%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC218-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:30:33 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 64
% Syntax : Number of formulae : 157 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 954 ( 309 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1432 ( 690 ~; 648 |; 0 &)
% ( 94 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 55 ( 55 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; 6 con; 0-2 aty)
% Number of variables : 270 ( 243 !; 0 ?; 270 :)
% Comments :
%------------------------------------------------------------------------------
tff(nil_type,type,
nil: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( ( app(app(sk5,cons(sk7,nil)),sk6) = sk3 )
<=> ( app(app(sk5,cons(sk7,nil)),sk6) = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
app(app(sk5,cons(sk7,nil)),sk6) = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(4,plain,
app(app(sk5,cons(sk7,nil)),sk6) = sk3,
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( ( app(app(sk5,cons(sk7,nil)),sk6) = nil )
<=> ( sk3 = nil ) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( ( app(app(sk5,cons(sk7,nil)),sk6) = nil )
<=> ( nil = sk3 ) ),
inference(transitivity,[status(thm)],[5,1]) ).
tff(7,plain,
( ( nil = sk3 )
<=> ( app(app(sk5,cons(sk7,nil)),sk6) = nil ) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( ( sk3 = nil )
<=> ( app(app(sk5,cons(sk7,nil)),sk6) = nil ) ),
inference(transitivity,[status(thm)],[1,7]) ).
tff(9,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(11,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( neq(sk3,nil)
<=> neq(sk1,nil) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( neq(sk1,nil)
<=> neq(sk3,nil) ),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk3,nil) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk1,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
~ neq(sk1,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
tff(18,plain,
~ neq(sk1,nil),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
~ neq(sk3,nil),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(22,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(29,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(35,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( sk3 = nil )
| neq(sk3,nil) ),
inference(unit_resolution,[status(thm)],[38,35,32,22]) ).
tff(40,plain,
sk3 = nil,
inference(unit_resolution,[status(thm)],[39,19]) ).
tff(41,plain,
app(app(sk5,cons(sk7,nil)),sk6) = nil,
inference(modus_ponens,[status(thm)],[40,8]) ).
tff(42,plain,
( ( sk3 = sk6 )
<=> ( nil = sk6 ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(43,plain,
( ( sk3 != sk6 )
<=> ( nil != sk6 ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(46,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(51,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk6)
| ( app(nil,sk6) = sk6 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk6)
| ( app(nil,sk6) = sk6 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk6)
| ( app(nil,sk6) = sk6 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk6)
| ( app(nil,sk6) = sk6 ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
app(nil,sk6) = sk6,
inference(unit_resolution,[status(thm)],[56,53,46]) ).
tff(58,plain,
( ( app(app(sk5,cons(sk7,nil)),sk6) = app(nil,sk6) )
<=> ( sk3 = sk6 ) ),
inference(monotonicity,[status(thm)],[4,57]) ).
tff(59,plain,
( ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) )
<=> ( sk3 != sk6 ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( nil = cons(sk7,nil) )
<=> ( cons(sk7,nil) = nil ) ),
inference(commutativity,[status(thm)],[]) ).
tff(61,plain,
( ( cons(sk7,nil) = nil )
<=> ( nil = cons(sk7,nil) ) ),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ( cons(sk7,nil) != nil )
<=> ( nil != cons(sk7,nil) ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ssItem(sk7)
<=> ssItem(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
ssItem(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(65,plain,
ssItem(sk7),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( cons(U,V) != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause99) ).
tff(72,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ( cons(sk7,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ( cons(sk7,nil) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ( cons(sk7,nil) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ( cons(sk7,nil) != nil ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
cons(sk7,nil) != nil,
inference(unit_resolution,[status(thm)],[78,35,75,65]) ).
tff(80,plain,
nil != cons(sk7,nil),
inference(modus_ponens,[status(thm)],[79,62]) ).
tff(81,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(82,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)],[81]) ).
tff(83,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(84,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(85,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)],[84]) ).
tff(86,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(87,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
ssList(cons(sk7,nil)),
inference(unit_resolution,[status(thm)],[93,35,90,65]) ).
tff(95,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,axiom,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(97,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(99,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
tff(104,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ( app(sk5,cons(sk7,nil)) != nil )
| ( nil = cons(sk7,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ( app(sk5,cons(sk7,nil)) != nil )
| ( nil = cons(sk7,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ( app(sk5,cons(sk7,nil)) != nil )
| ( nil = cons(sk7,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ( app(sk5,cons(sk7,nil)) != nil )
| ( nil = cons(sk7,nil) ) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
( ( app(sk5,cons(sk7,nil)) != nil )
| ( nil = cons(sk7,nil) ) ),
inference(unit_resolution,[status(thm)],[110,107,97,94]) ).
