<=> ssList(skaf43(U,V)) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause52) ).
tff(56,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf43(U,V))
| ssList(skaf43(sk5(skac3),sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
ssList(skaf43(sk5(skac3),sk3)),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,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(62,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)],[61]) ).
tff(63,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(64,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(65,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)],[64]) ).
tff(66,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(67,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5(skac3))
| ~ ssList(skaf43(sk5(skac3),sk3))
| ssList(cons(sk5(skac3),skaf43(sk5(skac3),sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5(skac3))
| ~ ssList(skaf43(sk5(skac3),sk3))
| ssList(cons(sk5(skac3),skaf43(sk5(skac3),sk3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5(skac3))
| ~ ssList(skaf43(sk5(skac3),sk3))
| ssList(cons(sk5(skac3),skaf43(sk5(skac3),sk3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5(skac3))
| ~ ssList(skaf43(sk5(skac3),sk3))
| ssList(cons(sk5(skac3),skaf43(sk5(skac3),sk3))) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ ssList(skaf43(sk5(skac3),sk3))
| ssList(cons(sk5(skac3),skaf43(sk5(skac3),sk3))) ),
inference(unit_resolution,[status(thm)],[73,70,15]) ).
tff(75,plain,
ssList(cons(sk5(skac3),skaf43(sk5(skac3),sk3))),
inference(unit_resolution,[status(thm)],[74,60]) ).
tff(76,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf42(U,V))
<=> ssList(skaf42(U,V)) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause53) ).
tff(80,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf42(U,V))
| ssList(skaf42(sk3,sk5(skac3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
ssList(skaf42(sk3,sk5(skac3))),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
( ( cons(sk5(skac3),skaf43(sk5(skac3),sk3)) = nil )
<=> ( nil = cons(sk5(skac3),skaf43(sk5(skac3),sk3)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(86,plain,
( ( cons(sk5(skac3),skaf43(sk5(skac3),sk3)) != nil )
<=> ( nil != cons(sk5(skac3),skaf43(sk5(skac3),sk3)) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ( cons(U,V) != nil )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != nil ) ) )),
( ( ( cons(U,V) != nil )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != nil )
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssItem(U)
| ( cons(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) )),
( ( ( cons(U,V) != nil )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [V: $i,U: $i] :
( ( cons(U,V) != nil )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != nil )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
tff(93,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[95,88]) ).
tff(97,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(sk5(skac3))
| ~ ssList(skaf43(sk5(skac3),sk3))
| ( cons(sk5(skac3),skaf43(sk5(skac3),sk3)) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(sk5(skac3))
| ~ ssList(skaf43(sk5(skac3),sk3))
| ( cons(sk5(skac3),skaf43(sk5(skac3),sk3)) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(sk5(skac3))
| ~ ssList(skaf43(sk5(skac3),sk3))
| ( cons(sk5(skac3),skaf43(sk5(skac3),sk3)) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != nil ) )
| ~ ssItem(sk5(skac3))
| ~ ssList(skaf43(sk5(skac3),sk3))
| ( cons(sk5(skac3),skaf43(sk5(skac3),sk3)) != nil ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ~ ssList(skaf43(sk5(skac3),sk3))
| ( cons(sk5(skac3),skaf43(sk5(skac3),sk3)) != nil ) ),
inference(unit_resolution,[status(thm)],[99,96,15]) ).
tff(101,plain,
cons(sk5(skac3),skaf43(sk5(skac3),sk3)) != nil,
inference(unit_resolution,[status(thm)],[100,60]) ).
tff(102,plain,
nil != cons(sk5(skac3),skaf43(sk5(skac3),sk3)),
inference(modus_ponens,[status(thm)],[101,86]) ).
tff(103,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
tff(109,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[111,104]) ).
