%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC363-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:31:01 AM UTC 2025
% Result : Unsatisfiable 0.84s 1.06s
% Output : Proof 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 82
% Syntax : Number of formulae : 205 ( 68 unt; 0 typ; 0 def)
% Number of atoms : 1131 ( 135 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 1669 ( 807 ~; 760 |; 0 &)
% ( 102 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 64 ( 64 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 359 ( 326 !; 0 ?; 359 :)
% Comments :
%------------------------------------------------------------------------------
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(skaf43_type,type,
skaf43: ( $i * $i ) > $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(nil_type,type,
nil: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(skaf45_type,type,
skaf45: ( $i * $i ) > $i ).
tff(skaf42_type,type,
skaf42: ( $i * $i ) > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(1,plain,
^ [V: $i,U: $i] :
refl(( ssList(skaf43(U,V))
<=> ssList(skaf43(U,V)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).
tff(5,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf43(U,V))
| ssList(skaf43(sk5,sk4)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ssList(skaf43(sk5,sk4)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(12,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(16,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(20,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[20,17]) ).
tff(22,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(23,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)],[22]) ).
tff(24,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(25,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(26,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)],[25]) ).
tff(27,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(28,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ),
inference(unit_resolution,[status(thm)],[34,31,21]) ).
tff(36,plain,
app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)),
inference(unit_resolution,[status(thm)],[35,9]) ).
tff(37,plain,
( ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(39,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[39,37]) ).
tff(41,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[42,37]) ).
tff(44,plain,
cons(sk5,nil) = sk3,
inference(unit_resolution,[status(thm)],[43,17]) ).
tff(45,plain,
sk3 = cons(sk5,nil),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(48,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(53,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,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(57,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[58,55,48]) ).
tff(60,plain,
app(nil,sk3) = cons(sk5,nil),
inference(transitivity,[status(thm)],[59,45]) ).
tff(61,plain,
app(app(nil,sk3),skaf43(sk5,sk4)) = app(cons(sk5,nil),skaf43(sk5,sk4)),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
app(app(nil,sk3),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)),
inference(transitivity,[status(thm)],[61,36]) ).
tff(63,plain,
( segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3)
<=> segmentP(cons(sk5,skaf43(sk5,sk4)),sk3) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
<=> segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3) ),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
<=> ~ segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,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(67,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,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(69,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(70,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)],[69]) ).
tff(71,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(72,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ssList(cons(sk5,skaf43(sk5,sk4))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ssList(cons(sk5,skaf43(sk5,sk4))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ssList(cons(sk5,skaf43(sk5,sk4))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ssList(cons(sk5,skaf43(sk5,sk4))) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( ~ ssList(skaf43(sk5,sk4))
| ssList(cons(sk5,skaf43(sk5,sk4))) ),
inference(unit_resolution,[status(thm)],[78,75,21]) ).
tff(80,plain,
ssList(cons(sk5,skaf43(sk5,sk4))),
inference(unit_resolution,[status(thm)],[79,9]) ).
tff(81,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(83,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[12]) ).
tff(86,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
tff(88,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| frontsegP(U,U) )
<=> ( ~ ssList(U)
| frontsegP(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause61) ).
tff(93,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk4)
| frontsegP(sk4,sk4) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk4)
| frontsegP(sk4,sk4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk4)
| frontsegP(sk4,sk4) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk4)
| frontsegP(sk4,sk4) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
frontsegP(sk4,sk4),
inference(unit_resolution,[status(thm)],[98,95,88]) ).
tff(100,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(101,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ frontsegP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ~ frontsegP(U,V)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ~ frontsegP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(104,plain,
( ! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,axiom,
! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause132) ).
tff(106,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk4)
| ( app(sk4,skaf45(sk4,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk4)
| ( app(sk4,skaf45(sk4,sk4)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk4)
| ( app(sk4,skaf45(sk4,sk4)) = sk4 ) )
<=> ( ~ ssList(sk4)
| ~ frontsegP(sk4,sk4)
| ( app(sk4,skaf45(sk4,sk4)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk4)
| ( app(sk4,skaf45(sk4,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk4)
| ( app(sk4,skaf45(sk4,sk4)) = sk4 ) ) ),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk4)
| ( app(sk4,skaf45(sk4,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk4)
| ( app(sk4,skaf45(sk4,sk4)) = sk4 ) ) ),
inference(transitivity,[status(thm)],[112,110]) ).
tff(114,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk4)
| ( app(sk4,skaf45(sk4,sk4)) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk4)
| ( app(sk4,skaf45(sk4,sk4)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
app(sk4,skaf45(sk4,sk4)) = sk4,
inference(unit_resolution,[status(thm)],[115,109,88,99]) ).
tff(117,plain,
( ( memberP(sk4,sk5)
| ~ neq(sk4,nil) )
<=> ( memberP(sk4,sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,axiom,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(119,plain,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[119,117]) ).
tff(121,plain,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[120,117]) ).
tff(122,plain,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[122,117]) ).
tff(124,plain,
memberP(sk4,sk5),
inference(unit_resolution,[status(thm)],[123,17]) ).
tff(125,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,axiom,
! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
tff(131,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4,
inference(unit_resolution,[status(thm)],[137,134,88,21,124]) ).
tff(139,plain,
app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)) = app(sk4,skaf45(sk4,sk4)),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)) = sk2,
inference(transitivity,[status(thm)],[139,116,85]) ).
