%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC045-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:01 AM UTC 2025
% Result : Unsatisfiable 1.60s 1.76s
% Output : Proof 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 99
% Syntax : Number of formulae : 252 ( 70 unt; 0 typ; 0 def)
% Number of atoms : 1364 ( 330 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1983 ( 938 ~; 907 |; 0 &)
% ( 138 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 67 ( 67 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 : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 393 ( 354 !; 0 ?; 393 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssList_type,type,
ssList: $i > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(hd_type,type,
hd: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk5_type,type,
sk5: $i > $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(skaf83_type,type,
skaf83: $i > $i ).
tff(skaf82_type,type,
skaf82: $i > $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
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,
( ( nil = sk3 )
<=> ( nil = sk1 ) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(10,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(14,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(21,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,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(26,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(unit_resolution,[status(thm)],[27,24,14]) ).
tff(29,plain,
ssItem(hd(sk3)),
inference(unit_resolution,[status(thm)],[28,11]) ).
tff(30,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(31,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)],[30]) ).
tff(32,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(33,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(34,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)],[33]) ).
tff(35,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(36,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(42,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,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(44,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(45,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)],[44]) ).
tff(46,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)],[45,43]) ).
tff(47,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(48,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)],[47,46]) ).
tff(49,plain,
ssList(cons(hd(sk3),nil)),
inference(unit_resolution,[status(thm)],[48,42,39,29]) ).
tff(50,plain,
^ [U: $i] :
refl(( ssList(skaf82(U))
<=> ssList(skaf82(U)) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
! [U: $i] : ssList(skaf82(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
tff(54,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [U: $i] : ssList(skaf82(U)),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [U: $i] : ssList(skaf82(U))
| ssList(skaf82(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
ssList(skaf82(sk3)),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
^ [U: $i] :
refl(( ssItem(skaf83(U))
<=> ssItem(skaf83(U)) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
! [U: $i] : ssItem(skaf83(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
tff(63,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ~ ! [U: $i] : ssItem(skaf83(U))
| ssItem(skaf83(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
ssItem(skaf83(sk3)),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,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(69,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)],[68]) ).
tff(70,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(71,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(72,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)],[71]) ).
tff(73,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
tff(74,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,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(79,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(80,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)],[79,78]) ).
tff(81,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3) ) ),
inference(unit_resolution,[status(thm)],[80,77]) ).
tff(82,plain,
hd(cons(skaf83(sk3),skaf82(sk3))) = skaf83(sk3),
inference(unit_resolution,[status(thm)],[81,67,58]) ).
tff(83,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(84,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)],[83]) ).
tff(85,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(86,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(87,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)],[86]) ).
tff(88,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
tff(89,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,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(94,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(95,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)],[94,93]) ).
tff(96,plain,
( ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(unit_resolution,[status(thm)],[95,92,14]) ).
tff(97,plain,
cons(skaf83(sk3),skaf82(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[96,11]) ).
tff(98,plain,
hd(cons(skaf83(sk3),skaf82(sk3))) = hd(sk3),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
hd(sk3) = hd(cons(skaf83(sk3),skaf82(sk3))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
hd(sk3) = skaf83(sk3),
inference(transitivity,[status(thm)],[99,82]) ).
tff(101,plain,
sk3 = cons(skaf83(sk3),skaf82(sk3)),
inference(symmetry,[status(thm)],[97]) ).
tff(102,plain,
( memberP(sk3,hd(sk3))
<=> memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) ),
inference(monotonicity,[status(thm)],[101,100]) ).
tff(103,plain,
( memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3))
<=> memberP(sk3,hd(sk3)) ),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
^ [W: $i,V: $i] :
refl(( ( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
<=> ( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
<=> ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
<=> ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
^ [W: $i,V: $i] :
rewrite(( ( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) )
<=> ( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) )),
inference(bind,[status(th)],[]) ).
