TSTP Solution File: SWC403-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC403-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 11:57:43 EDT 2022
% Result : Unsatisfiable 0.19s 0.54s
% Output : Proof 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 114
% Syntax : Number of formulae : 257 ( 80 unt; 16 typ; 0 def)
% Number of atoms : 1638 ( 228 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 2535 (1229 ~;1162 |; 0 &)
% ( 144 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 91 ( 91 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 10 >; 8 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 535 ( 490 !; 0 ?; 535 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssList_type,type,
ssList: $i > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(skaf42_type,type,
skaf42: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(skaf47_type,type,
skaf47: ( $i * $i ) > $i ).
tff(sk4_type,type,
sk4: $i ).
tff(nil_type,type,
nil: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(skaf43_type,type,
skaf43: ( $i * $i ) > $i ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(skaf48_type,type,
skaf48: ( $i * $i ) > $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(1,plain,
( memberP(sk1,sk5)
<=> memberP(sk3,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( memberP(sk1,sk5)
<=> memberP(sk1,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
memberP(sk1,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(4,plain,
memberP(sk1,sk5),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
memberP(sk3,sk5),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(8,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(12,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,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(15,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)],[14]) ).
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(rewrite,[status(thm)],]) ).
tff(17,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(18,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)],[17]) ).
tff(19,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/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
tff(20,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)],[19,18]) ).
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)],[20,16]) ).
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(skolemize,[status(sab)],[21]) ).
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(modus_ponens,[status(thm)],[22,15]) ).
tff(24,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)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,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)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
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(sk3)
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ),
inference(quant_inst,[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(sk3)
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3,
inference(unit_resolution,[status(thm)],[26,23,13,8,5]) ).
tff(28,plain,
sk3 = app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
app(skaf47(sk4,sk3),sk3) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf47(U,V))
<=> ssList(skaf47(U,V)) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [V: $i,U: $i] : ssList(skaf47(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf47(U,V)) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [V: $i,U: $i] : ssList(skaf47(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf47(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause49) ).
tff(34,plain,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf47(U,V))
| ssList(skaf47(sk4,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
ssList(skaf47(sk4,sk3)),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(43,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(skaf47(sk4,sk3))
| ( app(nil,skaf47(sk4,sk3)) = skaf47(sk4,sk3) ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(skaf47(sk4,sk3))
| ( app(nil,skaf47(sk4,sk3)) = skaf47(sk4,sk3) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(skaf47(sk4,sk3))
| ( app(nil,skaf47(sk4,sk3)) = skaf47(sk4,sk3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(skaf47(sk4,sk3))
| ( app(nil,skaf47(sk4,sk3)) = skaf47(sk4,sk3) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
app(nil,skaf47(sk4,sk3)) = skaf47(sk4,sk3),
inference(unit_resolution,[status(thm)],[48,45,38]) ).
tff(50,plain,
app(app(nil,skaf47(sk4,sk3)),sk3) = app(skaf47(sk4,sk3),sk3),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(57,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(63,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(nil)
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(nil)
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(nil)
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ) ),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(nil)
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)),
inference(unit_resolution,[status(thm)],[69,63,60,13,38]) ).
tff(71,plain,
app(nil,app(skaf47(sk4,sk3),sk3)) = app(app(nil,skaf47(sk4,sk3)),sk3),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) = app(skaf47(sk4,sk3),sk3),
inference(symmetry,[status(thm)],[29]) ).
tff(73,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf42(U,V))
<=> ssList(skaf42(U,V)) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).
tff(77,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf42(U,V))
| ssList(skaf42(sk3,sk5)) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
ssList(skaf42(sk3,sk5)),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf43(U,V))
<=> ssList(skaf43(U,V)) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).
tff(86,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf43(U,V))
| ssList(skaf43(sk5,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
ssList(skaf43(sk5,sk3)),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,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(92,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)],[91]) ).
tff(93,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(94,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(95,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)],[94]) ).
tff(96,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(97,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[99,92]) ).
tff(101,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
( ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ),
inference(unit_resolution,[status(thm)],[103,100,8]) ).
tff(105,plain,
ssList(cons(sk5,skaf43(sk5,sk3))),
inference(unit_resolution,[status(thm)],[104,90]) ).
tff(106,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ( ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ssList(skaf47(sk4,sk3))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(transitivity,[status(thm)],[108,106]) ).
tff(110,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
( ~ ssList(skaf47(sk4,sk3))
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(unit_resolution,[status(thm)],[111,60]) ).
tff(113,plain,
app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),
inference(unit_resolution,[status(thm)],[112,105,81,38]) ).
tff(114,plain,
app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),sk3),
inference(transitivity,[status(thm)],[113,72]) ).
tff(115,plain,
app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) = app(nil,app(skaf47(sk4,sk3),sk3)),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],]) ).
tff(117,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(122,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ( ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ssList(skaf47(sk4,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) ) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) ) ),
inference(transitivity,[status(thm)],[128,126]) ).
tff(130,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(skaf47(sk4,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))),
inference(unit_resolution,[status(thm)],[131,125,38,81]) ).
tff(133,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(nil)
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(nil)
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(nil)
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(transitivity,[status(thm)],[135,133]) ).
tff(137,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(nil)
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
( ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(unit_resolution,[status(thm)],[138,63,60,105]) ).
tff(140,plain,
app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))),
inference(unit_resolution,[status(thm)],[139,132]) ).
tff(141,plain,
app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),
inference(transitivity,[status(thm)],[140,115,71,50,29]) ).
