%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC247-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:30:40 AM UTC 2025
% Result : Unsatisfiable 3.90s 4.09s
% Output : Proof 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 110
% Syntax : Number of formulae : 281 ( 83 unt; 0 typ; 0 def)
% Number of atoms : 1826 ( 466 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 2743 (1288 ~;1307 |; 0 &)
% ( 148 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 90 ( 90 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 569 ( 511 !; 0 ?; 569 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk5_type,type,
sk5: ( $i * $i * $i ) > $i ).
tff(hd_type,type,
hd: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(nil_type,type,
nil: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(tl_type,type,
tl: $i > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(skaf82_type,type,
skaf82: $i > $i ).
tff(skaf83_type,type,
skaf83: $i > $i ).
tff(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(leq_type,type,
leq: ( $i * $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(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[17,14,7]) ).
tff(19,plain,
( ( nil = sk3 )
<=> ( nil = sk1 ) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(20,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(24,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[24,21]) ).
tff(26,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
tff(32,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(unit_resolution,[status(thm)],[38,35,7]) ).
tff(40,plain,
cons(skaf83(sk3),skaf82(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[39,25]) ).
tff(41,plain,
^ [U: $i] :
refl(( ssList(skaf82(U))
<=> ssList(skaf82(U)) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
! [U: $i] : ssList(skaf82(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
tff(45,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [U: $i] : ssList(skaf82(U)),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [U: $i] : ssList(skaf82(U))
| ssList(skaf82(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
ssList(skaf82(sk3)),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
^ [U: $i] :
refl(( ssItem(skaf83(U))
<=> ssItem(skaf83(U)) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
! [U: $i] : ssItem(skaf83(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
tff(54,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [U: $i] : ssItem(skaf83(U))
| ssItem(skaf83(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
ssItem(skaf83(sk3)),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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(62,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(63,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)],[62]) ).
tff(64,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(65,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(unit_resolution,[status(thm)],[71,68]) ).
tff(73,plain,
app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)),
inference(unit_resolution,[status(thm)],[72,58,49]) ).
tff(74,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
tff(80,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( tl(cons(skaf83(sk3),skaf82(sk3))) = skaf82(sk3) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( tl(cons(skaf83(sk3),skaf82(sk3))) = skaf82(sk3) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( tl(cons(skaf83(sk3),skaf82(sk3))) = skaf82(sk3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( tl(cons(skaf83(sk3),skaf82(sk3))) = skaf82(sk3) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( tl(cons(skaf83(sk3),skaf82(sk3))) = skaf82(sk3) ) ),
inference(unit_resolution,[status(thm)],[86,83]) ).
tff(88,plain,
tl(cons(skaf83(sk3),skaf82(sk3))) = skaf82(sk3),
inference(unit_resolution,[status(thm)],[87,58,49]) ).
tff(89,plain,
tl(cons(skaf83(sk3),skaf82(sk3))) = tl(sk3),
inference(monotonicity,[status(thm)],[40]) ).
tff(90,plain,
tl(sk3) = tl(cons(skaf83(sk3),skaf82(sk3))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(95,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,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(99,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[100,97,7]) ).
tff(102,plain,
sk3 = app(sk3,nil),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
tl(sk3) = tl(app(sk3,nil)),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
tl(app(sk3,nil)) = tl(sk3),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
inference(bind,[status(th)],[]) ).
tff(106,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
inference(bind,[status(th)],[]) ).
tff(109,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause133) ).
tff(111,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(117,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( nil = sk3 )
| ( tl(app(sk3,nil)) = app(tl(sk3),nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( nil = sk3 )
| ( tl(app(sk3,nil)) = app(tl(sk3),nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( nil = sk3 )
| ( tl(app(sk3,nil)) = app(tl(sk3),nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( nil = sk3 )
| ( tl(app(sk3,nil)) = app(tl(sk3),nil) ) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
tl(app(sk3,nil)) = app(tl(sk3),nil),
inference(unit_resolution,[status(thm)],[120,117,114,7,25]) ).
