%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC232-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:30:36 AM UTC 2025
% Result : Unsatisfiable 1.69s 1.88s
% Output : Proof 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 67
% Syntax : Number of formulae : 159 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 997 ( 232 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1522 ( 731 ~; 706 |; 0 &)
% ( 85 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 332 ( 299 !; 0 ?; 332 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: ( $i * $i * $i ) > $i ).
tff(skaf83_type,type,
skaf83: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(nil_type,type,
nil: $i ).
tff(skaf82_type,type,
skaf82: $i > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(7,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[17,14,7]) ).
tff(19,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(20,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(23,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
tff(31,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
cons(skaf83(sk3),skaf82(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[37,34,7,24]) ).
tff(39,plain,
^ [U: $i] :
refl(( ssList(skaf82(U))
<=> ssList(skaf82(U)) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
! [U: $i] : ssList(skaf82(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
tff(43,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [U: $i] : ssList(skaf82(U)),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [U: $i] : ssList(skaf82(U))
| ssList(skaf82(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
ssList(skaf82(sk3)),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
^ [U: $i] :
refl(( ssItem(skaf83(U))
<=> ssItem(skaf83(U)) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
! [U: $i] : ssItem(skaf83(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
tff(52,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [U: $i] : ssItem(skaf83(U))
| ssItem(skaf83(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
ssItem(skaf83(sk3)),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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(61,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,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(63,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(unit_resolution,[status(thm)],[69,66]) ).
tff(71,plain,
app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)),
inference(unit_resolution,[status(thm)],[70,56,47]) ).
tff(72,plain,
app(cons(skaf83(sk3),nil),skaf82(sk3)) = sk3,
inference(transitivity,[status(thm)],[71,38]) ).
tff(73,plain,
app(nil,app(cons(skaf83(sk3),nil),skaf82(sk3))) = app(nil,sk3),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,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(75,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)],[74]) ).
tff(76,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(77,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(78,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)],[77]) ).
tff(79,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(80,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(86,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ssList(cons(skaf83(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ssList(cons(skaf83(sk3),nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssList(cons(skaf83(sk3),nil)) )
<=> ( ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ssList(cons(skaf83(sk3),nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssList(cons(skaf83(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ssList(cons(skaf83(sk3),nil)) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssList(cons(skaf83(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ssList(cons(skaf83(sk3),nil)) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssList(cons(skaf83(sk3),nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ssList(cons(skaf83(sk3),nil)) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
ssList(cons(skaf83(sk3),nil)),
inference(unit_resolution,[status(thm)],[92,86,83,56]) ).
tff(94,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(95,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)],[94]) ).
tff(96,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(97,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(98,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)],[97]) ).
tff(99,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(100,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)],[99,98]) ).
tff(101,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)],[100,96]) ).
tff(102,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)],[101]) ).
tff(103,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)],[102,95]) ).
tff(104,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(skaf82(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(skaf83(sk3),nil),skaf82(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(skaf82(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(skaf83(sk3),nil),skaf82(sk3))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ( ~ ssList(skaf82(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(skaf83(sk3),nil),skaf82(sk3))) ) )
<=> ( ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(skaf83(sk3),nil),skaf82(sk3))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(skaf83(sk3),nil),skaf82(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(skaf82(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(skaf83(sk3),nil),skaf82(sk3))) ) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(skaf83(sk3),nil),skaf82(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(skaf82(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(skaf83(sk3),nil),skaf82(sk3))) ) ) ),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(skaf83(sk3),nil),skaf82(sk3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,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(skaf82(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(skaf83(sk3),nil),skaf82(sk3))) ) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(skaf83(sk3),nil),skaf82(sk3))),
inference(unit_resolution,[status(thm)],[109,86,103,47,93]) ).
tff(111,plain,
app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) = sk1,
inference(transitivity,[status(thm)],[110,73,18,4]) ).
tff(112,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(113,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(118,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[120,113]) ).
tff(122,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,plain,
( ( ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) )
<=> ( ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) ) ),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) ) ),
inference(transitivity,[status(thm)],[124,122]) ).
tff(126,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))),
inference(unit_resolution,[status(thm)],[127,86,121,47,56,111]) ).
tff(129,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(133,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(135,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(skolemize,[status(sab)],[136]) ).
tff(138,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[137,130]) ).
tff(139,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,skaf83(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,skaf83(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,plain,
( ( ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssItem(sk5(skaf82(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 ) )
<=> ( ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,skaf83(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssItem(sk5(skaf82(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,skaf83(sk3))) ) ),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssItem(sk5(skaf82(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,skaf83(sk3))) ) ),
inference(transitivity,[status(thm)],[141,139]) ).
tff(143,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssItem(sk5(skaf82(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,skaf83(sk3))) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
ssItem(sk5(skaf82(sk3),nil,skaf83(sk3))),
inference(unit_resolution,[status(thm)],[144,86,138,47,56,111]) ).
tff(146,plain,
^ [U: $i] :
refl(( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(147,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,plain,
^ [U: $i] :
rewrite(( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(150,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(152,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[152,148]) ).
tff(154,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[153]) ).
tff(155,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[154,147]) ).
tff(156,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf82(sk3),nil,skaf83(sk3)))
| ~ memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf82(sk3),nil,skaf83(sk3)))
| ~ memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf82(sk3),nil,skaf83(sk3)))
| ~ memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf82(sk3),nil,skaf83(sk3)))
| ~ memberP(nil,sk5(skaf82(sk3),nil,skaf83(sk3))) ),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
$false,
inference(unit_resolution,[status(thm)],[158,155,145,128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWC232-1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 08:41:23 EDT 2025
% 0.14/0.36 % CPUTime :
% 1.69/1.88 % SZS status Unsatisfiable
% 1.69/1.88 % SZS output start Proof
% See solution above
% 1.69/1.91 % E exiting
%------------------------------------------------------------------------------