TSTP Solution File: SWC409-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC409-1 : 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 11:57:47 EDT 2022
% Result : Unsatisfiable 42.09s 26.93s
% Output : Proof 42.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 116
% Syntax : Number of formulae : 263 ( 65 unt; 15 typ; 0 def)
% Number of atoms : 1965 ( 295 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 2993 (1404 ~;1422 |; 0 &)
% ( 167 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 128 ( 128 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 9 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 533 ( 479 !; 0 ?; 533 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(tl_type,type,
tl: $i > $i ).
tff(sk4_type,type,
sk4: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(hd_type,type,
hd: $i > $i ).
tff(skaf43_type,type,
skaf43: ( $i * $i ) > $i ).
tff(skaf42_type,type,
skaf42: ( $i * $i ) > $i ).
tff(sk2_type,type,
sk2: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ( sk4 = nil )
<=> ( nil = sk4 ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( memberP(sk2,sk5)
<=> memberP(sk4,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( memberP(sk2,sk5)
<=> memberP(sk2,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
memberP(sk2,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(5,plain,
memberP(sk2,sk5),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
memberP(sk4,sk5),
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(9,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
tff(13,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,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(19,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)],[18]) ).
tff(20,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(21,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)],[20,19]) ).
tff(22,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)],[21,17]) ).
tff(23,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)],[22]) ).
tff(24,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)],[23,16]) ).
tff(25,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4,
inference(unit_resolution,[status(thm)],[27,24,14,9,6]) ).
tff(29,plain,
( ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = nil )
<=> ( sk4 = nil ) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = nil )
<=> ( nil = sk4 ) ),
inference(transitivity,[status(thm)],[29,1]) ).
tff(31,plain,
( ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil )
<=> ( nil != sk4 ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf42(U,V))
<=> ssList(skaf42(U,V)) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause53) ).
tff(36,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf42(U,V))
| ssList(skaf42(sk4,sk5)) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
ssList(skaf42(sk4,sk5)),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf43(U,V))
<=> ssList(skaf43(U,V)) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause52) ).
tff(45,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf43(U,V))
| ssList(skaf43(sk5,sk4)) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
ssList(skaf43(sk5,sk4)),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
^ [U: $i] :
rewrite(
( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(56,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ memberP(nil,sk5),
inference(unit_resolution,[status(thm)],[62,59,9]) ).
tff(64,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause175) ).
tff(70,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(76,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ( ~ ssList(nil)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil ) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil ) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil ) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil ) ),
inference(unit_resolution,[status(thm)],[82,76,73,9,63]) ).
tff(84,plain,
app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) != nil,
inference(unit_resolution,[status(thm)],[83,49,40]) ).
tff(85,plain,
nil != sk4,
inference(modus_ponens,[status(thm)],[84,31]) ).
tff(86,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(87,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)],[86]) ).
tff(88,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(89,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(90,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)],[89]) ).
tff(91,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
tff(92,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[94,87]) ).
tff(96,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
( ( nil = sk4 )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(unit_resolution,[status(thm)],[98,95,14]) ).
tff(100,plain,
cons(hd(sk4),tl(sk4)) = sk4,
inference(unit_resolution,[status(thm)],[99,85]) ).
tff(101,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
tff(107,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ( ~ ssList(sk4)
| ( nil = sk4 )
| ssList(tl(sk4)) )
<=> ( ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssList(tl(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssList(tl(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) ) ),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssList(tl(sk4)) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
ssList(tl(sk4)),
inference(unit_resolution,[status(thm)],[116,110,14,85]) ).
tff(118,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(124,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[126,119]) ).
tff(128,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(129,plain,
( ( ~ ssList(sk4)
| ( nil = sk4 )
| ssItem(hd(sk4)) )
<=> ( ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssItem(hd(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) ) ),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssItem(hd(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) ) ),
inference(transitivity,[status(thm)],[130,128]) ).
tff(132,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssItem(hd(sk4)) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
( ( nil = sk4 )
| ssItem(hd(sk4)) ),
inference(unit_resolution,[status(thm)],[133,127,14]) ).
tff(135,plain,
ssItem(hd(sk4)),
inference(unit_resolution,[status(thm)],[134,85]) ).
tff(136,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(137,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(140,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(142,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[142,138]) ).
tff(144,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[143]) ).
tff(145,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[144,137]) ).
tff(146,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)) ) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
( ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)) ) ),
inference(unit_resolution,[status(thm)],[148,145,135]) ).
tff(150,plain,
app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)),
inference(unit_resolution,[status(thm)],[149,117]) ).
tff(151,plain,
app(cons(hd(sk4),nil),tl(sk4)) = sk4,
inference(transitivity,[status(thm)],[150,100]) ).
tff(152,plain,
( memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5)
<=> memberP(sk4,sk5) ),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
( memberP(sk4,sk5)
<=> memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) ),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5),
inference(modus_ponens,[status(thm)],[6,153]) ).