tff(113,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf42(sk3,sk5(skac3)))
| ~ ssList(cons(sk5(skac3),skaf43(sk5(skac3),sk3)))
| ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) != nil )
| ( nil = cons(sk5(skac3),skaf43(sk5(skac3),sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf42(sk3,sk5(skac3)))
| ~ ssList(cons(sk5(skac3),skaf43(sk5(skac3),sk3)))
| ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) != nil )
| ( nil = cons(sk5(skac3),skaf43(sk5(skac3),sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf42(sk3,sk5(skac3)))
| ~ ssList(cons(sk5(skac3),skaf43(sk5(skac3),sk3)))
| ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) != nil )
| ( nil = cons(sk5(skac3),skaf43(sk5(skac3),sk3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(skaf42(sk3,sk5(skac3)))
| ~ ssList(cons(sk5(skac3),skaf43(sk5(skac3),sk3)))
| ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) != nil )
| ( nil = cons(sk5(skac3),skaf43(sk5(skac3),sk3)) ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ ssList(skaf42(sk3,sk5(skac3)))
| ~ ssList(cons(sk5(skac3),skaf43(sk5(skac3),sk3)))
| ( app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) != nil )
| ( nil = cons(sk5(skac3),skaf43(sk5(skac3),sk3)) ) ),
inference(unit_resolution,[status(thm)],[115,112]) ).
tff(117,plain,
app(skaf42(sk3,sk5(skac3)),cons(sk5(skac3),skaf43(sk5(skac3),sk3))) != nil,
inference(unit_resolution,[status(thm)],[116,102,84,75]) ).
tff(118,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[117,51]) ).
tff(119,plain,
( ( ( nil = sk3 )
| ( cons(sk6,nil) = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk6,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk6,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,axiom,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(122,plain,
( ( nil = sk3 )
| ( cons(sk6,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( ( nil = sk3 )
| ( cons(sk6,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[122,119]) ).
tff(124,plain,
cons(sk6,nil) = sk3,
inference(unit_resolution,[status(thm)],[123,118]) ).
tff(125,plain,
( memberP(cons(sk6,nil),sk5(skac3))
<=> memberP(sk3,sk5(skac3)) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( memberP(sk3,sk5(skac3))
<=> memberP(cons(sk6,nil),sk5(skac3)) ),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
memberP(cons(sk6,nil),sk5(skac3)),
inference(modus_ponens,[status(thm)],[29,126]) ).
tff(128,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(129,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
^ [U: $i] :
rewrite(
( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(134,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[136,129]) ).
tff(138,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skac3))
| ~ memberP(nil,sk5(skac3)) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skac3))
| ~ memberP(nil,sk5(skac3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skac3))
| ~ memberP(nil,sk5(skac3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skac3))
| ~ memberP(nil,sk5(skac3)) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
~ memberP(nil,sk5(skac3)),
inference(unit_resolution,[status(thm)],[140,137,15]) ).
tff(142,plain,
( ( ssItem(sk6)
| ( nil = sk3 ) )
<=> ( ssItem(sk6)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,axiom,
( ssItem(sk6)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(144,plain,
( ssItem(sk6)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
ssItem(sk6),
inference(unit_resolution,[status(thm)],[144,118]) ).
tff(146,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) )),
inference(bind,[status(th)],]) ).
tff(147,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U) )
<=> ( ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(U) ) )),
rewrite(
( ( ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(W) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W)
| ~ ssItem(W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W)
| memberP(V,W) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(cons(U,V),W)
| memberP(V,W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W)
| ( W = U ) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(cons(U,V),W)
| ( W = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) )),
( ( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) )),
inference(bind,[status(th)],]) ).
tff(150,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause161) ).
tff(152,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(modus_ponens,[status(thm)],[152,148]) ).
tff(154,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(skolemize,[status(sab)],[153]) ).
tff(155,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) ),
inference(modus_ponens,[status(thm)],[154,147]) ).
