TSTP Solution File: SWC182-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC182-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 11:55:55 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 57
% Syntax : Number of formulae : 113 ( 30 unt; 11 typ; 0 def)
% Number of atoms : 752 ( 150 equ)
% Maximal formula atoms : 23 ( 7 avg)
% Number of connectives : 1178 ( 584 ~; 525 |; 0 &)
% ( 69 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 56 ( 56 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 223 ( 198 !; 0 ?; 223 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(1,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(3,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,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(8,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)],[7]) ).
tff(9,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(10,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ssList(nil)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(17,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ssList(cons(sk5,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ssList(cons(sk5,sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ssList(cons(sk5,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ssList(cons(sk5,sk3)) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
ssList(cons(sk5,sk3)),
inference(unit_resolution,[status(thm)],[21,18,13,3]) ).
tff(23,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(25,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(32,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ~ ssList(cons(sk5,sk3))
| ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk6) )
<=> ( ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,sk3))
| ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk6) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk3)) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,sk3))
| ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk6) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk3)) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,sk3))
| ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk6) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk3)) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
ssList(app(sk6,cons(sk5,sk3))),
inference(unit_resolution,[status(thm)],[41,35,25,22]) ).
tff(43,plain,
( ( app(app(sk6,cons(sk5,nil)),sk7) = sk1 )
<=> ( app(app(sk6,cons(sk5,sk3)),sk7) = sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( app(app(sk6,cons(sk5,nil)),sk7) = sk1 )
<=> ( app(app(sk6,cons(sk5,nil)),sk7) = sk1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(46,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
app(app(sk6,cons(sk5,sk3)),sk7) = sk3,
inference(modus_ponens,[status(thm)],[46,43]) ).
tff(48,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(50,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( nil = U )
<=> ( sk3 = U ) )),
rewrite(
( ( app(U,V) != nil )
<=> ( app(U,V) != sk3 ) )),
( ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ( ~ ssList(U)
| ( sk3 = U )
| ~ ssList(V)
| ( app(U,V) != sk3 ) ) )),
rewrite(
( ( ~ ssList(U)
| ( sk3 = U )
| ~ ssList(V)
| ( app(U,V) != sk3 ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) ) )),
( ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
tff(59,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) ),
inference(modus_ponens,[status(thm)],[60,54]) ).
tff(62,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) ),
inference(modus_ponens,[status(thm)],[62,52]) ).
tff(64,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) )
| ~ ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk7)
| ( sk3 = app(sk6,cons(sk5,sk3)) )
| ( app(app(sk6,cons(sk5,sk3)),sk7) != sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) )
| ~ ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk7)
| ( sk3 = app(sk6,cons(sk5,sk3)) )
| ( app(app(sk6,cons(sk5,sk3)),sk7) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) )
| ~ ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk7)
| ( sk3 = app(sk6,cons(sk5,sk3)) )
| ( app(app(sk6,cons(sk5,sk3)),sk7) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( sk3 = U )
| ( app(U,V) != sk3 ) )
| ~ ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk7)
| ( sk3 = app(sk6,cons(sk5,sk3)) )
| ( app(app(sk6,cons(sk5,sk3)),sk7) != sk3 ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
sk3 = app(sk6,cons(sk5,sk3)),
inference(unit_resolution,[status(thm)],[66,63,50,47,42]) ).
tff(68,plain,
app(sk6,cons(sk5,sk3)) = sk3,
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ memberP(sk3,U) )
<=> ( ~ ssItem(U)
| ~ memberP(sk3,U) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk3,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk3,U) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
^ [U: $i] :
rewrite(
( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(sk3,U) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk3,U) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
^ [U: $i] :
rewrite(
( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(77,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk3,U) ),
inference(modus_ponens,[status(thm)],[78,72]) ).
tff(80,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk3,U) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk3,U) ),
inference(modus_ponens,[status(thm)],[80,70]) ).
tff(82,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk3,U) )
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk3,U) )
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk3,U) )
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(sk3,U) )
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
~ memberP(sk3,sk5),
inference(unit_resolution,[status(thm)],[84,81,3]) ).
tff(86,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause175) ).
tff(92,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[94,87]) ).
tff(96,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| memberP(sk3,sk5)
| ( app(sk6,cons(sk5,sk3)) != sk3 ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| memberP(sk3,sk5)
| ( app(sk6,cons(sk5,sk3)) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ( ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| memberP(sk3,sk5)
| ~ ssList(sk3)
| ( app(sk6,cons(sk5,sk3)) != sk3 ) )
<=> ( ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| memberP(sk3,sk5)
| ( app(sk6,cons(sk5,sk3)) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| memberP(sk3,sk5)
| ~ ssList(sk3)
| ( app(sk6,cons(sk5,sk3)) != sk3 ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| memberP(sk3,sk5)
| ( app(sk6,cons(sk5,sk3)) != sk3 ) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| memberP(sk3,sk5)
| ~ ssList(sk3)
| ( app(sk6,cons(sk5,sk3)) != sk3 ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| memberP(sk3,sk5)
| ( app(sk6,cons(sk5,sk3)) != sk3 ) ) ),
inference(transitivity,[status(thm)],[98,96]) ).
tff(100,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| memberP(sk3,sk5)
| ~ ssList(sk3)
| ( app(sk6,cons(sk5,sk3)) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| memberP(sk3,sk5)
| ( app(sk6,cons(sk5,sk3)) != sk3 ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
$false,
inference(unit_resolution,[status(thm)],[101,18,95,3,25,85,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC182-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 22:21:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.18/0.41 % SZS status Unsatisfiable
% 0.18/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------