%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC265-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:30:44 AM UTC 2025
% Result : Unsatisfiable 0.68s 0.84s
% Output : Proof 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 107
% Syntax : Number of formulae : 264 ( 80 unt; 0 typ; 0 def)
% Number of atoms : 1853 ( 227 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 2847 (1361 ~;1332 |; 0 &)
% ( 154 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 103 ( 103 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 : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 564 ( 514 !; 0 ?; 564 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(skaf64_type,type,
skaf64: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(skaf67_type,type,
skaf67: $i > $i ).
tff(skaf66_type,type,
skaf66: $i > $i ).
tff(nil_type,type,
nil: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(skaf68_type,type,
skaf68: $i > $i ).
tff(skaf65_type,type,
skaf65: $i > $i ).
tff(totalorderedP_type,type,
totalorderedP: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(1,plain,
^ [U: $i] :
refl(( ssList(skaf66(U))
<=> ssList(skaf66(U)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [U: $i] : ssList(skaf66(U))
<=> ! [U: $i] : ssList(skaf66(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [U: $i] : ssList(skaf66(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause29) ).
tff(5,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [U: $i] : ssList(skaf66(U)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [U: $i] : ssList(skaf66(U)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [U: $i] : ssList(skaf66(U))
| ssList(skaf66(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ssList(skaf66(sk3)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [U: $i] :
refl(( ssItem(skaf64(U))
<=> ssItem(skaf64(U)) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [U: $i] : ssItem(skaf64(U))
<=> ! [U: $i] : ssItem(skaf64(U)) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [U: $i] : ssItem(skaf64(U))
<=> ! [U: $i] : ssItem(skaf64(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [U: $i] : ssItem(skaf64(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause31) ).
tff(14,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [U: $i] : ssItem(skaf64(U)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [U: $i] : ssItem(skaf64(U))
| ssItem(skaf64(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ssItem(skaf64(sk3)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [U: $i] :
refl(( ssList(skaf67(U))
<=> ssList(skaf67(U)) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [U: $i] : ssList(skaf67(U))
<=> ! [U: $i] : ssList(skaf67(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [U: $i] : ssList(skaf67(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause28) ).
tff(23,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [U: $i] : ssList(skaf67(U)),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [U: $i] : ssList(skaf67(U)),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [U: $i] : ssList(skaf67(U))
| ssList(skaf67(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
ssList(skaf67(sk3)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,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(29,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)],[28]) ).
tff(30,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(31,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(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(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(34,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ssList(cons(skaf64(sk3),skaf67(sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ssList(cons(skaf64(sk3),skaf67(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ssList(cons(skaf64(sk3),skaf67(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ssList(cons(skaf64(sk3),skaf67(sk3))) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ssList(cons(skaf64(sk3),skaf67(sk3))) ),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
ssList(cons(skaf64(sk3),skaf67(sk3))),
inference(unit_resolution,[status(thm)],[41,27,18]) ).
tff(43,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(44,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)],[43]) ).
tff(45,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(46,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(47,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)],[46]) ).
tff(48,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(49,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf66(sk3)) )
<=> ( ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf66(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf66(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(skaf66(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(cons(skaf64(sk3),skaf67(sk3)))
| ~ ssList(skaf66(sk3)) ),
inference(unit_resolution,[status(thm)],[58,52]) ).
tff(60,plain,
ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),
inference(unit_resolution,[status(thm)],[59,42,9]) ).
tff(61,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(65,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))) = app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),
inference(unit_resolution,[status(thm)],[70,67,60]) ).
tff(72,plain,
( memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3))
<=> memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3))
<=> memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3)) ),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
^ [W: $i,V: $i,U: $i] :
rewrite(( ( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(80,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(81,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) ) ),
inference(transitivity,[status(thm)],[80,79]) ).
tff(82,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(transitivity,[status(thm)],[81,78]) ).
tff(83,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause175) ).
tff(87,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(modus_ponens,[status(thm)],[87,76]) ).
tff(89,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(modus_ponens,[status(thm)],[89,75]) ).
tff(91,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(skaf66(sk3))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(skaf66(sk3))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ( ~ ssList(skaf66(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) )
<=> ( ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(skaf66(sk3))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(skaf66(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(skaf66(sk3))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) ) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(skaf66(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(skaf66(sk3))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) ) ),
inference(transitivity,[status(thm)],[93,91]) ).
tff(95,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(skaf66(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(skaf66(sk3))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
( ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssItem(skaf64(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(skaf66(sk3))
| memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)) ),
inference(unit_resolution,[status(thm)],[96,90]) ).