tff(112,plain,
app(sk5,cons(sk7,nil)) != nil,
inference(unit_resolution,[status(thm)],[111,80]) ).
tff(113,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(114,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)],[113]) ).
tff(115,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(116,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(117,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)],[116]) ).
tff(118,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(119,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[121,114]) ).
tff(123,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk5)
| ssList(app(sk5,cons(sk7,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk5)
| ssList(app(sk5,cons(sk7,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
( ( ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk5) )
<=> ( ~ ssList(cons(sk7,nil))
| ~ ssList(sk5)
| ssList(app(sk5,cons(sk7,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk5)
| ssList(app(sk5,cons(sk7,nil))) ) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk5)
| ssList(app(sk5,cons(sk7,nil))) ) ),
inference(transitivity,[status(thm)],[125,123]) ).
tff(127,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk5)
| ssList(app(sk5,cons(sk7,nil))) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
ssList(app(sk5,cons(sk7,nil))),
inference(unit_resolution,[status(thm)],[128,122,97,94]) ).
tff(130,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != app(W,V) )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( app(U,V) != app(W,V) ) ) )),
( ( ( app(U,V) != app(W,V) )
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ( app(U,V) != app(W,V) )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssList(U)
| ( app(U,V) != app(W,V) )
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != app(W,V) ) ) )),
( ( ( app(U,V) != app(W,V) )
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != app(W,V) ) ) )),
( ( ( app(U,V) != app(W,V) )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != app(W,V) )
| ~ ssList(W) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != app(W,V) )
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != app(W,V) ) ) )),
( ( ( app(U,V) != app(W,V) )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != app(W,V) ) ) )),
( ( ( app(U,V) != app(W,V) )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != app(W,V) )
| ( U = W ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != app(W,V) )
| ( U = W ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) ) )),
( ( ( app(U,V) != app(W,V) )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(134,plain,
( ! [W: $i,V: $i,U: $i] :
( ( app(U,V) != app(W,V) )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,axiom,
! [W: $i,V: $i,U: $i] :
( ( app(U,V) != app(W,V) )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause151) ).
tff(136,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) ),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) ),
inference(skolemize,[status(sab)],[137]) ).
tff(139,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) ),
inference(modus_ponens,[status(thm)],[138,131]) ).
tff(140,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(sk5,cons(sk7,nil)) = nil )
| ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(sk5,cons(sk7,nil)) = nil )
| ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ( ~ ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk6)
| ~ ssList(nil)
| ( app(sk5,cons(sk7,nil)) = nil )
| ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(sk5,cons(sk7,nil)) = nil )
| ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk6)
| ~ ssList(nil)
| ( app(sk5,cons(sk7,nil)) = nil )
| ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(sk5,cons(sk7,nil)) = nil )
| ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) ) ) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk6)
| ~ ssList(nil)
| ( app(sk5,cons(sk7,nil)) = nil )
| ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(sk5,cons(sk7,nil)) = nil )
| ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) ) ) ),
inference(transitivity,[status(thm)],[142,140]) ).
tff(144,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk6)
| ~ ssList(nil)
| ( app(sk5,cons(sk7,nil)) = nil )
| ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W )
| ( app(U,V) != app(W,V) ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(sk5,cons(sk7,nil)) = nil )
| ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) ) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
( ( app(sk5,cons(sk7,nil)) = nil )
| ( app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6) ) ),
inference(unit_resolution,[status(thm)],[145,35,139,46,129]) ).
tff(147,plain,
app(app(sk5,cons(sk7,nil)),sk6) != app(nil,sk6),
inference(unit_resolution,[status(thm)],[146,112]) ).
tff(148,plain,
sk3 != sk6,
inference(modus_ponens,[status(thm)],[147,59]) ).
tff(149,plain,
nil != sk6,
inference(modus_ponens,[status(thm)],[148,43]) ).
tff(150,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk6)
| ( nil = sk6 )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk6)
| ( nil = sk6 )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(151,plain,
( ( ~ ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk6)
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil )
| ( nil = sk6 ) )
<=> ( ~ ssList(sk6)
| ( nil = sk6 )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk6)
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil )
| ( nil = sk6 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk6)
| ( nil = sk6 )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ) ),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk6)
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil )
| ( nil = sk6 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk6)
| ( nil = sk6 )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ) ),
inference(transitivity,[status(thm)],[152,150]) ).
tff(154,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk6)
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil )
| ( nil = sk6 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk6)
| ( nil = sk6 )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
( ( nil = sk6 )
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ),
inference(unit_resolution,[status(thm)],[155,107,46,129]) ).
tff(157,plain,
$false,
inference(unit_resolution,[status(thm)],[156,149,41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC218-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:38:39 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48 % SZS output start Proof
% See solution above
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------