%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC404-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 : Sat Jun 21 05:31:08 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 38
% Syntax : Number of formulae : 86 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 592 ( 15 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 908 ( 444 ~; 408 |; 0 &)
% ( 56 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 156 ( 140 !; 0 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk7_type,type,
sk7: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk6_type,type,
sk6: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( memberP(sk3,sk7)
<=> memberP(sk1,sk7) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( memberP(sk1,sk7)
<=> memberP(sk3,sk7) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( memberP(sk1,sk7)
<=> memberP(sk1,sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
memberP(sk1,sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(9,plain,
memberP(sk1,sk7),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
memberP(sk3,sk7),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(13,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(16,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,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(18,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)],[17]) ).
tff(19,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(20,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(21,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)],[20]) ).
tff(22,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(23,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk5,sk3))
| ~ ssList(sk3)
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk5,sk3))
| ~ ssList(sk3)
| ~ ssList(sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ ssList(sk3)
| ssList(app(sk5,sk3))
| ~ ssList(sk5) )
<=> ( ssList(app(sk5,sk3))
| ~ ssList(sk3)
| ~ ssList(sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(sk5,sk3))
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk5,sk3))
| ~ ssList(sk3)
| ~ ssList(sk5) ) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(sk5,sk3))
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk5,sk3))
| ~ ssList(sk3)
| ~ ssList(sk5) ) ),
inference(transitivity,[status(thm)],[29,27]) ).
tff(31,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(sk5,sk3))
| ~ ssList(sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk5,sk3))
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
ssList(app(sk5,sk3)),
inference(unit_resolution,[status(thm)],[32,26,16,13]) ).
tff(34,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(36,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( ( app(app(sk5,sk3),sk6) = sk4 )
<=> ( app(app(sk5,sk3),sk6) = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
app(app(sk5,sk3),sk6) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(40,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
app(app(sk5,sk3),sk6) = sk2,
inference(transitivity,[status(thm)],[40,37]) ).
tff(42,plain,
( memberP(app(app(sk5,sk3),sk6),sk7)
<=> memberP(sk2,sk7) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( memberP(sk2,sk7)
<=> memberP(app(app(sk5,sk3),sk6),sk7) ),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( ~ memberP(sk2,sk7)
<=> ~ memberP(app(app(sk5,sk3),sk6),sk7) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ~ memberP(sk2,sk7)
<=> ~ memberP(sk2,sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
~ memberP(sk2,sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(47,plain,
~ memberP(sk2,sk7),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
~ memberP(app(app(sk5,sk3),sk6),sk7),
inference(modus_ponens,[status(thm)],[47,44]) ).
tff(49,plain,
( ssItem(sk7)
<=> ssItem(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
ssItem(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(51,plain,
ssItem(sk7),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(54,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,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(56,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)],[55]) ).
tff(57,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(58,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(59,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)],[58]) ).
tff(60,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(61,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)],[60,59]) ).
tff(62,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)],[61,57]) ).
tff(63,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)],[62]) ).
tff(64,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)],[63,56]) ).
tff(65,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(sk5,sk3))
| ~ ssItem(sk7)
| ~ ssList(sk6)
| ~ memberP(app(sk5,sk3),sk7)
| memberP(app(app(sk5,sk3),sk6),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(sk5,sk3))
| ~ ssItem(sk7)
| ~ ssList(sk6)
| ~ memberP(app(sk5,sk3),sk7)
| memberP(app(app(sk5,sk3),sk6),sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(sk5,sk3))
| ~ ssItem(sk7)
| ~ ssList(sk6)
| ~ memberP(app(sk5,sk3),sk7)
| memberP(app(app(sk5,sk3),sk6),sk7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(sk5,sk3))
| ~ ssItem(sk7)
| ~ ssList(sk6)
| ~ memberP(app(sk5,sk3),sk7)
| memberP(app(app(sk5,sk3),sk6),sk7) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ ssList(app(sk5,sk3))
| ~ memberP(app(sk5,sk3),sk7)
| memberP(app(app(sk5,sk3),sk6),sk7) ),
inference(unit_resolution,[status(thm)],[67,64,54,51]) ).
tff(69,plain,
~ memberP(app(sk5,sk3),sk7),
inference(unit_resolution,[status(thm)],[68,48,33]) ).
tff(70,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(71,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)],[70]) ).
tff(72,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(73,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(74,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)],[73]) ).
tff(75,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(76,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)],[75,74]) ).
tff(77,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)],[76,72]) ).
tff(78,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)],[77]) ).
tff(79,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)],[78,71]) ).
tff(80,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk7)
| memberP(app(sk5,sk3),sk7)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk7)
| memberP(app(sk5,sk3),sk7)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ( ~ ssList(sk3)
| ~ ssItem(sk7)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) )
<=> ( ~ ssItem(sk7)
| memberP(app(sk5,sk3),sk7)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssItem(sk7)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk7)
| memberP(app(sk5,sk3),sk7)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7) ) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssItem(sk7)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk7)
| memberP(app(sk5,sk3),sk7)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7) ) ),
inference(transitivity,[status(thm)],[82,80]) ).
tff(84,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssItem(sk7)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssItem(sk7)
| memberP(app(sk5,sk3),sk7)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
$false,
inference(unit_resolution,[status(thm)],[85,79,16,13,51,69,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWC404-1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 09:15:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% See solution above
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------