tff(98,plain,
memberP(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),skaf64(sk3)),
inference(unit_resolution,[status(thm)],[97,60,27,9,18]) ).
tff(99,plain,
memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3)),
inference(modus_ponens,[status(thm)],[98,73]) ).
tff(100,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(102,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,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(104,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[105,67,102]) ).
tff(107,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(109,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
( totalorderedP(sk3)
<=> totalorderedP(sk1) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( totalorderedP(sk1)
<=> totalorderedP(sk3) ),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
( ~ totalorderedP(sk1)
<=> ~ totalorderedP(sk3) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ~ totalorderedP(sk1)
<=> ~ totalorderedP(sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,axiom,
~ totalorderedP(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(116,plain,
~ totalorderedP(sk1),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
~ totalorderedP(sk3),
inference(modus_ponens,[status(thm)],[116,113]) ).
tff(118,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| totalorderedP(U) )
<=> ( ~ ssList(U)
| totalorderedP(U) ) )),
( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
rewrite(( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
( ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,axiom,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause164) ).
tff(124,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ),
inference(modus_ponens,[status(thm)],[126,119]) ).
tff(128,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
( totalorderedP(sk3)
| ( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ) ),
inference(unit_resolution,[status(thm)],[130,127,102]) ).
tff(132,plain,
app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3,
inference(unit_resolution,[status(thm)],[131,117]) ).
tff(133,plain,
app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) = app(nil,sk3),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
^ [U: $i] :
refl(( ssItem(skaf65(U))
<=> ssItem(skaf65(U)) )),
inference(bind,[status(th)],[]) ).
tff(135,plain,
( ! [U: $i] : ssItem(skaf65(U))
<=> ! [U: $i] : ssItem(skaf65(U)) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,plain,
( ! [U: $i] : ssItem(skaf65(U))
<=> ! [U: $i] : ssItem(skaf65(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,axiom,
! [U: $i] : ssItem(skaf65(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause30) ).
tff(138,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [U: $i] : ssItem(skaf65(U)),
inference(modus_ponens,[status(thm)],[139,135]) ).
tff(141,plain,
( ~ ! [U: $i] : ssItem(skaf65(U))
| ssItem(skaf65(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
ssItem(skaf65(sk3)),
inference(unit_resolution,[status(thm)],[141,140]) ).
tff(143,plain,
^ [U: $i] :
refl(( ssList(skaf68(U))
<=> ssList(skaf68(U)) )),
inference(bind,[status(th)],[]) ).
tff(144,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,plain,
( ! [U: $i] : ssList(skaf68(U))
<=> ! [U: $i] : ssList(skaf68(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,axiom,
! [U: $i] : ssList(skaf68(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause27) ).
tff(147,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
! [U: $i] : ssList(skaf68(U)),
inference(skolemize,[status(sab)],[147]) ).
tff(149,plain,
! [U: $i] : ssList(skaf68(U)),
inference(modus_ponens,[status(thm)],[148,144]) ).
tff(150,plain,
( ~ ! [U: $i] : ssList(skaf68(U))
| ssList(skaf68(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
ssList(skaf68(sk3)),
inference(unit_resolution,[status(thm)],[150,149]) ).
tff(152,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ssList(cons(skaf65(sk3),skaf68(sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ssList(cons(skaf65(sk3),skaf68(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ssList(cons(skaf65(sk3),skaf68(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ssList(cons(skaf65(sk3),skaf68(sk3))) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
( ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ssList(cons(skaf65(sk3),skaf68(sk3))) ),
inference(unit_resolution,[status(thm)],[154,37]) ).
tff(156,plain,
ssList(cons(skaf65(sk3),skaf68(sk3))),
inference(unit_resolution,[status(thm)],[155,151,142]) ).
tff(157,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(158,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(161,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[160]) ).
tff(162,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(163,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[163,159]) ).
tff(165,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(skolemize,[status(sab)],[164]) ).
tff(166,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[165,158]) ).
tff(167,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(168,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(169,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,plain,
( ( ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(nil)
| ( app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) )
<=> ( ~ ssList(nil)
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(nil)
| ( app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) ) ),
inference(monotonicity,[status(thm)],[171]) ).
tff(173,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(nil)
| ( app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) ) ),
inference(transitivity,[status(thm)],[172,170]) ).
tff(174,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ~ ssList(nil)
| ( app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
( ~ ssList(cons(skaf65(sk3),skaf68(sk3)))
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ( app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ) ),
inference(unit_resolution,[status(thm)],[175,169,166]) ).
