TSTP Solution File: SWC220-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC220-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 11:56:14 EDT 2022
% Result : Unsatisfiable 0.77s 0.96s
% Output : Proof 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 77
% Syntax : Number of formulae : 179 ( 31 unt; 13 typ; 0 def)
% Number of atoms : 1843 ( 370 equ)
% Maximal formula atoms : 20 ( 11 avg)
% Number of connectives : 2940 (1411 ~;1381 |; 0 &)
% ( 148 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 148 ( 148 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 7 >; 6 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 400 ( 352 !; 0 ?; 400 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: ( $i * $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(1,plain,
( ( $false
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) )
<=> ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(5,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
( ( nil = sk3 )
<=> $false ),
inference(iff_false,[status(thm)],[6]) ).
tff(8,plain,
( ( ( nil = sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) )
<=> ( $false
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ( ( nil = sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) )
<=> ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ),
inference(transitivity,[status(thm)],[8,1]) ).
tff(10,plain,
( ( ( nil = sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) )
<=> ( ( nil = sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
( ( nil = sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(12,plain,
( ( nil = sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
app(app(sk7,cons(sk6,nil)),sk8) = sk3,
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
( ( $false
| ssList(sk8) )
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ( ( nil = sk3 )
| ssList(sk8) )
<=> ( $false
| ssList(sk8) ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(16,plain,
( ( ( nil = sk3 )
| ssList(sk8) )
<=> ssList(sk8) ),
inference(transitivity,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ( nil = sk3 )
| ssList(sk8) )
<=> ( ( nil = sk3 )
| ssList(sk8) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
( ( nil = sk3 )
| ssList(sk8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
tff(19,plain,
( ( nil = sk3 )
| ssList(sk8) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ( nil = sk3 )
| ssList(sk8) ),
inference(modus_ponens,[status(thm)],[19,17]) ).
tff(21,plain,
( ( nil = sk3 )
| ssList(sk8) ),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
( ( nil = sk3 )
| ssList(sk8) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ( nil = sk3 )
| ssList(sk8) ),
inference(modus_ponens,[status(thm)],[22,17]) ).
tff(24,plain,
( ( nil = sk3 )
| ssList(sk8) ),
inference(modus_ponens,[status(thm)],[23,17]) ).
tff(25,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[24,16]) ).
tff(26,plain,
( ( ssList(sk7)
| $false )
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( ssList(sk7)
| ( nil = sk3 ) )
<=> ( ssList(sk7)
| $false ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(28,plain,
( ( ssList(sk7)
| ( nil = sk3 ) )
<=> ssList(sk7) ),
inference(transitivity,[status(thm)],[27,26]) ).
tff(29,plain,
( ( ssList(sk7)
| ( nil = sk3 ) )
<=> ( ssList(sk7)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ( nil = sk3 )
| ssList(sk7) )
<=> ( ssList(sk7)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
( ( nil = sk3 )
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(32,plain,
( ssList(sk7)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ssList(sk7)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[33,28]) ).
tff(35,plain,
( ( $false
| ssItem(sk6) )
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ( nil = sk3 )
| ssItem(sk6) )
<=> ( $false
| ssItem(sk6) ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(37,plain,
( ( ( nil = sk3 )
| ssItem(sk6) )
<=> ssItem(sk6) ),
inference(transitivity,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ( nil = sk3 )
| ssItem(sk6) )
<=> ( ( nil = sk3 )
| ssItem(sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
( ( nil = sk3 )
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(40,plain,
( ( nil = sk3 )
| ssItem(sk6) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ( nil = sk3 )
| ssItem(sk6) ),
inference(modus_ponens,[status(thm)],[40,38]) ).
tff(42,plain,
( ( nil = sk3 )
| ssItem(sk6) ),
inference(modus_ponens,[status(thm)],[41,38]) ).
tff(43,plain,
( ( nil = sk3 )
| ssItem(sk6) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ( nil = sk3 )
| ssItem(sk6) ),
inference(modus_ponens,[status(thm)],[43,38]) ).
tff(45,plain,
( ( nil = sk3 )
| ssItem(sk6) ),
inference(modus_ponens,[status(thm)],[44,38]) ).
tff(46,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[45,37]) ).
tff(47,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(48,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)],[47]) ).
tff(49,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(50,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)],[49]) ).
tff(51,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(52,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(53,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)],[52]) ).
tff(54,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(55,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)],[54,53]) ).
tff(56,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)],[55,51]) ).
tff(57,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)],[56,50]) ).