tff(156,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(157,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(158,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(sk5(skac3))
| memberP(nil,sk5(skac3))
| ~ ssItem(sk6)
| ( sk5(skac3) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(skac3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(sk5(skac3))
| memberP(nil,sk5(skac3))
| ~ ssItem(sk6)
| ( sk5(skac3) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(skac3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,plain,
( ( ~ ssItem(sk6)
| ~ ssList(nil)
| ~ ssItem(sk5(skac3))
| memberP(nil,sk5(skac3))
| ( sk5(skac3) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(skac3)) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk5(skac3))
| memberP(nil,sk5(skac3))
| ~ ssItem(sk6)
| ( sk5(skac3) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(skac3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ ssItem(sk5(skac3))
| memberP(nil,sk5(skac3))
| ( sk5(skac3) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(skac3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(sk5(skac3))
| memberP(nil,sk5(skac3))
| ~ ssItem(sk6)
| ( sk5(skac3) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(skac3)) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ ssItem(sk5(skac3))
| memberP(nil,sk5(skac3))
| ( sk5(skac3) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(skac3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(sk5(skac3))
| memberP(nil,sk5(skac3))
| ~ ssItem(sk6)
| ( sk5(skac3) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(skac3)) ) ),
inference(transitivity,[status(thm)],[161,159]) ).
tff(163,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ ssItem(sk5(skac3))
| memberP(nil,sk5(skac3))
| ( sk5(skac3) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(skac3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(sk5(skac3))
| memberP(nil,sk5(skac3))
| ~ ssItem(sk6)
| ( sk5(skac3) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(skac3)) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
( ( sk5(skac3) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(skac3)) ),
inference(unit_resolution,[status(thm)],[164,158,155,145,15,141]) ).
tff(166,plain,
sk5(skac3) = sk6,
inference(unit_resolution,[status(thm)],[165,127]) ).
tff(167,plain,
sk6 = sk5(skac3),
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],]) ).
tff(169,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[168]) ).
tff(170,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(171,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],]) ).
tff(172,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[171]) ).
tff(173,axiom,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
tff(174,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[174,170]) ).
tff(176,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(skolemize,[status(sab)],[175]) ).
tff(177,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[176,169]) ).
tff(178,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(180,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(transitivity,[status(thm)],[180,178]) ).
tff(182,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
ssList(tl(sk3)),
inference(unit_resolution,[status(thm)],[183,177,34,118]) ).
tff(185,plain,
sk3 = cons(sk6,nil),
inference(symmetry,[status(thm)],[124]) ).
tff(186,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(187,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[186]) ).
tff(188,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(189,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(190,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[189]) ).
tff(191,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
tff(192,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[191,190]) ).
tff(193,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[192,188]) ).
tff(194,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(skolemize,[status(sab)],[193]) ).
tff(195,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[194,187]) ).
tff(196,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(197,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(198,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
( ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(unit_resolution,[status(thm)],[198,195,34]) ).
tff(200,plain,
cons(hd(sk3),tl(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[199,118]) ).
tff(201,plain,
cons(hd(sk3),tl(sk3)) = cons(sk6,nil),
inference(transitivity,[status(thm)],[200,185]) ).
tff(202,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],]) ).
tff(203,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[202]) ).
tff(204,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(205,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],]) ).
tff(206,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[205]) ).
tff(207,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(208,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[208,204]) ).
tff(210,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(skolemize,[status(sab)],[209]) ).
tff(211,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[210,203]) ).
tff(212,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(213,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(214,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(transitivity,[status(thm)],[214,212]) ).
tff(216,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(217,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
( ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(unit_resolution,[status(thm)],[217,211,34]) ).
tff(219,plain,
ssItem(hd(sk3)),
inference(unit_resolution,[status(thm)],[218,118]) ).
tff(220,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(221,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[220]) ).
tff(222,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(223,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W) )
<=> ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssItem(U) ) )),
rewrite(
( ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(X) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( U = W ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( U = W ) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( U = W ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( U = W ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(224,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( U = W ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[223]) ).
tff(225,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( U = W ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause170) ).
tff(226,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[225,224]) ).
tff(227,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[226,222]) ).
tff(228,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(skolemize,[status(sab)],[227]) ).
tff(229,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[228,221]) ).
