TSTP Solution File: SWC153-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC153-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 11:55:40 EDT 2022
% Result : Unsatisfiable 10.10s 6.76s
% Output : Proof 10.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 72
% Syntax : Number of formulae : 158 ( 38 unt; 14 typ; 0 def)
% Number of atoms : 2376 ( 247 equ)
% Maximal formula atoms : 39 ( 16 avg)
% Number of connectives : 4149 (2073 ~;1940 |; 0 &)
% ( 136 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 156 ( 156 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 480 ( 424 !; 0 ?; 480 :)
% Comments :
%------------------------------------------------------------------------------
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk9_type,type,
sk9: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk10_type,type,
sk10: $i ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(1,plain,
( leq(sk6,sk5)
<=> leq(sk6,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
leq(sk6,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(3,plain,
leq(sk6,sk5),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ssList(sk9)
<=> ssList(sk9) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
ssList(sk9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(6,plain,
ssList(sk9),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ssList(sk8)
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(9,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(12,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(15,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(18,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
^ [B: $i,D: $i,A: $i,E: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [B: $i,D: $i,A: $i,E: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
<=> ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )),
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) )),
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [B: $i,D: $i,A: $i,E: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(D) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ~ ssList(E) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ~ ssList(E) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| leq(A,B) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| leq(A,B) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| leq(A,B) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| leq(A,B) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| leq(A,B) )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| leq(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(27,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(modus_ponens,[status(thm)],[28,22]) ).
tff(30,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| leq(sk5,sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ leq(sk6,sk5) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| leq(sk5,sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ leq(sk6,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ ssList(sk7)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| leq(sk5,sk6)
| ~ leq(sk6,sk5)
| $false )
<=> ( leq(sk5,sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ leq(sk6,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) )
<=> $false ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ( ~ ssList(sk7)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| leq(sk5,sk6)
| ~ leq(sk6,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| leq(sk5,sk6)
| ~ leq(sk6,sk5)
| $false ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ssList(sk7)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| leq(sk5,sk6)
| ~ leq(sk6,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( leq(sk5,sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ leq(sk6,sk5) ) ),
inference(transitivity,[status(thm)],[38,33]) ).
tff(40,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| leq(sk5,sk6)
| ~ leq(sk6,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| leq(sk5,sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ leq(sk6,sk5) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| leq(sk5,sk6)
| ~ leq(sk6,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| leq(sk5,sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ leq(sk6,sk5) ) ),
inference(transitivity,[status(thm)],[40,32]) ).
tff(42,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| leq(sk5,sk6)
| ~ leq(sk6,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] :
( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| leq(A,B)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| leq(sk5,sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ leq(sk6,sk5) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
leq(sk5,sk6),
inference(unit_resolution,[status(thm)],[43,31,18,15,12,9,6,3]) ).
tff(45,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) )
<=> ( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ leq(U,V)
| ~ leq(V,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ leq(U,V)
| ~ leq(V,U) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ~ ssItem(U)
| ~ ssItem(V) )
<=> ( ~ ssItem(U)
| ~ leq(U,V)
| ~ leq(V,U)
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ leq(U,V)
| ~ leq(V,U)
| ~ ssItem(V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ~ ssItem(U)
| ~ ssItem(V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ~ ssItem(U)
| ~ ssItem(V)
| ( V = U ) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U)
| ( V = U ) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U)
| ( V = U ) )
<=> ( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ~ ssItem(U)
| ~ ssItem(V)
| ( V = U ) )
<=> ( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [V: $i,U: $i] :
( ~ leq(U,V)
| ~ leq(V,U)
| ~ ssItem(U)
| ~ ssItem(V)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,axiom,
! [V: $i,U: $i] :
( ~ leq(U,V)
| ~ leq(V,U)
| ~ ssItem(U)
| ~ ssItem(V)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause130) ).
tff(51,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) )
| ~ leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk6 = sk5 )
| ~ leq(sk6,sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) )
| ~ leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk6 = sk5 )
| ~ leq(sk6,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( ~ ssItem(sk5)
| ( sk6 = sk5 )
| ~ ssItem(sk6)
| ~ leq(sk5,sk6)
| ~ leq(sk6,sk5) )
<=> ( ~ leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk6 = sk5 )
| ~ leq(sk6,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) )
| ~ ssItem(sk5)
| ( sk6 = sk5 )
| ~ ssItem(sk6)
| ~ leq(sk5,sk6)
| ~ leq(sk6,sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) )
| ~ leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk6 = sk5 )
| ~ leq(sk6,sk5) ) ),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) )
| ~ ssItem(sk5)
| ( sk6 = sk5 )
| ~ ssItem(sk6)
| ~ leq(sk5,sk6)
| ~ leq(sk6,sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) )
| ~ leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk6 = sk5 )
| ~ leq(sk6,sk5) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) )
| ~ ssItem(sk5)
| ( sk6 = sk5 )
| ~ ssItem(sk6)
| ~ leq(sk5,sk6)
| ~ leq(sk6,sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) )
| ~ leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk6 = sk5 )
| ~ leq(sk6,sk5) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ leq(sk5,sk6)
| ( sk6 = sk5 ) ),
inference(unit_resolution,[status(thm)],[60,54,18,15,3]) ).
tff(62,plain,
sk6 = sk5,
inference(unit_resolution,[status(thm)],[61,44]) ).
tff(63,plain,
cons(sk6,nil) = cons(sk5,nil),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
cons(sk5,nil) = cons(sk6,nil),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)) = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) = app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| leq(U,U) )
<=> ( ~ ssItem(U)
| leq(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,axiom,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause62) ).