tff(122,plain,
app(tl(sk3),nil) = tl(app(sk3,nil)),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
app(tl(sk3),nil) = skaf82(sk3),
inference(transitivity,[status(thm)],[122,104,90,88]) ).
tff(124,plain,
hd(cons(skaf83(sk3),skaf82(sk3))) = hd(sk3),
inference(monotonicity,[status(thm)],[40]) ).
tff(125,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
tff(131,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3) ) ),
inference(unit_resolution,[status(thm)],[137,134]) ).
tff(139,plain,
hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3),
inference(unit_resolution,[status(thm)],[138,58,49]) ).
tff(140,plain,
skaf83(sk3) = hd(cons(skaf83(sk3),skaf82(sk3))),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
skaf83(sk3) = hd(sk3),
inference(transitivity,[status(thm)],[140,124]) ).
tff(142,plain,
cons(skaf83(sk3),nil) = cons(hd(sk3),nil),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
cons(hd(sk3),nil) = cons(skaf83(sk3),nil),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
app(cons(hd(sk3),nil),app(tl(sk3),nil)) = app(cons(skaf83(sk3),nil),skaf82(sk3)),
inference(monotonicity,[status(thm)],[143,123]) ).
tff(145,plain,
app(cons(hd(sk3),nil),app(tl(sk3),nil)) = sk3,
inference(transitivity,[status(thm)],[144,73,40]) ).
tff(146,plain,
app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))) = app(nil,sk3),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(151,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[150]) ).
tff(152,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(153,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[153,149]) ).
tff(155,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(skolemize,[status(sab)],[154]) ).
tff(156,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[155,148]) ).
tff(157,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
( ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(unit_resolution,[status(thm)],[159,156,7]) ).
tff(161,plain,
ssItem(hd(sk3)),
inference(unit_resolution,[status(thm)],[160,25]) ).
tff(162,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(163,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)],[162]) ).
tff(164,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(165,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(166,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)],[165]) ).
tff(167,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(168,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[168,164]) ).
tff(170,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[169]) ).
tff(171,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[170,163]) ).
tff(172,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,plain,
( ( ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssList(cons(hd(sk3),nil)) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssList(cons(hd(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) ) ),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssList(cons(hd(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) ) ),
inference(transitivity,[status(thm)],[174,172]) ).
tff(176,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssList(cons(hd(sk3),nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) ),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
ssList(cons(hd(sk3),nil)),
inference(unit_resolution,[status(thm)],[177,117,171,161]) ).
tff(179,plain,
tl(sk3) = app(tl(sk3),nil),
inference(transitivity,[status(thm)],[103,121]) ).
tff(180,plain,
( ssList(tl(sk3))
<=> ssList(app(tl(sk3),nil)) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(182,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(185,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[184]) ).
tff(186,axiom,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
tff(187,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[186,185]) ).
tff(188,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[187,183]) ).
tff(189,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(skolemize,[status(sab)],[188]) ).
tff(190,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[189,182]) ).
tff(191,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(192,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
ssList(tl(sk3)),
inference(unit_resolution,[status(thm)],[193,190,7,25]) ).
tff(195,plain,
ssList(app(tl(sk3),nil)),
inference(modus_ponens,[status(thm)],[194,180]) ).
tff(196,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(197,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)],[196]) ).
tff(198,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(199,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(200,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)],[199]) ).
tff(201,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(202,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)],[201,200]) ).
tff(203,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)],[202,198]) ).
tff(204,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)],[203]) ).
tff(205,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)],[204,197]) ).
tff(206,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(app(tl(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))) ) )
<=> ( ~ ! [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(app(tl(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,plain,
( ( ~ ssList(app(tl(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))) ) )
<=> ( ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(208,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))) ) )
<=> ( ~ ! [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(app(tl(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))) ) ) ),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))) ) )
<=> ( ~ ! [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(app(tl(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))) ) ) ),
inference(transitivity,[status(thm)],[208,206]) ).
tff(210,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(211,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(app(tl(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))) ) ),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = app(nil,app(cons(hd(sk3),nil),app(tl(sk3),nil))),
inference(unit_resolution,[status(thm)],[211,117,205,195,178]) ).