tff(155,plain,
^ [B: $i,A: $i] :
refl(
( ( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
<=> ( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(156,plain,
( ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
<=> ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
<=> ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
^ [B: $i,A: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 ) )
<=> ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) )
<=> ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) ) )),
rewrite(
( ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) )
<=> ( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) )
<=> ( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(159,plain,
( ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) )
<=> ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) ),
inference(quant_intro,[status(thm)],[158]) ).
tff(160,axiom,
! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(161,plain,
! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[161,157]) ).
tff(163,plain,
! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ),
inference(skolemize,[status(sab)],[162]) ).
tff(164,plain,
! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[163,156]) ).
tff(165,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) != sk4 )
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 ) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) != sk4 )
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(166,plain,
( ~ ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) != sk4 )
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
( ~ ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) != sk4 )
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
app(tl(sk4),cons(hd(sk4),nil)) = sk3,
inference(unit_resolution,[status(thm)],[167,164,135,117,151]) ).
tff(169,plain,
( memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5)
<=> memberP(sk3,sk5) ),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( memberP(sk3,sk5)
<=> memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) ),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
( ~ memberP(sk3,sk5)
<=> ~ memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) ),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
( ~ memberP(sk1,sk5)
<=> ~ memberP(sk3,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
( ~ memberP(sk1,sk5)
<=> ~ memberP(sk1,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(174,axiom,
~ memberP(sk1,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(175,plain,
~ memberP(sk1,sk5),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
~ memberP(sk3,sk5),
inference(modus_ponens,[status(thm)],[175,172]) ).
tff(177,plain,
~ memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5),
inference(modus_ponens,[status(thm)],[176,171]) ).
tff(178,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(179,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)],[178]) ).
tff(180,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(181,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(182,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)],[181]) ).
tff(183,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(184,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[184,180]) ).
tff(186,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[185]) ).
tff(187,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[186,179]) ).
tff(188,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(189,plain,
( ( ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ssList(cons(hd(sk4),nil)) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(190,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ssList(cons(hd(sk4),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) ) ),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ssList(cons(hd(sk4),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) ) ),
inference(transitivity,[status(thm)],[190,188]) ).
tff(192,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ssList(cons(hd(sk4),nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(193,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
ssList(cons(hd(sk4),nil)),
inference(unit_resolution,[status(thm)],[193,76,187,135]) ).
tff(195,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
inference(bind,[status(th)],]) ).
tff(196,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(quant_intro,[status(thm)],[195]) ).
tff(197,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(198,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ memberP(U,V)
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ~ memberP(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(W)
| ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
inference(bind,[status(th)],]) ).
tff(199,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(quant_intro,[status(thm)],[198]) ).
tff(200,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause140) ).
tff(201,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[200,199]) ).
tff(202,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[201,197]) ).
tff(203,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(skolemize,[status(sab)],[202]) ).
tff(204,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[203,196]) ).
tff(205,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ memberP(tl(sk4),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ memberP(tl(sk4),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(206,plain,
( ( ~ ssList(tl(sk4))
| ~ ssItem(sk5)
| ~ ssList(cons(hd(sk4),nil))
| ~ memberP(tl(sk4),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) )
<=> ( ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ memberP(tl(sk4),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(207,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(tl(sk4))
| ~ ssItem(sk5)
| ~ ssList(cons(hd(sk4),nil))
| ~ memberP(tl(sk4),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ memberP(tl(sk4),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) ) ),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(tl(sk4))
| ~ ssItem(sk5)
| ~ ssList(cons(hd(sk4),nil))
| ~ memberP(tl(sk4),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ memberP(tl(sk4),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) ) ),
inference(transitivity,[status(thm)],[207,205]) ).
tff(209,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(tl(sk4))
| ~ ssItem(sk5)
| ~ ssList(cons(hd(sk4),nil))
| ~ memberP(tl(sk4),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(210,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ memberP(tl(sk4),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
( ~ memberP(tl(sk4),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) ),
inference(unit_resolution,[status(thm)],[210,204,9,117,194]) ).
tff(212,plain,
~ memberP(tl(sk4),sk5),
inference(unit_resolution,[status(thm)],[211,177]) ).
tff(213,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
inference(bind,[status(th)],]) ).
tff(214,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) ),
inference(quant_intro,[status(thm)],[213]) ).
tff(215,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(216,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ memberP(U,V)
| ~ ssList(W) ) )),
rewrite(
( ( ~ ssList(U)
| ~ memberP(U,V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
inference(bind,[status(th)],]) ).
tff(217,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) ),
inference(quant_intro,[status(thm)],[216]) ).
tff(218,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause141) ).
tff(219,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(modus_ponens,[status(thm)],[219,215]) ).
tff(221,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(skolemize,[status(sab)],[220]) ).
tff(222,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(modus_ponens,[status(thm)],[221,214]) ).
tff(223,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5)
| ~ memberP(cons(hd(sk4),nil),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5)
| ~ memberP(cons(hd(sk4),nil),sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(224,plain,
( ( ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ memberP(cons(hd(sk4),nil),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) )
<=> ( ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5)
| ~ memberP(cons(hd(sk4),nil),sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(225,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ memberP(cons(hd(sk4),nil),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5)
| ~ memberP(cons(hd(sk4),nil),sk5) ) ),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ memberP(cons(hd(sk4),nil),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5)
| ~ memberP(cons(hd(sk4),nil),sk5) ) ),
inference(transitivity,[status(thm)],[225,223]) ).