tff(141,plain,
( segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3)
<=> segmentP(sk2,sk1) ),
inference(monotonicity,[status(thm)],[140,84]) ).
tff(142,plain,
( segmentP(sk2,sk1)
<=> segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3) ),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(sk2,sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,axiom,
~ segmentP(sk2,sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(146,plain,
~ segmentP(sk2,sk1),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
~ segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3),
inference(modus_ponens,[status(thm)],[146,143]) ).
tff(148,plain,
^ [V: $i,U: $i] :
refl(( ssList(skaf45(U,V))
<=> ssList(skaf45(U,V)) )),
inference(bind,[status(th)],[]) ).
tff(149,plain,
( ! [V: $i,U: $i] : ssList(skaf45(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf45(U,V)) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,plain,
( ! [V: $i,U: $i] : ssList(skaf45(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf45(U,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(151,axiom,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
tff(152,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(skolemize,[status(sab)],[152]) ).
tff(154,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(modus_ponens,[status(thm)],[153,149]) ).
tff(155,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf45(U,V))
| ssList(skaf45(sk4,sk4)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
ssList(skaf45(sk4,sk4)),
inference(unit_resolution,[status(thm)],[155,154]) ).
tff(157,plain,
^ [V: $i,U: $i] :
refl(( ssList(skaf42(U,V))
<=> ssList(skaf42(U,V)) )),
inference(bind,[status(th)],[]) ).
tff(158,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,axiom,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).
tff(161,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(skolemize,[status(sab)],[161]) ).
tff(163,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[162,158]) ).
tff(164,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf42(U,V))
| ssList(skaf42(sk4,sk5)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
ssList(skaf42(sk4,sk5)),
inference(unit_resolution,[status(thm)],[164,163]) ).
tff(166,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
inference(bind,[status(th)],[]) ).
tff(167,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ segmentP(U,V)
| ~ ssList(W) )
<=> ( ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) ) )),
rewrite(( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(V) ) )),
rewrite(( ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(app(app(X,U),W),V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
inference(bind,[status(th)],[]) ).
tff(170,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause172) ).
tff(172,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[172,168]) ).
tff(174,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(skolemize,[status(sab)],[173]) ).
tff(175,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[174,167]) ).
tff(176,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| ~ ssList(skaf45(sk4,sk4))
| ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
| segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| ~ ssList(skaf45(sk4,sk4))
| ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
| segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,plain,
( ( ~ ssList(skaf42(sk4,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| ~ ssList(sk3)
| ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
| segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3)
| ~ ssList(skaf45(sk4,sk4)) )
<=> ( ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| ~ ssList(skaf45(sk4,sk4))
| ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
| segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| ~ ssList(sk3)
| ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
| segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3)
| ~ ssList(skaf45(sk4,sk4)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| ~ ssList(skaf45(sk4,sk4))
| ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
| segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3) ) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| ~ ssList(sk3)
| ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
| segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3)
| ~ ssList(skaf45(sk4,sk4)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| ~ ssList(skaf45(sk4,sk4))
| ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
| segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3) ) ),
inference(transitivity,[status(thm)],[178,176]) ).
tff(180,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| ~ ssList(sk3)
| ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
| segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3)
| ~ ssList(skaf45(sk4,sk4)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| ~ ssList(skaf45(sk4,sk4))
| ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
| segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
( ~ ssList(cons(sk5,skaf43(sk5,sk4)))
| ~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3)
| segmentP(app(app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),skaf45(sk4,sk4)),sk3) ),
inference(unit_resolution,[status(thm)],[181,175,48,165,156]) ).
tff(183,plain,
~ segmentP(cons(sk5,skaf43(sk5,sk4)),sk3),
inference(unit_resolution,[status(thm)],[182,147,80]) ).
tff(184,plain,
~ segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3),
inference(modus_ponens,[status(thm)],[183,65]) ).
tff(185,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| segmentP(U,U) )
<=> ( ~ ssList(U)
| segmentP(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(186,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(quant_intro,[status(thm)],[185]) ).
tff(187,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
tff(189,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(skolemize,[status(sab)],[189]) ).
tff(191,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[190,186]) ).
tff(192,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(193,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[193,192]) ).
tff(195,plain,
segmentP(sk3,sk3),
inference(unit_resolution,[status(thm)],[194,191,48]) ).
tff(196,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(198,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ~ ssList(skaf43(sk5,sk4))
| segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ~ ssList(skaf43(sk5,sk4))
| segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(200,plain,
( ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3)
| ~ ssList(skaf43(sk5,sk4)) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ~ ssList(skaf43(sk5,sk4))
| segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3)
| ~ ssList(skaf43(sk5,sk4)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ~ ssList(skaf43(sk5,sk4))
| segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3) ) ),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3)
| ~ ssList(skaf43(sk5,sk4)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ~ ssList(skaf43(sk5,sk4))
| segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3) ) ),
inference(transitivity,[status(thm)],[201,199]) ).
tff(203,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3)
| ~ ssList(skaf43(sk5,sk4)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ~ ssList(skaf43(sk5,sk4))
| segmentP(app(app(nil,sk3),skaf43(sk5,sk4)),sk3) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
$false,
inference(unit_resolution,[status(thm)],[204,198,175,48,195,9,184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC363-1 : TPTP v9.0.0. Released v2.4.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:07:37 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.84/1.06 % SZS status Unsatisfiable
% 0.84/1.06 % SZS output start Proof
% See solution above
% 0.92/1.09 % E exiting
%------------------------------------------------------------------------------