tff(230,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) )
| ( hd(sk3) = sk6 ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) )
| ( hd(sk3) = sk6 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(231,plain,
( ( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) )
| ( hd(sk3) = sk6 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(232,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) )
| ( hd(sk3) = sk6 ) ) ),
inference(monotonicity,[status(thm)],[231]) ).
tff(233,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) )
| ( hd(sk3) = sk6 ) ) ),
inference(transitivity,[status(thm)],[232,230]) ).
tff(234,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( hd(sk3) = sk6 )
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(235,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssItem(sk6)
| ( cons(hd(sk3),tl(sk3)) != cons(sk6,nil) )
| ( hd(sk3) = sk6 ) ),
inference(modus_ponens,[status(thm)],[234,233]) ).
tff(236,plain,
( ~ ssList(tl(sk3))
| ( hd(sk3) = sk6 ) ),
inference(unit_resolution,[status(thm)],[235,158,229,145,219,201]) ).
tff(237,plain,
hd(sk3) = sk6,
inference(unit_resolution,[status(thm)],[236,184]) ).
tff(238,plain,
hd(sk3) = sk5(skac3),
inference(transitivity,[status(thm)],[237,167]) ).
tff(239,plain,
sk5(hd(sk3)) = sk5(sk5(skac3)),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
sk5(sk5(skac3)) = sk5(hd(sk3)),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
( memberP(cons(sk6,nil),sk5(sk5(skac3)))
<=> memberP(sk3,sk5(sk5(skac3))) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(242,plain,
( memberP(sk3,sk5(sk5(skac3)))
<=> memberP(cons(sk6,nil),sk5(sk5(skac3))) ),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) )
| ~ ssItem(sk5(skac3))
| memberP(sk3,sk5(sk5(skac3))) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) )
| ~ ssItem(sk5(skac3))
| memberP(sk3,sk5(sk5(skac3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(244,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) )
| ~ ssItem(sk5(skac3))
| memberP(sk3,sk5(sk5(skac3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(245,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| memberP(sk3,sk5(A)) )
| ~ ssItem(sk5(skac3))
| memberP(sk3,sk5(sk5(skac3))) ),
inference(modus_ponens,[status(thm)],[244,243]) ).
tff(246,plain,
memberP(sk3,sk5(sk5(skac3))),
inference(unit_resolution,[status(thm)],[245,25,15]) ).
tff(247,plain,
memberP(cons(sk6,nil),sk5(sk5(skac3))),
inference(modus_ponens,[status(thm)],[246,242]) ).
tff(248,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(sk5(skac3))
| ssItem(sk5(sk5(skac3))) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(sk5(skac3))
| ssItem(sk5(sk5(skac3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(249,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(sk5(skac3))
| ssItem(sk5(sk5(skac3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(250,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ssItem(sk5(A)) )
| ~ ssItem(sk5(skac3))
| ssItem(sk5(sk5(skac3))) ),
inference(modus_ponens,[status(thm)],[249,248]) ).
tff(251,plain,
ssItem(sk5(sk5(skac3))),
inference(unit_resolution,[status(thm)],[250,8,15]) ).
tff(252,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(sk5(skac3)))
| ~ memberP(nil,sk5(sk5(skac3))) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(sk5(skac3)))
| ~ memberP(nil,sk5(sk5(skac3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(253,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(sk5(skac3)))
| ~ memberP(nil,sk5(sk5(skac3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(254,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(sk5(skac3)))
| ~ memberP(nil,sk5(sk5(skac3))) ),
inference(modus_ponens,[status(thm)],[253,252]) ).
tff(255,plain,
~ memberP(nil,sk5(sk5(skac3))),
inference(unit_resolution,[status(thm)],[254,137,251]) ).