tff(58,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)],[57]) ).
tff(59,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)],[58,48]) ).
tff(60,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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk7,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| memberP(sk7,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,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(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| memberP(sk7,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != 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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,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(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| memberP(sk7,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != 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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,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(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| memberP(sk7,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk7,sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
memberP(sk7,sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[65,59,46,34,25,13]) ).
tff(67,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(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 ) )
<=> ! [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)],[67]) ).
tff(69,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(70,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)],[69]) ).
tff(71,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(72,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(73,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)],[72]) ).
tff(74,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(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) != sk1 ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
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) != sk1 ) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
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 ) ),
inference(modus_ponens,[status(thm)],[76,70]) ).
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 ) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,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)],[78,68]) ).
tff(80,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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| ssItem(sk5(sk8,sk7,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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,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(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != 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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,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(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != 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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[82,80]) ).
tff(84,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(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| ssItem(sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
ssItem(sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[85,79,46,34,25,13]) ).
tff(87,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(88,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)],[87]) ).
tff(89,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(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)) )
<=> ! [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)],[89]) ).
tff(91,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(92,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(93,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)],[92]) ).
tff(94,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/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(95,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)],[94,93]) ).
tff(96,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)],[95,91]) ).
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 ) ),
inference(modus_ponens,[status(thm)],[96,90]) ).
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 ) ),
inference(skolemize,[status(sab)],[97]) ).
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 ) ),
inference(modus_ponens,[status(thm)],[98,88]) ).
tff(100,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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk8,sk5(sk8,sk7,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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk8,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| memberP(sk8,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk8,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,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(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| memberP(sk8,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != 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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk8,sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,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(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| memberP(sk8,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != 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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk8,sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[102,100]) ).
tff(104,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(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| memberP(sk8,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,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(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| memberP(sk8,sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
memberP(sk8,sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[105,99,46,34,25,13]) ).
tff(107,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(108,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,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 )
| leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| leq(A,sk5(C,B,A)) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,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 )
| leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,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 )
| leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) ) )),
inference(bind,[status(th)],]) ).
tff(113,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(115,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| leq(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[116,110]) ).
tff(118,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[118,108]) ).
tff(120,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| leq(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| leq(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| leq(sk6,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| leq(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| leq(sk6,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| leq(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| leq(sk6,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| leq(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[122,120]) ).
tff(124,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| leq(sk6,sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| leq(A,sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
| leq(sk6,sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
leq(sk6,sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[125,119,46,34,25,13]) ).
tff(127,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(128,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,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 )
| ~ leq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ leq(sk5(C,B,A),A) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ leq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(130,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) ) )),
inference(bind,[status(th)],]) ).
tff(133,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(135,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(sk5(C,B,A),A) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[136,130]) ).
tff(138,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(skolemize,[status(sab)],[137]) ).
tff(139,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[138,128]) ).
tff(140,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ leq(sk5(sk8,sk7,sk6),sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ leq(sk5(sk8,sk7,sk6),sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ leq(sk5(sk8,sk7,sk6),sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ leq(sk5(sk8,sk7,sk6),sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ leq(sk5(sk8,sk7,sk6),sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ leq(sk5(sk8,sk7,sk6),sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ leq(sk5(sk8,sk7,sk6),sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ leq(sk5(sk8,sk7,sk6),sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ) ),
inference(transitivity,[status(thm)],[142,140]) ).
tff(144,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ leq(sk5(sk8,sk7,sk6),sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ leq(sk5(C,B,A),A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ leq(sk5(sk8,sk7,sk6),sk6)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
~ leq(sk5(sk8,sk7,sk6),sk6),
inference(unit_resolution,[status(thm)],[145,139,46,34,25,13]) ).
tff(147,plain,
^ [A: $i] :
refl(
( ( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
<=> ( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) )),
inference(bind,[status(th)],]) ).
tff(148,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,plain,
^ [A: $i] :
trans(
monotonicity(
iff_false(
mp(
mp(asserted(nil != sk1),
rewrite(
( ( nil != sk1 )
<=> ( nil != sk1 ) )),
nil != sk1),
rewrite(
( ( nil != sk1 )
<=> ( nil != sk3 ) )),
nil != sk3),
( ( nil = sk3 )
<=> $false )),
( ( ~ ssItem(A)
| ( nil = sk3 )
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
<=> ( ~ ssItem(A)
| $false
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) )),
rewrite(
( ( ~ ssItem(A)
| $false
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
<=> ( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) )),
( ( ~ ssItem(A)
| ( nil = sk3 )
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
<=> ( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) )),
inference(bind,[status(th)],]) ).