tff(108,plain,
( ! [W: $i,V: $i] :
( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
( ! [W: $i,V: $i,U: $i] :
( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i] :
( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(110,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i,U: $i] :
( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(111,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i] :
( memberP(cons(V,W),V)
| ~ ssItem(V)
| ~ ssItem(V)
| ~ ssList(W) ) ),
inference(transitivity,[status(thm)],[110,109]) ).
tff(112,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) ),
inference(transitivity,[status(thm)],[111,108]) ).
tff(113,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( U != V )
| ~ ssList(W) )
<=> ( ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) ) )),
rewrite(( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) )),
( ( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ( U != V )
| ~ ssList(W)
| memberP(cons(V,W),U) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) )
<=> ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ) ),
inference(transitivity,[status(thm)],[114,112]) ).
tff(116,axiom,
! [W: $i,V: $i,U: $i] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause138) ).
tff(117,plain,
! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ),
inference(modus_ponens,[status(thm)],[117,106]) ).
tff(119,plain,
! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) ),
inference(modus_ponens,[status(thm)],[119,105]) ).
tff(121,plain,
( ( ~ ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) )
<=> ( ~ ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ~ ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [W: $i,V: $i] :
( ~ ssItem(V)
| ~ ssList(W)
| memberP(cons(V,W),V) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)) ),
inference(unit_resolution,[status(thm)],[123,120]) ).
tff(125,plain,
memberP(cons(skaf83(sk3),skaf82(sk3)),skaf83(sk3)),
inference(unit_resolution,[status(thm)],[124,67,58]) ).
tff(126,plain,
memberP(sk3,hd(sk3)),
inference(modus_ponens,[status(thm)],[125,103]) ).
tff(127,plain,
^ [A: $i] :
refl(( ( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
<=> ( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) ) )),
inference(bind,[status(th)],[]) ).
tff(128,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
^ [A: $i] :
rewrite(( ( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
<=> ( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,axiom,
! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(133,plain,
! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) ),
inference(modus_ponens,[status(thm)],[135,128]) ).
tff(137,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk3,hd(sk3))
| ssList(sk5(hd(sk3))) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk3,hd(sk3))
| ssList(sk5(hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
( ( ~ ssItem(hd(sk3))
| ssList(sk5(hd(sk3)))
| ~ memberP(sk3,hd(sk3)) )
<=> ( ~ ssItem(hd(sk3))
| ~ memberP(sk3,hd(sk3))
| ssList(sk5(hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| ssList(sk5(hd(sk3)))
| ~ memberP(sk3,hd(sk3)) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk3,hd(sk3))
| ssList(sk5(hd(sk3))) ) ),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| ssList(sk5(hd(sk3)))
| ~ memberP(sk3,hd(sk3)) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk3,hd(sk3))
| ssList(sk5(hd(sk3))) ) ),
inference(transitivity,[status(thm)],[139,137]) ).
tff(141,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| ssList(sk5(hd(sk3)))
| ~ memberP(sk3,hd(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ssList(sk5(A))
| ~ memberP(sk3,A) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk3,hd(sk3))
| ssList(sk5(hd(sk3))) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
( ~ memberP(sk3,hd(sk3))
| ssList(sk5(hd(sk3))) ),
inference(unit_resolution,[status(thm)],[142,136,29]) ).
tff(144,plain,
ssList(sk5(hd(sk3))),
inference(unit_resolution,[status(thm)],[143,126]) ).
tff(145,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(146,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(149,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(151,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[152]) ).
tff(154,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[153,146]) ).
tff(155,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(sk5(hd(sk3)))
| ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(sk5(hd(sk3)))
| ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
( ( ~ ssList(sk5(hd(sk3)))
| ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ~ ssList(cons(hd(sk3),nil)) )
<=> ( ~ ssList(cons(hd(sk3),nil))
| ~ ssList(sk5(hd(sk3)))
| ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5(hd(sk3)))
| ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ~ ssList(cons(hd(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(sk5(hd(sk3)))
| ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))) ) ),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5(hd(sk3)))
| ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ~ ssList(cons(hd(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(sk5(hd(sk3)))
| ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))) ) ),
inference(transitivity,[status(thm)],[157,155]) ).