tff(177,plain,
app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))) = app(nil,app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))),
inference(unit_resolution,[status(thm)],[176,60,156]) ).
tff(178,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(179,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)],[178]) ).
tff(180,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(181,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(182,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)],[181]) ).
tff(183,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(184,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[184,180]) ).
tff(186,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[185]) ).
tff(187,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[186,179]) ).
tff(188,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ( app(cons(skaf65(sk3),nil),skaf68(sk3)) = cons(skaf65(sk3),skaf68(sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ( app(cons(skaf65(sk3),nil),skaf68(sk3)) = cons(skaf65(sk3),skaf68(sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(189,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ( app(cons(skaf65(sk3),nil),skaf68(sk3)) = cons(skaf65(sk3),skaf68(sk3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ( app(cons(skaf65(sk3),nil),skaf68(sk3)) = cons(skaf65(sk3),skaf68(sk3)) ) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
( ~ ssItem(skaf65(sk3))
| ~ ssList(skaf68(sk3))
| ( app(cons(skaf65(sk3),nil),skaf68(sk3)) = cons(skaf65(sk3),skaf68(sk3)) ) ),
inference(unit_resolution,[status(thm)],[190,187]) ).
tff(192,plain,
app(cons(skaf65(sk3),nil),skaf68(sk3)) = cons(skaf65(sk3),skaf68(sk3)),
inference(unit_resolution,[status(thm)],[191,151,142]) ).
tff(193,plain,
app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),app(cons(skaf65(sk3),nil),skaf68(sk3))) = app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),skaf68(sk3))),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(195,plain,
( ( ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ~ ssList(nil) )
<=> ( ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(196,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ~ ssList(nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) ) ),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ~ ssList(nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) ) ),
inference(transitivity,[status(thm)],[196,194]) ).
tff(198,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ~ ssList(nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))
| ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))))),
inference(unit_resolution,[status(thm)],[199,169,52,60]) ).
tff(201,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf65(sk3))
| ssList(cons(skaf65(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf65(sk3))
| ssList(cons(skaf65(sk3),nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(202,plain,
( ( ~ ssItem(skaf65(sk3))
| ~ ssList(nil)
| ssList(cons(skaf65(sk3),nil)) )
<=> ( ~ ssList(nil)
| ~ ssItem(skaf65(sk3))
| ssList(cons(skaf65(sk3),nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(203,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(nil)
| ssList(cons(skaf65(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf65(sk3))
| ssList(cons(skaf65(sk3),nil)) ) ),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(nil)
| ssList(cons(skaf65(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf65(sk3))
| ssList(cons(skaf65(sk3),nil)) ) ),
inference(transitivity,[status(thm)],[203,201]) ).
tff(205,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf65(sk3))
| ~ ssList(nil)
| ssList(cons(skaf65(sk3),nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(206,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf65(sk3))
| ssList(cons(skaf65(sk3),nil)) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
ssList(cons(skaf65(sk3),nil)),
inference(unit_resolution,[status(thm)],[206,169,37,142]) ).
tff(208,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf68(sk3))
| ~ ssList(cons(skaf65(sk3),nil))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) = app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),app(cons(skaf65(sk3),nil),skaf68(sk3))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf68(sk3))
| ~ ssList(cons(skaf65(sk3),nil))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) = app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),app(cons(skaf65(sk3),nil),skaf68(sk3))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(209,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf68(sk3))
| ~ ssList(cons(skaf65(sk3),nil))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) = app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),app(cons(skaf65(sk3),nil),skaf68(sk3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf68(sk3))
| ~ ssList(cons(skaf65(sk3),nil))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) = app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),app(cons(skaf65(sk3),nil),skaf68(sk3))) ) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
( ~ ssList(cons(skaf65(sk3),nil))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) = app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),app(cons(skaf65(sk3),nil),skaf68(sk3))) ) ),
inference(unit_resolution,[status(thm)],[210,166,151]) ).
tff(212,plain,
app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) = app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),app(cons(skaf65(sk3),nil),skaf68(sk3))),
inference(unit_resolution,[status(thm)],[211,207,200]) ).
tff(213,plain,
app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) = sk3,
inference(transitivity,[status(thm)],[212,193,177,133,106]) ).
tff(214,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(215,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) ),
inference(quant_intro,[status(thm)],[214]) ).
tff(216,plain,
( ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(217,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
( ( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) )
<=> ( ~ ssList(U)
| ~ leq(skaf64(U),skaf65(U))
| totalorderedP(U) ) )),
rewrite(( ( ~ ssList(U)
| ~ leq(skaf64(U),skaf65(U))
| totalorderedP(U) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
( ( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) )
<=> ( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(218,plain,
( ! [U: $i] :
( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) )
<=> ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ) ),
inference(quant_intro,[status(thm)],[217]) ).