tff(150,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ( nil = sk3 )
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ( nil = sk3 )
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ( nil = sk3 )
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
^ [A: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( nil = sk3 )
| ~ ssItem(A) )
<=> ( ~ ssItem(A)
| ( nil = sk3 ) ) )),
( ( ( nil = sk3 )
| ~ ssItem(A)
| leq(A,sk6) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| leq(A,sk6) ) )),
rewrite(
( ( ~ ssItem(A)
| ( nil = sk3 )
| leq(A,sk6) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| leq(A,sk6) ) )),
( ( ( nil = sk3 )
| ~ ssItem(A)
| leq(A,sk6) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| leq(A,sk6) ) )),
( ( ( nil = sk3 )
| ~ ssItem(A)
| leq(A,sk6)
| ~ memberP(sk7,A) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| leq(A,sk6)
| ~ memberP(sk7,A) ) )),
rewrite(
( ( ~ ssItem(A)
| ( nil = sk3 )
| leq(A,sk6)
| ~ memberP(sk7,A) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| ~ memberP(sk7,A)
| leq(A,sk6) ) )),
( ( ( nil = sk3 )
| ~ ssItem(A)
| leq(A,sk6)
| ~ memberP(sk7,A) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| ~ memberP(sk7,A)
| leq(A,sk6) ) )),
( ( ( nil = sk3 )
| ~ ssItem(A)
| leq(A,sk6)
| ~ memberP(sk7,A)
| ~ memberP(sk8,A) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| ~ memberP(sk7,A)
| leq(A,sk6)
| ~ memberP(sk8,A) ) )),
rewrite(
( ( ~ ssItem(A)
| ( nil = sk3 )
| ~ memberP(sk7,A)
| leq(A,sk6)
| ~ memberP(sk8,A) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) )),
( ( ( nil = sk3 )
| ~ ssItem(A)
| leq(A,sk6)
| ~ memberP(sk7,A)
| ~ memberP(sk8,A) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) )),
( ( ( nil = sk3 )
| ~ ssItem(A)
| leq(A,sk6)
| ~ memberP(sk7,A)
| ~ memberP(sk8,A)
| ~ leq(sk6,A) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6)
| ~ leq(sk6,A) ) )),
rewrite(
( ( ~ ssItem(A)
| ( nil = sk3 )
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6)
| ~ leq(sk6,A) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) )),
( ( ( nil = sk3 )
| ~ ssItem(A)
| leq(A,sk6)
| ~ memberP(sk7,A)
| ~ memberP(sk8,A)
| ~ leq(sk6,A) )
<=> ( ~ ssItem(A)
| ( nil = sk3 )
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) )),
inference(bind,[status(th)],]) ).
tff(153,plain,
( ! [A: $i] :
( ( nil = sk3 )
| ~ ssItem(A)
| leq(A,sk6)
| ~ memberP(sk7,A)
| ~ memberP(sk8,A)
| ~ leq(sk6,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ( nil = sk3 )
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,axiom,
! [A: $i] :
( ( nil = sk3 )
| ~ ssItem(A)
| leq(A,sk6)
| ~ memberP(sk7,A)
| ~ memberP(sk8,A)
| ~ leq(sk6,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
tff(155,plain,
! [A: $i] :
( ~ ssItem(A)
| ( nil = sk3 )
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
! [A: $i] :
( ~ ssItem(A)
| ( nil = sk3 )
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ),
inference(modus_ponens,[status(thm)],[156,150]) ).
tff(158,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ),
inference(skolemize,[status(sab)],[157]) ).
tff(159,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) ),
inference(modus_ponens,[status(thm)],[158,148]) ).
tff(160,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
| leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
| leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ( ~ ssItem(sk5(sk8,sk7,sk6))
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6))
| leq(sk5(sk8,sk7,sk6),sk6) )
<=> ( leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6))
| leq(sk5(sk8,sk7,sk6),sk6) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
| leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6))
| leq(sk5(sk8,sk7,sk6),sk6) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
| leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[162,160]) ).
tff(164,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6))
| leq(sk5(sk8,sk7,sk6),sk6) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6) )
| leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
$false,
inference(unit_resolution,[status(thm)],[165,159,146,126,106,86,66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC220-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 22:53:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.77/0.96 % SZS status Unsatisfiable
% 0.77/0.96 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------