TSTP Solution File: SWC239-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC239-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 11:56:25 EDT 2022
% Result : Unsatisfiable 0.15s 0.54s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 56
% Syntax : Number of formulae : 125 ( 29 unt; 10 typ; 0 def)
% Number of atoms : 739 ( 193 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 1117 ( 539 ~; 510 |; 0 &)
% ( 68 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 46 ( 46 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 193 ( 171 !; 0 ?; 193 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk5_type,type,
sk5: ( $i * $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(nil_type,type,
nil: $i ).
tff(sk3_type,type,
sk3: $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(memberP_type,type,
memberP: ( $i * $i ) > $o ).
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/sandbox2/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(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(10,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[15,12,5]) ).
tff(17,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(21,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,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(25,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[26,23,5]) ).
tff(28,plain,
( ( ( cons(sk6,nil) = sk3 )
| $false )
<=> ( cons(sk6,nil) = sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(32,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
( ( nil = sk3 )
<=> $false ),
inference(iff_false,[status(thm)],[33]) ).
tff(35,plain,
( ( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( cons(sk6,nil) = sk3 )
| $false ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( cons(sk6,nil) = sk3 ) ),
inference(transitivity,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
tff(39,plain,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[39,37]) ).
tff(41,plain,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[42,37]) ).
tff(44,plain,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[43,37]) ).
tff(45,plain,
cons(sk6,nil) = sk3,
inference(modus_ponens,[status(thm)],[44,36]) ).
tff(46,plain,
app(nil,cons(sk6,nil)) = app(nil,sk3),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
app(nil,cons(sk6,nil)) = sk3,
inference(transitivity,[status(thm)],[46,27]) ).
tff(48,plain,
app(app(nil,cons(sk6,nil)),nil) = app(sk3,nil),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
app(app(nil,cons(sk6,nil)),nil) = sk3,
inference(transitivity,[status(thm)],[48,16]) ).
tff(50,plain,
( ( ssItem(sk6)
| $false )
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( ssItem(sk6)
| ( nil = sk3 ) )
<=> ( ssItem(sk6)
| $false ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(52,plain,
( ( ssItem(sk6)
| ( nil = sk3 ) )
<=> ssItem(sk6) ),
inference(transitivity,[status(thm)],[51,50]) ).
tff(53,plain,
( ( ssItem(sk6)
| ( nil = sk3 ) )
<=> ( ssItem(sk6)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
( ssItem(sk6)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(55,plain,
( ssItem(sk6)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[55,52]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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(62,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(63,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)],[62]) ).
tff(64,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/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(65,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)],[64,63]) ).
tff(66,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)],[65,61]) ).
tff(67,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)],[66,60]) ).
tff(68,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)],[67]) ).
tff(69,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)],[68,58]) ).
tff(70,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(72,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,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(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| ssItem(sk5(nil,nil,sk6)) )
<=> ( ~ ! [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(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| ssItem(sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssItem(sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 ) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| ssItem(sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,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(sk6)
| ~ ssList(nil)
| ssItem(sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != 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(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| ssItem(sk5(nil,nil,sk6)) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,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(sk6)
| ~ ssList(nil)
| ssItem(sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != 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(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| ssItem(sk5(nil,nil,sk6)) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,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(sk6)
| ~ ssList(nil)
| ssItem(sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,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(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| ssItem(sk5(nil,nil,sk6)) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| ssItem(sk5(nil,nil,sk6)) ),
inference(unit_resolution,[status(thm)],[78,72,69,56]) ).
tff(80,plain,
ssItem(sk5(nil,nil,sk6)),
inference(unit_resolution,[status(thm)],[79,49]) ).
tff(81,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,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(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,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(C,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| memberP(C,sk5(C,B,A)) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| memberP(C,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,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(C,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(C,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(C,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(C,sk5(C,B,A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,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(C,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(C,sk5(C,B,A)) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(C,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(C,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(C,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(C,sk5(C,B,A)) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(C,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(C,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(C,sk5(C,B,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(89,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(C,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(C,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[90,84]) ).
tff(92,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[92,82]) ).
tff(94,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| memberP(nil,sk5(nil,nil,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| memberP(nil,sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| memberP(nil,sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 ) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| memberP(nil,sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| memberP(nil,sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| memberP(nil,sk5(nil,nil,sk6)) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| memberP(nil,sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| memberP(nil,sk5(nil,nil,sk6)) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| memberP(nil,sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| memberP(C,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| memberP(nil,sk5(nil,nil,sk6)) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ( app(app(nil,cons(sk6,nil)),nil) != sk3 )
| memberP(nil,sk5(nil,nil,sk6)) ),
inference(unit_resolution,[status(thm)],[99,72,93,56]) ).
tff(101,plain,
memberP(nil,sk5(nil,nil,sk6)),
inference(unit_resolution,[status(thm)],[100,49]) ).
tff(102,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
^ [U: $i] :
rewrite(
( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(108,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[110,103]) ).
tff(112,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(nil,nil,sk6))
| ~ memberP(nil,sk5(nil,nil,sk6)) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(nil,nil,sk6))
| ~ memberP(nil,sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(nil,nil,sk6))
| ~ memberP(nil,sk5(nil,nil,sk6)) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(nil,nil,sk6))
| ~ memberP(nil,sk5(nil,nil,sk6)) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
$false,
inference(unit_resolution,[status(thm)],[114,111,101,80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SWC239-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.29 % Computer : n006.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Sat Sep 3 22:58:38 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.30 Usage: tptp [options] [-file:]file
% 0.10/0.30 -h, -? prints this message.
% 0.10/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.30 -m, -model generate model.
% 0.10/0.30 -p, -proof generate proof.
% 0.10/0.30 -c, -core generate unsat core of named formulas.
% 0.10/0.30 -st, -statistics display statistics.
% 0.10/0.30 -t:timeout set timeout (in second).
% 0.10/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.30 -<param>:<value> configuration parameter and value.
% 0.10/0.30 -o:<output-file> file to place output in.
% 0.15/0.54 % SZS status Unsatisfiable
% 0.15/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------