TSTP Solution File: SWC229-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC229-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Tue Sep 20 11:56:19 EDT 2022
% Result : Unsatisfiable 1.25s 1.08s
% Output : Proof 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 109
% Syntax : Number of formulae : 245 ( 64 unt; 13 typ; 0 def)
% Number of atoms : 1692 ( 460 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 2555 (1188 ~;1228 |; 0 &)
% ( 139 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 93 ( 93 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 10 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 499 ( 446 !; 0 ?; 499 :)
% 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(tl_type,type,
tl: $i > $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(sk1_type,type,
sk1: $i ).
tff(skaf82_type,type,
skaf82: $i > $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(hd_type,type,
hd: $i > $i ).
tff(1,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(4,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(10,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,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(14,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[15,12,5]) ).
tff(17,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(20,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,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(23,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)],[22]) ).
tff(24,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(25,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(26,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)],[25]) ).
tff(27,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
tff(28,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,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(33,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(34,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)],[33,32]) ).
tff(35,plain,
cons(skaf83(sk3),skaf82(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[34,31,5,21]) ).
tff(36,plain,
^ [U: $i] :
refl(
( ssList(skaf82(U))
<=> ssList(skaf82(U)) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
! [U: $i] : ssList(skaf82(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
tff(40,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [U: $i] : ssList(skaf82(U)),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [U: $i] : ssList(skaf82(U))
| ssList(skaf82(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
ssList(skaf82(sk3)),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
^ [U: $i] :
refl(
( ssItem(skaf83(U))
<=> ssItem(skaf83(U)) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
! [U: $i] : ssItem(skaf83(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
tff(49,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [U: $i] : ssItem(skaf83(U))
| ssItem(skaf83(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
ssItem(skaf83(sk3)),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,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(55,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)],[54]) ).
tff(56,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(57,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(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,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(60,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,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(65,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(66,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)],[65,64]) ).
tff(67,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ( app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(unit_resolution,[status(thm)],[66,63]) ).
tff(68,plain,
app(cons(skaf83(sk3),nil),skaf82(sk3)) = cons(skaf83(sk3),skaf82(sk3)),
inference(unit_resolution,[status(thm)],[67,53,44]) ).
tff(69,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
tff(75,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
ssList(tl(sk3)),
inference(unit_resolution,[status(thm)],[84,78,5,21]) ).
tff(86,plain,
sk3 = cons(skaf83(sk3),skaf82(sk3)),
inference(symmetry,[status(thm)],[35]) ).
tff(87,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
tff(93,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[95,88]) ).
tff(97,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
cons(hd(sk3),tl(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[99,96,5,21]) ).
tff(101,plain,
cons(hd(sk3),tl(sk3)) = cons(skaf83(sk3),skaf82(sk3)),
inference(transitivity,[status(thm)],[100,86]) ).
tff(102,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(108,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[110,103]) ).
tff(112,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(transitivity,[status(thm)],[114,112]) ).
tff(116,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
ssItem(hd(sk3)),
inference(unit_resolution,[status(thm)],[117,111,5,21]) ).
tff(119,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W) )
<=> ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssItem(U) ) )),
rewrite(
( ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(X) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( X = V ) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( X = V ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause171) ).
tff(125,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[127,120]) ).
tff(129,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ( ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(transitivity,[status(thm)],[131,129]) ).
tff(133,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( ~ ssItem(skaf83(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) ) ),
inference(unit_resolution,[status(thm)],[134,128,118,101]) ).
tff(136,plain,
skaf82(sk3) = tl(sk3),
inference(unit_resolution,[status(thm)],[135,53,85,44]) ).
tff(137,plain,
tl(sk3) = skaf82(sk3),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
app(cons(skaf83(sk3),nil),tl(sk3)) = app(cons(skaf83(sk3),nil),skaf82(sk3)),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
app(cons(skaf83(sk3),nil),tl(sk3)) = sk3,
inference(transitivity,[status(thm)],[138,68,35]) ).
tff(140,plain,
app(nil,app(cons(skaf83(sk3),nil),tl(sk3))) = app(nil,sk3),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,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(142,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)],[141]) ).
tff(143,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(144,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(145,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)],[144]) ).
tff(146,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(147,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[147,143]) ).
tff(149,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[149,142]) ).
tff(151,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(152,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(153,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,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(155,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(156,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)],[155]) ).
tff(157,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)],[156,154]) ).
tff(158,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(159,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)],[158,157]) ).
tff(160,plain,
ssList(cons(skaf83(sk3),nil)),
inference(unit_resolution,[status(thm)],[159,153,150,53]) ).
tff(161,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(162,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)],[161]) ).
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)) ) )
<=> ! [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(164,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(165,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)],[164]) ).
tff(166,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(167,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)],[166,165]) ).
tff(168,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)],[167,163]) ).
tff(169,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)],[168]) ).
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)) ) ),
inference(modus_ponens,[status(thm)],[169,162]) ).
tff(171,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(tl(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = app(nil,app(cons(skaf83(sk3),nil),tl(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(tl(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = app(nil,app(cons(skaf83(sk3),nil),tl(sk3))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(172,plain,
( ( ~ ssList(tl(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = app(nil,app(cons(skaf83(sk3),nil),tl(sk3))) ) )
<=> ( ~ ssList(nil)
| ~ ssList(tl(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = app(nil,app(cons(skaf83(sk3),nil),tl(sk3))) ) ) ),
inference(rewrite,[status(thm)],]) ).
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(tl(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = app(nil,app(cons(skaf83(sk3),nil),tl(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(tl(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = app(nil,app(cons(skaf83(sk3),nil),tl(sk3))) ) ) ),
inference(monotonicity,[status(thm)],[172]) ).