tff(142,plain,
( memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5)
<=> memberP(app(skaf47(sk4,sk3),sk3),sk5) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(143,plain,
( memberP(app(skaf47(sk4,sk3),sk3),sk5)
<=> memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5) ),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
<=> ~ memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,plain,
( ( ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(transitivity,[status(thm)],[147,145]) ).
tff(149,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
( ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ),
inference(unit_resolution,[status(thm)],[150,125,13]) ).
tff(152,plain,
ssList(app(skaf47(sk4,sk3),sk3)),
inference(unit_resolution,[status(thm)],[151,38]) ).
tff(153,plain,
( segmentP(sk4,sk3)
<=> segmentP(sk4,sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(154,axiom,
segmentP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(155,plain,
segmentP(sk4,sk3),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(158,axiom,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
tff(159,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[159,156]) ).
tff(161,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(162,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(164,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ segmentP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(165,plain,
( ! [V: $i,U: $i] :
( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) ),
inference(quant_intro,[status(thm)],[164]) ).
tff(166,axiom,
! [V: $i,U: $i] :
( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause168) ).
tff(167,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(modus_ponens,[status(thm)],[167,163]) ).
tff(169,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(modus_ponens,[status(thm)],[169,162]) ).
tff(171,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(172,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(transitivity,[status(thm)],[173,171]) ).
tff(175,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4,
inference(unit_resolution,[status(thm)],[176,170,13,160,155]) ).
tff(178,plain,
( memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5)
<=> memberP(sk4,sk5) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( memberP(sk4,sk5)
<=> memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
( ~ memberP(sk4,sk5)
<=> ~ memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ~ memberP(sk2,sk5)
<=> ~ memberP(sk4,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(182,plain,
( ~ memberP(sk2,sk5)
<=> ~ memberP(sk2,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(183,axiom,
~ memberP(sk2,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(184,plain,
~ memberP(sk2,sk5),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
~ memberP(sk4,sk5),
inference(modus_ponens,[status(thm)],[184,181]) ).
tff(186,plain,
~ memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5),
inference(modus_ponens,[status(thm)],[185,180]) ).
tff(187,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf48(U,V))
<=> ssList(skaf48(U,V)) )),
inference(bind,[status(th)],]) ).
tff(188,plain,
( ! [V: $i,U: $i] : ssList(skaf48(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf48(U,V)) ),
inference(quant_intro,[status(thm)],[187]) ).
tff(189,plain,
( ! [V: $i,U: $i] : ssList(skaf48(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf48(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(190,axiom,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause48) ).
tff(191,plain,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
inference(skolemize,[status(sab)],[191]) ).
tff(193,plain,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
inference(modus_ponens,[status(thm)],[192,188]) ).
tff(194,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf48(U,V))
| ssList(skaf48(sk3,sk4)) ),
inference(quant_inst,[status(thm)],]) ).
tff(195,plain,
ssList(skaf48(sk3,sk4)),
inference(unit_resolution,[status(thm)],[194,193]) ).
tff(196,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(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(quant_intro,[status(thm)],[196]) ).
tff(198,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(199,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(200,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)],[199]) ).
tff(201,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause140) ).
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)],[201,200]) ).
tff(203,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)],[202,198]) ).
tff(204,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)],[203]) ).
tff(205,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)],[204,197]) ).
tff(206,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(207,plain,
( ( ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(208,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(transitivity,[status(thm)],[208,206]) ).
tff(210,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(211,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
( ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(unit_resolution,[status(thm)],[211,205,8,195]) ).
tff(213,plain,
~ memberP(app(skaf47(sk4,sk3),sk3),sk5),
inference(unit_resolution,[status(thm)],[212,186,152]) ).
tff(214,plain,
~ memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5),
inference(modus_ponens,[status(thm)],[213,144]) ).
tff(215,plain,
( ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))))
<=> ssList(app(skaf47(sk4,sk3),sk3)) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(216,plain,
( ssList(app(skaf47(sk4,sk3),sk3))
<=> ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))))) ),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))))),
inference(modus_ponens,[status(thm)],[152,216]) ).
tff(218,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(219,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [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)],[218]) ).
tff(220,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [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(221,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(222,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)],[221]) ).
tff(223,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/sandbox/benchmark/Axioms/SWC001-0.ax',clause175) ).
tff(224,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)],[223,222]) ).
tff(225,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)],[224,220]) ).
tff(226,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)],[225]) ).
tff(227,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)],[226,219]) ).
tff(228,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(229,plain,
( ( ~ ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))))
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssItem(sk5)
| memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(230,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))))
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssItem(sk5)
| memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))))
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssItem(sk5)
| memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(transitivity,[status(thm)],[230,228]) ).
tff(232,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))))
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssItem(sk5)
| memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(233,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))),
inference(unit_resolution,[status(thm)],[233,227,8,90,217,214,141]) ).
tff(235,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(236,plain,
( ( ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssList(nil) )
<=> ( ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(237,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssList(nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) ) ),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssList(nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) ) ),
inference(transitivity,[status(thm)],[237,235]) ).
tff(239,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssList(nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(240,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) ),
inference(modus_ponens,[status(thm)],[239,238]) ).
tff(241,plain,
$false,
inference(unit_resolution,[status(thm)],[240,63,125,132,234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC403-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n018.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 : Sun Sep 4 00:48:15 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.19/0.54 % SZS status Unsatisfiable
% 0.19/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------