TSTP Solution File: SWC420-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC420-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 11:57:52 EDT 2022
% Result : Unsatisfiable 0.19s 0.57s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 95
% Syntax : Number of formulae : 211 ( 50 unt; 12 typ; 0 def)
% Number of atoms : 1286 ( 427 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1959 ( 931 ~; 918 |; 0 &)
% ( 110 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 59 ( 59 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 7 >; 3 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 375 ( 336 !; 0 ?; 375 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(hd_type,type,
hd: $i > $i ).
tff(sk4_type,type,
sk4: $i ).
tff(tl_type,type,
tl: $i > $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(4,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(10,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,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(14,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[15,12,5]) ).
tff(17,plain,
( ( sk4 = nil )
<=> ( nil = sk4 ) ),
inference(commutativity,[status(thm)],]) ).
tff(18,plain,
( ( sk4 != nil )
<=> ( nil != sk4 ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(22,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
tff(27,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause115) ).
tff(35,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(41,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil )
| ~ neq(sk4,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil )
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ~ ssList(sk4)
| ~ ssList(nil)
| ( sk4 != nil )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil )
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( sk4 != nil )
| ~ neq(sk4,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil )
| ~ neq(sk4,nil) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( sk4 != nil )
| ~ neq(sk4,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil )
| ~ neq(sk4,nil) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( sk4 != nil )
| ~ neq(sk4,nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
sk4 != nil,
inference(unit_resolution,[status(thm)],[47,41,38,28,23]) ).
tff(49,plain,
nil != sk4,
inference(modus_ponens,[status(thm)],[48,18]) ).
tff(50,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
tff(56,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
( ( nil = sk4 )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(unit_resolution,[status(thm)],[62,59,28]) ).
tff(64,plain,
cons(hd(sk4),tl(sk4)) = sk4,
inference(unit_resolution,[status(thm)],[63,49]) ).
tff(65,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
tff(71,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ( ~ ssList(sk4)
| ( nil = sk4 )
| ssList(tl(sk4)) )
<=> ( ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssList(tl(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssList(tl(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssList(tl(sk4)) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssList(tl(sk4)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
ssList(tl(sk4)),
inference(unit_resolution,[status(thm)],[80,74,28,49]) ).
tff(82,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(88,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ( ~ ssList(sk4)
| ( nil = sk4 )
| ssItem(hd(sk4)) )
<=> ( ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssItem(hd(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssItem(hd(sk4)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) ) ),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk4)
| ( nil = sk4 )
| ssItem(hd(sk4)) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk4 )
| ~ ssList(sk4)
| ssItem(hd(sk4)) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
( ( nil = sk4 )
| ssItem(hd(sk4)) ),
inference(unit_resolution,[status(thm)],[97,91,28]) ).
tff(99,plain,
ssItem(hd(sk4)),
inference(unit_resolution,[status(thm)],[98,49]) ).
tff(100,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(106,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)) ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)) ) ),
inference(unit_resolution,[status(thm)],[112,109,99]) ).
tff(114,plain,
app(cons(hd(sk4),nil),tl(sk4)) = cons(hd(sk4),tl(sk4)),
inference(unit_resolution,[status(thm)],[113,81]) ).
tff(115,plain,
app(cons(hd(sk4),nil),tl(sk4)) = sk4,
inference(transitivity,[status(thm)],[114,64]) ).
tff(116,plain,
^ [B: $i,A: $i] :
refl(
( ( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
<=> ( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(117,plain,
( ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
<=> ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
( ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
<=> ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
^ [B: $i,A: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 ) )
<=> ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) )
<=> ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) ) )),
rewrite(
( ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) )
<=> ( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) )
<=> ( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) )
<=> ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,axiom,
! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(B,cons(A,nil)) = sk3 )
| ( app(cons(A,nil),B) != sk4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(122,plain,
! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) != sk4 )
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 ) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) != sk4 )
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ~ ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) != sk4 )
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
( ~ ! [B: $i,A: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ( app(cons(A,nil),B) != sk4 )
| ( app(B,cons(A,nil)) = sk3 ) )
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(cons(hd(sk4),nil),tl(sk4)) != sk4 )
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
app(tl(sk4),cons(hd(sk4),nil)) = sk3,
inference(unit_resolution,[status(thm)],[128,125,99,81,115]) ).
tff(130,plain,
app(app(tl(sk4),cons(hd(sk4),nil)),nil) = app(sk3,nil),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
app(app(tl(sk4),cons(hd(sk4),nil)),nil) = sk3,
inference(transitivity,[status(thm)],[130,16]) ).
tff(132,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(133,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(136,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[136]) ).
tff(138,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,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(140,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
app(nil,sk4) = sk4,
inference(unit_resolution,[status(thm)],[141,138,28]) ).