tff(219,axiom,
! [U: $i] :
( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause91) ).
tff(220,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[220,216]) ).
tff(222,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(skolemize,[status(sab)],[221]) ).
tff(223,plain,
! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) ),
inference(modus_ponens,[status(thm)],[222,215]) ).
tff(224,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(225,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(226,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| totalorderedP(U)
| ~ leq(skaf64(U),skaf65(U)) )
| ~ ssList(sk3)
| totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(modus_ponens,[status(thm)],[225,224]) ).
tff(227,plain,
( totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(unit_resolution,[status(thm)],[226,223,102]) ).
tff(228,plain,
~ leq(skaf64(sk3),skaf65(sk3)),
inference(unit_resolution,[status(thm)],[227,117]) ).
tff(229,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(230,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(quant_intro,[status(thm)],[229]) ).
tff(231,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(232,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ lt(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ~ lt(U,V)
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(V)
| ~ lt(U,V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| leq(U,V) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(233,plain,
( ! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(quant_intro,[status(thm)],[232]) ).
tff(234,axiom,
! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause103) ).
tff(235,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[234,233]) ).
tff(236,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[235,231]) ).
tff(237,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(skolemize,[status(sab)],[236]) ).
tff(238,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[237,230]) ).
tff(239,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(240,plain,
( ( ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| leq(skaf64(sk3),skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) )
<=> ( leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(241,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| leq(skaf64(sk3),skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| leq(skaf64(sk3),skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ) ),
inference(transitivity,[status(thm)],[241,239]) ).
tff(243,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| leq(skaf64(sk3),skaf65(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(244,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ),
inference(modus_ponens,[status(thm)],[243,242]) ).
tff(245,plain,
( ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ lt(skaf64(sk3),skaf65(sk3)) ),
inference(unit_resolution,[status(thm)],[244,238,228]) ).
tff(246,plain,
~ lt(skaf64(sk3),skaf65(sk3)),
inference(unit_resolution,[status(thm)],[245,18,142]) ).
tff(247,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) ) )),
inference(bind,[status(th)],[]) ).
tff(248,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) ) ),
inference(quant_intro,[status(thm)],[247]) ).
tff(249,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(250,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(D,A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| lt(D,A) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| lt(D,A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| lt(D,A) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(D,A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| lt(D,A) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(D,A)
| ~ memberP(B,D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| lt(D,A)
| ~ memberP(B,D) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| lt(D,A)
| ~ memberP(B,D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(D,A)
| ~ memberP(B,D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) ) )),
inference(bind,[status(th)],[]) ).
tff(251,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(D,A)
| ~ memberP(B,D) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) ) ),
inference(quant_intro,[status(thm)],[250]) ).
tff(252,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ ssItem(D)
| lt(D,A)
| ~ memberP(B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(253,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) ),
inference(modus_ponens,[status(thm)],[252,251]) ).
tff(254,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) ),
inference(modus_ponens,[status(thm)],[253,249]) ).
tff(255,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) ),
inference(skolemize,[status(sab)],[254]) ).
tff(256,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) ),
inference(modus_ponens,[status(thm)],[255,248]) ).
tff(257,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) != sk3 )
| ~ memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3)) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) != sk3 )
| ~ memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(258,plain,
( ( ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) != sk3 )
| ~ memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) != sk3 )
| ~ memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(259,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) != sk3 )
| ~ memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) != sk3 )
| ~ memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3)) ) ),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) != sk3 )
| ~ memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3)) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) != sk3 )
| ~ memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3)) ) ),
inference(transitivity,[status(thm)],[259,257]) ).
tff(261,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) != sk3 )
| ~ memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(262,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(D)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,D)
| lt(D,A) )
| ~ ssList(skaf68(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))))
| ( app(app(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),cons(skaf65(sk3),nil)),skaf68(sk3)) != sk3 )
| ~ memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3)) ),
inference(modus_ponens,[status(thm)],[261,260]) ).
tff(263,plain,
~ memberP(app(nil,app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3)))),skaf64(sk3)),
inference(unit_resolution,[status(thm)],[262,256,151,142,18,246,200,213]) ).
tff(264,plain,
$false,
inference(unit_resolution,[status(thm)],[263,99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC265-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:48:01 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.68/0.84 % SZS status Unsatisfiable
% 0.68/0.84 % SZS output start Proof
% See solution above
% 0.72/0.87 % E exiting
%------------------------------------------------------------------------------