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(tl(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = app(nil,app(cons(skaf83(sk3),nil),tl(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(tl(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = app(nil,app(cons(skaf83(sk3),nil),tl(sk3))) ) ) ),
inference(transitivity,[status(thm)],[173,171]) ).
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(tl(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = app(nil,app(cons(skaf83(sk3),nil),tl(sk3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,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(tl(sk3))
| ~ ssList(cons(skaf83(sk3),nil))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = app(nil,app(cons(skaf83(sk3),nil),tl(sk3))) ) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = app(nil,app(cons(skaf83(sk3),nil),tl(sk3))),
inference(unit_resolution,[status(thm)],[176,153,170,85,160]) ).
tff(178,plain,
app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) = sk3,
inference(transitivity,[status(thm)],[177,140,16]) ).
tff(179,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(180,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[179]) ).
tff(181,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( app(app(B,cons(A,nil)),C) != sk1 )
<=> ( app(app(B,cons(A,nil)),C) != sk3 ) )),
( ( ~ 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) != sk3 )
| memberP(B,sk5(C,B,A)) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| memberP(B,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ 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)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(182,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)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,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(184,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(185,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)],[184]) ).
tff(186,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_10) ).
tff(187,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)],[186,185]) ).
tff(188,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)],[187,183]) ).
tff(189,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[188,182]) ).
tff(190,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(skolemize,[status(sab)],[189]) ).
tff(191,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[190,180]) ).
tff(192,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| memberP(nil,sk5(tl(sk3),nil,skaf83(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| memberP(nil,sk5(tl(sk3),nil,skaf83(sk3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(193,plain,
( ( ~ ssList(tl(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| memberP(nil,sk5(tl(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 ) )
<=> ( ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| memberP(nil,sk5(tl(sk3),nil,skaf83(sk3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(tl(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| memberP(nil,sk5(tl(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| memberP(nil,sk5(tl(sk3),nil,skaf83(sk3))) ) ),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(tl(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| memberP(nil,sk5(tl(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| memberP(nil,sk5(tl(sk3),nil,skaf83(sk3))) ) ),
inference(transitivity,[status(thm)],[194,192]) ).
tff(196,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(tl(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| memberP(nil,sk5(tl(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(197,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(B,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| memberP(nil,sk5(tl(sk3),nil,skaf83(sk3))) ),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
memberP(nil,sk5(tl(sk3),nil,skaf83(sk3))),
inference(unit_resolution,[status(thm)],[197,153,191,53,85,178]) ).
tff(199,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) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(200,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) != 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) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[199]) ).
tff(201,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( app(app(B,cons(A,nil)),C) != sk1 )
<=> ( app(app(B,cons(A,nil)),C) != sk3 ) )),
( ( ~ 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) != sk3 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ 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) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(202,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) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,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(204,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(205,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)],[204]) ).
tff(206,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_9) ).
tff(207,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)],[206,205]) ).
tff(208,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)],[207,203]) ).
tff(209,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) != sk3 ) ),
inference(modus_ponens,[status(thm)],[208,202]) ).
tff(210,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) != sk3 ) ),
inference(skolemize,[status(sab)],[209]) ).
tff(211,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) != sk3 ) ),
inference(modus_ponens,[status(thm)],[210,200]) ).
tff(212,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) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| ssItem(sk5(tl(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) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| ssItem(sk5(tl(sk3),nil,skaf83(sk3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(213,plain,
( ( ~ ssList(tl(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssItem(sk5(tl(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 ) )
<=> ( ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| ssItem(sk5(tl(sk3),nil,skaf83(sk3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(214,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) != sk3 ) )
| ~ ssList(tl(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssItem(sk5(tl(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != 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) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| ssItem(sk5(tl(sk3),nil,skaf83(sk3))) ) ),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(tl(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssItem(sk5(tl(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != 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) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| ssItem(sk5(tl(sk3),nil,skaf83(sk3))) ) ),
inference(transitivity,[status(thm)],[214,212]) ).
tff(216,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(tl(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ssItem(sk5(tl(sk3),nil,skaf83(sk3)))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(217,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) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3))
| ~ ssList(tl(sk3))
| ( app(app(nil,cons(skaf83(sk3),nil)),tl(sk3)) != sk3 )
| ssItem(sk5(tl(sk3),nil,skaf83(sk3))) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
ssItem(sk5(tl(sk3),nil,skaf83(sk3))),
inference(unit_resolution,[status(thm)],[217,153,211,53,85,178]) ).
tff(219,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(220,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[219]) ).
tff(221,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(222,plain,
^ [U: $i] :
rewrite(
( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(223,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[222]) ).
tff(224,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(225,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[224,223]) ).
tff(226,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[225,221]) ).
tff(227,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[226]) ).
tff(228,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[227,220]) ).
tff(229,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(tl(sk3),nil,skaf83(sk3)))
| ~ memberP(nil,sk5(tl(sk3),nil,skaf83(sk3))) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(tl(sk3),nil,skaf83(sk3)))
| ~ memberP(nil,sk5(tl(sk3),nil,skaf83(sk3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(230,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(tl(sk3),nil,skaf83(sk3)))
| ~ memberP(nil,sk5(tl(sk3),nil,skaf83(sk3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(231,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(tl(sk3),nil,skaf83(sk3)))
| ~ memberP(nil,sk5(tl(sk3),nil,skaf83(sk3))) ),
inference(modus_ponens,[status(thm)],[230,229]) ).
tff(232,plain,
$false,
inference(unit_resolution,[status(thm)],[231,228,218,198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC229-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 22:55:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.25/1.08 % SZS status Unsatisfiable
% 1.25/1.08 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------