tff(143,plain,
app(nil,app(cons(hd(sk4),nil),tl(sk4))) = app(nil,sk4),
inference(monotonicity,[status(thm)],[115]) ).
tff(144,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(145,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)],[144]) ).
tff(146,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(147,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(148,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)],[147]) ).
tff(149,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(150,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[152,145]) ).
tff(154,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(155,plain,
( ( ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ssList(cons(hd(sk4),nil)) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ssList(cons(hd(sk4),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) ) ),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ssList(cons(hd(sk4),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) ) ),
inference(transitivity,[status(thm)],[156,154]) ).
tff(158,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ssList(cons(hd(sk4),nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ssList(cons(hd(sk4),nil)) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
ssList(cons(hd(sk4),nil)),
inference(unit_resolution,[status(thm)],[159,41,153,99]) ).
tff(161,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(162,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)],[161]) ).
tff(163,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(164,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(165,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)],[164]) ).
tff(166,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(167,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)],[166,165]) ).
tff(168,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)],[167,163]) ).
tff(169,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)],[168]) ).
tff(170,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)],[169,162]) ).
tff(171,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(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = app(nil,app(cons(hd(sk4),nil),tl(sk4))) ) )
<=> ( ~ ! [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(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = app(nil,app(cons(hd(sk4),nil),tl(sk4))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(172,plain,
( ( ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = app(nil,app(cons(hd(sk4),nil),tl(sk4))) ) )
<=> ( ~ ssList(nil)
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = app(nil,app(cons(hd(sk4),nil),tl(sk4))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = app(nil,app(cons(hd(sk4),nil),tl(sk4))) ) )
<=> ( ~ ! [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(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = app(nil,app(cons(hd(sk4),nil),tl(sk4))) ) ) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = app(nil,app(cons(hd(sk4),nil),tl(sk4))) ) )
<=> ( ~ ! [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(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = app(nil,app(cons(hd(sk4),nil),tl(sk4))) ) ) ),
inference(transitivity,[status(thm)],[173,171]) ).
tff(175,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = app(nil,app(cons(hd(sk4),nil),tl(sk4))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,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(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = app(nil,app(cons(hd(sk4),nil),tl(sk4))) ) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = app(nil,app(cons(hd(sk4),nil),tl(sk4))),
inference(unit_resolution,[status(thm)],[176,41,170,81,160]) ).
tff(178,plain,
app(app(nil,cons(hd(sk4),nil)),tl(sk4)) = sk4,
inference(transitivity,[status(thm)],[177,143,142]) ).
tff(179,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(180,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[179]) ).
tff(181,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( app(app(C,cons(A,nil)),B) != sk1 )
<=> ( app(app(C,cons(A,nil)),B) != sk3 ) )),
rewrite(
( ( app(app(B,cons(A,nil)),C) != sk2 )
<=> ( app(app(B,cons(A,nil)),C) != sk4 ) )),
( ( ~ 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) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
( ( ~ 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) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(182,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) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,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(184,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(185,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)],[184]) ).
tff(186,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(187,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)],[186,185]) ).
tff(188,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)],[187,183]) ).
tff(189,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[188,182]) ).
tff(190,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(skolemize,[status(sab)],[189]) ).
tff(191,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[190,180]) ).
tff(192,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(app(tl(sk4),cons(hd(sk4),nil)),nil) != sk3 )
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(app(tl(sk4),cons(hd(sk4),nil)),nil) != sk3 )
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(193,plain,
( ( ~ ssList(tl(sk4))
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ( app(app(tl(sk4),cons(hd(sk4),nil)),nil) != sk3 )
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(app(tl(sk4),cons(hd(sk4),nil)),nil) != sk3 )
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(tl(sk4))
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ( app(app(tl(sk4),cons(hd(sk4),nil)),nil) != sk3 )
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(app(tl(sk4),cons(hd(sk4),nil)),nil) != sk3 )
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) ) ),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(tl(sk4))
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ( app(app(tl(sk4),cons(hd(sk4),nil)),nil) != sk3 )
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(app(tl(sk4),cons(hd(sk4),nil)),nil) != sk3 )
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) ) ),
inference(transitivity,[status(thm)],[194,192]) ).
tff(196,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(tl(sk4))
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ( app(app(tl(sk4),cons(hd(sk4),nil)),nil) != sk3 )
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(197,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ( app(app(tl(sk4),cons(hd(sk4),nil)),nil) != sk3 )
| ( app(app(nil,cons(hd(sk4),nil)),tl(sk4)) != sk4 ) ),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
app(app(tl(sk4),cons(hd(sk4),nil)),nil) != sk3,
inference(unit_resolution,[status(thm)],[197,41,191,99,81,178]) ).
tff(199,plain,
$false,
inference(unit_resolution,[status(thm)],[198,131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWC420-1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.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 : Sun Sep 4 00:51:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.57 % SZS status Unsatisfiable
% 0.19/0.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------