tff(159,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5(hd(sk3)))
| ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ~ ssList(cons(hd(sk3),nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(sk5(hd(sk3)))
| ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))),
inference(unit_resolution,[status(thm)],[160,154,144,49]) ).
tff(162,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(hd(sk3),nil))
| ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(hd(sk3),nil))
| ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(hd(sk3),nil))
| ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(hd(sk3),nil))
| ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
( ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3)))) ),
inference(unit_resolution,[status(thm)],[164,154,49]) ).
tff(166,plain,
ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))),
inference(unit_resolution,[status(thm)],[165,161]) ).
tff(167,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(168,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(169,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
( ( nil = sk2 )
<=> ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,axiom,
nil = sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(172,plain,
nil = sk2,
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
nil = sk4,
inference(transitivity,[status(thm)],[172,169]) ).
tff(174,plain,
( segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
<=> segmentP(sk4,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))) ),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
( segmentP(sk4,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
<=> segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))) ),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
^ [A: $i] :
refl(( ( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) )
<=> ( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) ) )),
inference(bind,[status(th)],[]) ).
tff(177,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) ) ),
inference(quant_intro,[status(thm)],[176]) ).
tff(178,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(179,plain,
^ [A: $i] :
rewrite(( ( ~ ssItem(A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil)))
| ~ memberP(sk3,A) )
<=> ( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) ) )),
inference(bind,[status(th)],[]) ).
tff(180,plain,
( ! [A: $i] :
( ~ ssItem(A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil)))
| ~ memberP(sk3,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) ) ),
inference(quant_intro,[status(thm)],[179]) ).
tff(181,axiom,
! [A: $i] :
( ~ ssItem(A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil)))
| ~ memberP(sk3,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(182,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) ),
inference(modus_ponens,[status(thm)],[182,178]) ).
tff(184,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) ),
inference(skolemize,[status(sab)],[183]) ).
tff(185,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) ),
inference(modus_ponens,[status(thm)],[184,177]) ).
tff(186,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk3,hd(sk3))
| segmentP(sk4,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk3,hd(sk3))
| segmentP(sk4,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk3,hd(sk3))
| segmentP(sk4,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(188,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ memberP(sk3,A)
| segmentP(sk4,app(app(cons(A,nil),sk5(A)),cons(A,nil))) )
| ~ ssItem(hd(sk3))
| ~ memberP(sk3,hd(sk3))
| segmentP(sk4,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
( ~ memberP(sk3,hd(sk3))
| segmentP(sk4,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))) ),
inference(unit_resolution,[status(thm)],[188,185,29]) ).
tff(190,plain,
segmentP(sk4,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))),
inference(unit_resolution,[status(thm)],[189,126]) ).
tff(191,plain,
segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))),
inference(modus_ponens,[status(thm)],[190,175]) ).
tff(192,plain,
( ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) )
<=> ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) = nil ) ),
inference(commutativity,[status(thm)],[]) ).
tff(193,plain,
( ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) = nil )
<=> ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) ) ),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
( ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil )
<=> ( nil != app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) ) ),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
( ( nil = cons(hd(sk3),nil) )
<=> ( cons(hd(sk3),nil) = nil ) ),
inference(commutativity,[status(thm)],[]) ).
tff(196,plain,
( ( cons(hd(sk3),nil) = nil )
<=> ( nil = cons(hd(sk3),nil) ) ),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
( ( cons(hd(sk3),nil) != nil )
<=> ( nil != cons(hd(sk3),nil) ) ),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(199,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[198]) ).
tff(200,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( cons(U,V) != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(202,plain,
( ! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
tff(204,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[204,200]) ).
tff(206,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(skolemize,[status(sab)],[205]) ).
tff(207,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[206,199]) ).