tff(71,plain,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk5)
| leq(sk5,sk5) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk5)
| leq(sk5,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk5)
| leq(sk5,sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk5)
| leq(sk5,sk5) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
leq(sk5,sk5),
inference(unit_resolution,[status(thm)],[76,73,18]) ).
tff(78,plain,
sk5 = sk6,
inference(symmetry,[status(thm)],[62]) ).
tff(79,plain,
( leq(sk10,sk5)
<=> leq(sk10,sk6) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ leq(sk5,sk6)
| memberP(sk8,sk10) )
<=> ( ~ leq(sk5,sk6)
| memberP(sk8,sk10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ( memberP(sk8,sk10)
| ~ leq(sk5,sk6) )
<=> ( ~ leq(sk5,sk6)
| memberP(sk8,sk10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,axiom,
( memberP(sk8,sk10)
| ~ leq(sk5,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
tff(83,plain,
( ~ leq(sk5,sk6)
| memberP(sk8,sk10) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( ~ leq(sk5,sk6)
| memberP(sk8,sk10) ),
inference(modus_ponens,[status(thm)],[83,80]) ).
tff(85,plain,
memberP(sk8,sk10),
inference(unit_resolution,[status(thm)],[84,44]) ).
tff(86,plain,
( ( ssItem(sk10)
| ~ leq(sk5,sk6) )
<=> ( ssItem(sk10)
| ~ leq(sk5,sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,axiom,
( ssItem(sk10)
| ~ leq(sk5,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
tff(88,plain,
( ssItem(sk10)
| ~ leq(sk5,sk6) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
ssItem(sk10),
inference(unit_resolution,[status(thm)],[88,44]) ).
tff(90,plain,
^ [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
^ [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
<=> ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )),
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) )
| ~ ssItem(B)
| leq(F,B) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) )
| ~ ssItem(B)
| leq(F,B) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) )),
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) )
<=> ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) )
<=> ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
^ [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(D) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ~ ssList(E) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ~ ssList(E) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ leq(B,A) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ leq(B,A) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ ssItem(F) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ ssItem(F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ memberP(D,F) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ memberP(D,F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F)
| leq(F,B) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F)
| leq(F,B) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F)
| leq(F,B) )
<=> ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,axiom,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F)
| leq(F,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(98,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(modus_ponens,[status(thm)],[99,93]) ).
tff(101,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(modus_ponens,[status(thm)],[101,91]) ).
tff(103,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| leq(sk10,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| leq(sk10,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ~ ssItem(sk5)
| leq(sk10,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| leq(sk10,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ~ ssItem(sk5)
| leq(sk10,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| leq(sk10,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ~ ssItem(sk5)
| leq(sk10,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| leq(sk10,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ~ ssItem(sk5)
| leq(sk10,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| leq(F,B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| leq(sk10,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( leq(sk10,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(unit_resolution,[status(thm)],[108,102,18,12,9,6,89,85,77]) ).
tff(110,plain,
leq(sk10,sk5),
inference(unit_resolution,[status(thm)],[109,66]) ).
tff(111,plain,
leq(sk10,sk6),
inference(modus_ponens,[status(thm)],[110,79]) ).
tff(112,plain,
( ( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) )
<=> ( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( ~ leq(sk10,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk5,sk6) )
<=> ( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,axiom,
( ~ leq(sk10,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk5,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
tff(115,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[115,112]) ).
tff(117,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[117,112]) ).
tff(119,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[118,112]) ).
tff(120,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[120,112]) ).
tff(122,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[121,112]) ).
tff(123,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[122,112]) ).
tff(124,plain,
~ leq(sk5,sk10),
inference(unit_resolution,[status(thm)],[123,111,44]) ).
tff(125,plain,
^ [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
^ [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
<=> ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )),
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) )
| ~ ssItem(B) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) )
| ~ ssItem(B) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) )),
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) )),
inference(bind,[status(th)],]) ).
tff(128,plain,
( ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) )
<=> ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
( ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) )
<=> ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
^ [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(D) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ~ ssList(E) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ~ ssList(E) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ leq(B,A) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ leq(B,A) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F) )
<=> ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ ssItem(F) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ ssItem(F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ memberP(D,F) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| ~ memberP(D,F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F)
| leq(A,F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(A,F) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(A,F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F)
| leq(A,F) )
<=> ( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) )),
inference(bind,[status(th)],]) ).
tff(131,plain,
( ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F)
| leq(A,F) )
<=> ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,axiom,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ~ ssList(E)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ leq(B,A)
| ~ ssItem(F)
| ~ memberP(D,F)
| leq(A,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(133,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(modus_ponens,[status(thm)],[134,128]) ).
tff(136,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(modus_ponens,[status(thm)],[136,126]) ).
tff(138,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| leq(sk5,sk10)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| leq(sk5,sk10)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ( ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| leq(sk5,sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ~ ssItem(sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( leq(sk5,sk10)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| leq(sk5,sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ~ ssItem(sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| leq(sk5,sk10)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| leq(sk5,sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ~ ssItem(sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| leq(sk5,sk10)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ) ),
inference(transitivity,[status(thm)],[140,138]) ).
tff(142,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| leq(sk5,sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ~ ssItem(sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,F: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(F)
| ~ ssList(E)
| ~ ssItem(A)
| ~ ssList(D)
| leq(A,F)
| ~ memberP(D,F)
| ~ leq(B,A)
| ~ ssItem(B)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) )
| leq(sk5,sk10)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) ) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
$false,
inference(unit_resolution,[status(thm)],[143,137,18,12,9,6,89,85,124,77,66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC153-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 21:54:18 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.
% 10.10/6.76 % SZS status Unsatisfiable
% 10.10/6.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------