tff(256,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(sk5(sk5(skac3)))
| memberP(nil,sk5(sk5(skac3)))
| ~ ssItem(sk6)
| ( sk5(sk5(skac3)) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(sk5(skac3))) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(sk5(sk5(skac3)))
| memberP(nil,sk5(sk5(skac3)))
| ~ ssItem(sk6)
| ( sk5(sk5(skac3)) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(sk5(skac3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(257,plain,
( ( ~ ssItem(sk6)
| ~ ssList(nil)
| ~ ssItem(sk5(sk5(skac3)))
| memberP(nil,sk5(sk5(skac3)))
| ( sk5(sk5(skac3)) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(sk5(skac3))) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk5(sk5(skac3)))
| memberP(nil,sk5(sk5(skac3)))
| ~ ssItem(sk6)
| ( sk5(sk5(skac3)) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(sk5(skac3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(258,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ ssItem(sk5(sk5(skac3)))
| memberP(nil,sk5(sk5(skac3)))
| ( sk5(sk5(skac3)) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(sk5(skac3))) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(sk5(sk5(skac3)))
| memberP(nil,sk5(sk5(skac3)))
| ~ ssItem(sk6)
| ( sk5(sk5(skac3)) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(sk5(skac3))) ) ),
inference(monotonicity,[status(thm)],[257]) ).
tff(259,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ ssItem(sk5(sk5(skac3)))
| memberP(nil,sk5(sk5(skac3)))
| ( sk5(sk5(skac3)) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(sk5(skac3))) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(sk5(sk5(skac3)))
| memberP(nil,sk5(sk5(skac3)))
| ~ ssItem(sk6)
| ( sk5(sk5(skac3)) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(sk5(skac3))) ) ),
inference(transitivity,[status(thm)],[258,256]) ).
tff(260,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ ssItem(sk5(sk5(skac3)))
| memberP(nil,sk5(sk5(skac3)))
| ( sk5(sk5(skac3)) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(sk5(skac3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(261,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U )
| ~ memberP(cons(U,V),W) )
| ~ ssList(nil)
| ~ ssItem(sk5(sk5(skac3)))
| memberP(nil,sk5(sk5(skac3)))
| ~ ssItem(sk6)
| ( sk5(sk5(skac3)) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(sk5(skac3))) ),
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
( ( sk5(sk5(skac3)) = sk6 )
| ~ memberP(cons(sk6,nil),sk5(sk5(skac3))) ),
inference(unit_resolution,[status(thm)],[261,158,155,145,251,255]) ).
tff(263,plain,
sk5(sk5(skac3)) = sk6,
inference(unit_resolution,[status(thm)],[262,247]) ).
tff(264,plain,
sk6 = sk5(sk5(skac3)),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
hd(sk3) = sk5(hd(sk3)),
inference(transitivity,[status(thm)],[237,264,240]) ).
tff(266,plain,
^ [A: $i] :
refl(
( ( ~ ssItem(A)
| ( A != sk5(A) ) )
<=> ( ~ ssItem(A)
| ( A != sk5(A) ) ) )),
inference(bind,[status(th)],]) ).
tff(267,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ) ),
inference(quant_intro,[status(thm)],[266]) ).
tff(268,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(269,axiom,
! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(270,plain,
! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ),
inference(modus_ponens,[status(thm)],[269,268]) ).
tff(271,plain,
! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ),
inference(skolemize,[status(sab)],[270]) ).
tff(272,plain,
! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) ),
inference(modus_ponens,[status(thm)],[271,267]) ).
tff(273,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
| ~ ssItem(hd(sk3))
| ( hd(sk3) != sk5(hd(sk3)) ) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
| ~ ssItem(hd(sk3))
| ( hd(sk3) != sk5(hd(sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(274,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
| ~ ssItem(hd(sk3))
| ( hd(sk3) != sk5(hd(sk3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(275,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ( A != sk5(A) ) )
| ~ ssItem(hd(sk3))
| ( hd(sk3) != sk5(hd(sk3)) ) ),
inference(modus_ponens,[status(thm)],[274,273]) ).
tff(276,plain,
hd(sk3) != sk5(hd(sk3)),
inference(unit_resolution,[status(thm)],[275,272,219]) ).
tff(277,plain,
$false,
inference(unit_resolution,[status(thm)],[276,265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC198-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 22:45:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 36.26/23.57 % SZS status Unsatisfiable
% 36.26/23.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------