tff(208,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ( cons(hd(sk3),nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ( cons(hd(sk3),nil) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(209,plain,
( ( ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( cons(hd(sk3),nil) != nil ) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ( cons(hd(sk3),nil) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(210,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( cons(hd(sk3),nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ( cons(hd(sk3),nil) != nil ) ) ),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( cons(hd(sk3),nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ( cons(hd(sk3),nil) != nil ) ) ),
inference(transitivity,[status(thm)],[210,208]) ).
tff(212,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( cons(hd(sk3),nil) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ( cons(hd(sk3),nil) != nil ) ),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
cons(hd(sk3),nil) != nil,
inference(unit_resolution,[status(thm)],[213,42,207,29]) ).
tff(215,plain,
nil != cons(hd(sk3),nil),
inference(modus_ponens,[status(thm)],[214,197]) ).
tff(216,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(217,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[216]) ).
tff(218,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(219,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(220,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[219]) ).
tff(221,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).
tff(222,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[222,218]) ).
tff(224,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(skolemize,[status(sab)],[223]) ).
tff(225,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[224,217]) ).
tff(226,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(hd(sk3),nil))
| ( nil = cons(hd(sk3),nil) )
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(hd(sk3),nil))
| ( nil = cons(hd(sk3),nil) )
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(227,plain,
( ( ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil )
| ( nil = cons(hd(sk3),nil) ) )
<=> ( ~ ssList(cons(hd(sk3),nil))
| ( nil = cons(hd(sk3),nil) )
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil )
| ( nil = cons(hd(sk3),nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(hd(sk3),nil))
| ( nil = cons(hd(sk3),nil) )
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil ) ) ),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil )
| ( nil = cons(hd(sk3),nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(hd(sk3),nil))
| ( nil = cons(hd(sk3),nil) )
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil ) ) ),
inference(transitivity,[status(thm)],[228,226]) ).
tff(230,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil )
| ( nil = cons(hd(sk3),nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(231,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(hd(sk3),nil))
| ( nil = cons(hd(sk3),nil) )
| ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil ) ),
inference(modus_ponens,[status(thm)],[230,229]) ).
tff(232,plain,
( ~ ssList(app(cons(hd(sk3),nil),sk5(hd(sk3))))
| ( app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil ) ),
inference(unit_resolution,[status(thm)],[231,225,49,215]) ).
tff(233,plain,
app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) != nil,
inference(unit_resolution,[status(thm)],[232,161]) ).
tff(234,plain,
nil != app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)),
inference(modus_ponens,[status(thm)],[233,194]) ).
tff(235,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(236,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(quant_intro,[status(thm)],[235]) ).
tff(237,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(238,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ~ segmentP(nil,U)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ segmentP(nil,U) ) )),
( ( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ segmentP(nil,U)
| ( nil = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ segmentP(nil,U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
( ( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(239,plain,
( ! [U: $i] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(quant_intro,[status(thm)],[238]) ).
tff(240,axiom,
! [U: $i] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause80) ).
tff(241,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[240,239]) ).
tff(242,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[241,237]) ).
tff(243,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(skolemize,[status(sab)],[242]) ).
tff(244,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[243,236]) ).
tff(245,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(246,plain,
( ( ~ ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) )
| ~ segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))) )
<=> ( ~ ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(247,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) )
| ~ segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) ) ) ),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) )
| ~ segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) ) ) ),
inference(transitivity,[status(thm)],[247,245]) ).
tff(249,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) )
| ~ segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) ) ),
inference(modus_ponens,[status(thm)],[249,248]) ).
tff(251,plain,
( ~ ssList(app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ~ segmentP(nil,app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)))
| ( nil = app(app(cons(hd(sk3),nil),sk5(hd(sk3))),cons(hd(sk3),nil)) ) ),
inference(unit_resolution,[status(thm)],[250,244]) ).
tff(252,plain,
$false,
inference(unit_resolution,[status(thm)],[251,234,191,166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC045-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 08:06:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.60/1.76 % SZS status Unsatisfiable
% 1.60/1.76 % SZS output start Proof
% See solution above
% 1.60/1.79 % E exiting
%------------------------------------------------------------------------------