tff(227,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ memberP(cons(hd(sk4),nil),sk5)
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5)
| ~ memberP(cons(hd(sk4),nil),sk5) ),
inference(modus_ponens,[status(thm)],[227,226]) ).
tff(229,plain,
( memberP(app(tl(sk4),cons(hd(sk4),nil)),sk5)
| ~ memberP(cons(hd(sk4),nil),sk5) ),
inference(unit_resolution,[status(thm)],[228,222,9,117,194]) ).
tff(230,plain,
~ memberP(cons(hd(sk4),nil),sk5),
inference(unit_resolution,[status(thm)],[229,177]) ).
tff(231,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ) )),
inference(bind,[status(th)],]) ).
tff(232,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ) ),
inference(quant_intro,[status(thm)],[231]) ).
tff(233,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(234,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ memberP(app(U,V),W)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ memberP(app(U,V),W) ) )),
( ( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ~ memberP(app(U,V),W)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ~ memberP(app(U,V),W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ memberP(app(U,V),W) ) )),
( ( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ memberP(app(U,V),W) ) )),
( ( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ memberP(app(U,V),W)
| ~ ssItem(W) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ memberP(app(U,V),W)
| ~ ssItem(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(app(U,V),W) ) )),
( ( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(app(U,V),W) ) )),
( ( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(W)
| memberP(V,W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(app(U,V),W)
| memberP(V,W) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ memberP(app(U,V),W)
| memberP(V,W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ) )),
( ( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(W)
| memberP(V,W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ) )),
( ( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(W)
| memberP(V,W)
| memberP(U,W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(app(U,V),W)
| memberP(U,W) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(V,W)
| ~ memberP(app(U,V),W)
| memberP(U,W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ) )),
( ( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(W)
| memberP(V,W)
| memberP(U,W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ) )),
inference(bind,[status(th)],]) ).
tff(235,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(W)
| memberP(V,W)
| memberP(U,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ) ),
inference(quant_intro,[status(thm)],[234]) ).
tff(236,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(W)
| memberP(V,W)
| memberP(U,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause158) ).
tff(237,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ),
inference(modus_ponens,[status(thm)],[236,235]) ).
tff(238,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ),
inference(modus_ponens,[status(thm)],[237,233]) ).
tff(239,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ),
inference(skolemize,[status(sab)],[238]) ).
tff(240,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) ),
inference(modus_ponens,[status(thm)],[239,232]) ).
tff(241,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| memberP(tl(sk4),sk5)
| ~ ssList(cons(hd(sk4),nil))
| memberP(cons(hd(sk4),nil),sk5)
| ~ memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| memberP(tl(sk4),sk5)
| ~ ssList(cons(hd(sk4),nil))
| memberP(cons(hd(sk4),nil),sk5)
| ~ memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(242,plain,
( ( ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ~ ssItem(sk5)
| memberP(cons(hd(sk4),nil),sk5)
| memberP(tl(sk4),sk5)
| ~ memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) )
<=> ( ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| memberP(tl(sk4),sk5)
| ~ ssList(cons(hd(sk4),nil))
| memberP(cons(hd(sk4),nil),sk5)
| ~ memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(243,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) )
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ~ ssItem(sk5)
| memberP(cons(hd(sk4),nil),sk5)
| memberP(tl(sk4),sk5)
| ~ memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| memberP(tl(sk4),sk5)
| ~ ssList(cons(hd(sk4),nil))
| memberP(cons(hd(sk4),nil),sk5)
| ~ memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) ) ),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) )
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ~ ssItem(sk5)
| memberP(cons(hd(sk4),nil),sk5)
| memberP(tl(sk4),sk5)
| ~ memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| memberP(tl(sk4),sk5)
| ~ ssList(cons(hd(sk4),nil))
| memberP(cons(hd(sk4),nil),sk5)
| ~ memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) ) ),
inference(transitivity,[status(thm)],[243,241]) ).
tff(245,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) )
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ~ ssItem(sk5)
| memberP(cons(hd(sk4),nil),sk5)
| memberP(tl(sk4),sk5)
| ~ memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(246,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssItem(W)
| memberP(U,W)
| memberP(V,W)
| ~ memberP(app(U,V),W) )
| ~ ssItem(sk5)
| ~ ssList(tl(sk4))
| memberP(tl(sk4),sk5)
| ~ ssList(cons(hd(sk4),nil))
| memberP(cons(hd(sk4),nil),sk5)
| ~ memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) ),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
( memberP(tl(sk4),sk5)
| memberP(cons(hd(sk4),nil),sk5)
| ~ memberP(app(cons(hd(sk4),nil),tl(sk4)),sk5) ),
inference(unit_resolution,[status(thm)],[246,240,9,117,194]) ).
tff(248,plain,
$false,
inference(unit_resolution,[status(thm)],[247,230,212,154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : SWC409-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n026.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun Sep 4 01:00:54 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 42.09/26.93 % SZS status Unsatisfiable
% 42.09/26.93 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------