%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC419-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:31:11 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 50
% Syntax : Number of formulae : 121 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 619 ( 190 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 940 ( 468 ~; 420 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 26 ( 26 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 186 ( 168 !; 0 ?; 186 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $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,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(7,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[17,14,7]) ).
tff(19,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(21,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(25,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
( ( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(29,plain,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[29,27]) ).
tff(31,plain,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[30,27]) ).
tff(32,plain,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[32,27]) ).
tff(34,plain,
app(sk6,cons(sk5,nil)) = sk3,
inference(unit_resolution,[status(thm)],[33,26]) ).
tff(35,plain,
app(app(sk6,cons(sk5,nil)),nil) = app(sk3,nil),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
app(app(sk6,cons(sk5,nil)),nil) = sk1,
inference(transitivity,[status(thm)],[35,18,4]) ).
tff(37,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[21]) ).
tff(38,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
tff(40,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(45,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
app(nil,sk4) = sk4,
inference(unit_resolution,[status(thm)],[50,47,40]) ).
tff(52,plain,
( ( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) )
<=> ( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
tff(54,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[54,52]) ).
tff(56,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[55,52]) ).
tff(57,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[57,52]) ).
tff(59,plain,
app(cons(sk5,nil),sk6) = sk4,
inference(unit_resolution,[status(thm)],[58,26]) ).
tff(60,plain,
app(nil,app(cons(sk5,nil),sk6)) = app(nil,sk4),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(63,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[63,26]) ).
tff(65,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(66,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)],[65]) ).
tff(67,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(68,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(69,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)],[68]) ).
tff(70,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(71,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(77,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[80,77,74,64]) ).
tff(82,plain,
( ( ssList(sk6)
| ~ neq(sk4,nil) )
<=> ( ssList(sk6)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(84,plain,
( ssList(sk6)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
ssList(sk6),
inference(unit_resolution,[status(thm)],[84,26]) ).
tff(86,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(87,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)],[86]) ).
tff(88,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(89,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(90,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)],[89]) ).
tff(91,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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(92,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)],[91,90]) ).
tff(93,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)],[92,88]) ).
tff(94,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)],[93]) ).
tff(95,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)],[94,87]) ).
tff(96,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(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) )
<=> ( ~ ! [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(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) )
<=> ( ~ ! [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(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) )
<=> ( ~ ! [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(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ) ),
inference(transitivity,[status(thm)],[98,96]) ).
tff(100,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,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(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)),
inference(unit_resolution,[status(thm)],[101,77,95,85,81]) ).
tff(103,plain,
app(app(nil,cons(sk5,nil)),sk6) = sk2,
inference(transitivity,[status(thm)],[102,60,51,37]) ).
tff(104,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(108,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(110,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[112,105]) ).
tff(114,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk1 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk1 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
( ( ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk1 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk2 ) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk1 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk1 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk1 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk2 ) ) ),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk1 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk1 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk2 ) ) ),
inference(transitivity,[status(thm)],[116,114]) ).
tff(118,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk1 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk1 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk2 ) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
( ( app(app(sk6,cons(sk5,nil)),nil) != sk1 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk2 ) ),
inference(unit_resolution,[status(thm)],[119,77,113,64,85]) ).
tff(121,plain,
$false,
inference(unit_resolution,[status(thm)],[120,103,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC419-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:17:25 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45 % SZS output start Proof
% See solution above
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------