tff(213,plain,
app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) = sk1,
inference(transitivity,[status(thm)],[212,146,18,4]) ).
tff(214,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(215,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[214]) ).
tff(216,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(217,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) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(218,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[217]) ).
tff(219,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(220,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[220,216]) ).
tff(222,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(skolemize,[status(sab)],[221]) ).
tff(223,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[222,215]) ).
tff(224,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(225,plain,
( ( ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 ) )
<=> ( ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(226,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(monotonicity,[status(thm)],[225]) ).
tff(227,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(transitivity,[status(thm)],[226,224]) ).
tff(228,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(229,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3))) ),
inference(modus_ponens,[status(thm)],[228,227]) ).
tff(230,plain,
ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3))),
inference(unit_resolution,[status(thm)],[229,117,223,161,195,213]) ).
tff(231,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(232,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[231]) ).
tff(233,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(234,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) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(235,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[234]) ).
tff(236,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(237,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[236,235]) ).
tff(238,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[237,233]) ).
tff(239,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ),
inference(skolemize,[status(sab)],[238]) ).
tff(240,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[239,232]) ).
tff(241,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(242,plain,
( ( ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(243,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(transitivity,[status(thm)],[243,241]) ).
tff(245,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(246,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))),
inference(unit_resolution,[status(thm)],[246,117,240,161,195,213]) ).
tff(248,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(249,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[248]) ).
tff(250,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(251,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) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(252,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[251]) ).
tff(253,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(254,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[253,252]) ).
tff(255,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[254,250]) ).
tff(256,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ),
inference(skolemize,[status(sab)],[255]) ).
tff(257,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[256,249]) ).
tff(258,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ~ leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ~ leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(259,plain,
( ( ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ~ leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ~ leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(260,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ~ leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ~ leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(monotonicity,[status(thm)],[259]) ).
tff(261,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ~ leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ~ leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(transitivity,[status(thm)],[260,258]) ).
tff(262,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ~ leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(263,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(app(tl(sk3),nil))
| ~ ssItem(hd(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),app(tl(sk3),nil)) != sk1 )
| ~ leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ),
inference(modus_ponens,[status(thm)],[262,261]) ).
tff(264,plain,
~ leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))),
inference(unit_resolution,[status(thm)],[263,117,257,161,195,213]) ).
tff(265,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(266,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(quant_intro,[status(thm)],[265]) ).
tff(267,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(268,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ lt(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ~ lt(U,V)
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(V)
| ~ lt(U,V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| leq(U,V) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(269,plain,
( ! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(quant_intro,[status(thm)],[268]) ).
tff(270,axiom,
! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause103) ).
tff(271,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[270,269]) ).
tff(272,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[271,267]) ).
tff(273,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(skolemize,[status(sab)],[272]) ).
tff(274,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[273,266]) ).
tff(275,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(hd(sk3))
| leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(hd(sk3))
| leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(276,plain,
( ( ~ ssItem(hd(sk3))
| ~ ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ssItem(hd(sk3))
| leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(277,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(hd(sk3))
| ~ ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(hd(sk3))
| leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(monotonicity,[status(thm)],[276]) ).
tff(278,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(hd(sk3))
| ~ ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(hd(sk3))
| leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ) ),
inference(transitivity,[status(thm)],[277,275]) ).
tff(279,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(hd(sk3))
| ~ ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(280,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(hd(sk3))
| leq(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ ssItem(sk5(app(tl(sk3),nil),nil,hd(sk3)))
| ~ lt(hd(sk3),sk5(app(tl(sk3),nil),nil,hd(sk3))) ),
inference(modus_ponens,[status(thm)],[279,278]) ).
tff(281,plain,
$false,
inference(unit_resolution,[status(thm)],[280,274,161,264,247,230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC247-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 08:43:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.90/4.09 % SZS status Unsatisfiable
% 3.90/4.09 % SZS output start Proof
% See solution above
% 3.97/4.14 % E exiting
%------------------------------------------------------------------------------