%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC153-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 : Sat Jun 21 05:30:20 AM UTC 2025
% Result : Unsatisfiable 6.66s 6.83s
% Output : Proof 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 57
% Syntax : Number of formulae : 134 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 2072 ( 227 equ)
% Maximal formula atoms : 39 ( 15 avg)
% Number of connectives : 3610 (1807 ~;1686 |; 0 &)
% ( 117 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 135 ( 135 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 412 ( 373 !; 0 ?; 412 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk3_type,type,
sk3: $i ).
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(sk5_type,type,
sk5: $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk10_type,type,
sk10: $i ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(1,plain,
( ( sk3 = sk1 )
<=> ( sk3 = sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk3 = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk3 = sk1,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk1 = sk3,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1 )
<=> ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
tff(7,plain,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk3,
inference(transitivity,[status(thm)],[7,4]) ).
tff(9,plain,
( leq(sk6,sk5)
<=> leq(sk6,sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
leq(sk6,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(11,plain,
leq(sk6,sk5),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
( ssList(sk9)
<=> ssList(sk9) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
ssList(sk9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(14,plain,
ssList(sk9),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
( ssList(sk8)
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(17,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(20,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(23,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(26,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,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) != 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) != sk3 ) ) )),
inference(bind,[status(th)],[]) ).
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 ) )
<=> ! [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)],[27]) ).
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) != 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(30,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(31,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)],[30]) ).
tff(32,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(33,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)],[32,31]) ).
tff(34,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)],[33,29]) ).
tff(35,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(skolemize,[status(sab)],[34]) ).
tff(36,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)],[35,28]) ).
tff(37,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 ) )
| leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk6,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != 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 ) )
| leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk6,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
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) != sk3 ) )
<=> ( leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk6,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,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 ) )
| ~ 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) != 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 ) )
| leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk6,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != sk3 ) ) ),
inference(monotonicity,[status(thm)],[38]) ).
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) != sk3 ) )
| ~ 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) != 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 ) )
| leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk6,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != sk3 ) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
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) != sk3 ) )
| ~ 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) != sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
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) != sk3 ) )
| leq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk6,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != sk3 ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
leq(sk5,sk6),
inference(unit_resolution,[status(thm)],[42,36,26,23,20,17,14,11,8]) ).
tff(44,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(45,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)],[44]) ).
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(rewrite,[status(thm)],[]) ).
tff(47,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(48,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)],[47]) ).
tff(49,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(50,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| ~ ssItem(V)
| ~ leq(U,V)
| ~ leq(V,U) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,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(55,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(56,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)],[55]) ).
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(transitivity,[status(thm)],[56,54]) ).
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) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,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)],[58,57]) ).
tff(60,plain,
( ~ leq(sk5,sk6)
| ( sk6 = sk5 ) ),
inference(unit_resolution,[status(thm)],[59,53,26,23,11]) ).
tff(61,plain,
sk6 = sk5,
inference(unit_resolution,[status(thm)],[60,43]) ).
tff(62,plain,
cons(sk6,nil) = cons(sk5,nil),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
cons(sk5,nil) = cons(sk6,nil),
inference(symmetry,[status(thm)],[62]) ).
tff(64,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)],[63]) ).
tff(65,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)],[64]) ).
tff(66,plain,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) = sk3,
inference(transitivity,[status(thm)],[65,7,4]) ).
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)],[76,73,26]) ).
tff(78,plain,
sk5 = sk6,
inference(symmetry,[status(thm)],[61]) ).
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)],[84,43]) ).
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)],[88,43]) ).
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)
| ( 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) ) )),
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)
| ( 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(quant_intro,[status(thm)],[90]) ).
tff(92,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(93,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(94,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)],[93]) ).
tff(95,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(96,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)],[95,94]) ).
tff(97,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)],[96,92]) ).
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(skolemize,[status(sab)],[97]) ).
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)],[98,91]) ).
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)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) )
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| leq(sk10,sk5) )
<=> ( ~ ! [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) )
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| leq(sk10,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| ~ ssItem(sk5)
| leq(sk10,sk5) )
<=> ( ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| leq(sk10,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
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)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| ~ ssItem(sk5)
| leq(sk10,sk5) )
<=> ( ~ ! [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) )
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| leq(sk10,sk5) ) ),
inference(monotonicity,[status(thm)],[101]) ).
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)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| ~ ssItem(sk5)
| leq(sk10,sk5) )
<=> ( ~ ! [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) )
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| leq(sk10,sk5) ) ),
inference(transitivity,[status(thm)],[102,100]) ).
tff(104,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) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| ~ ssItem(sk5)
| leq(sk10,sk5) ),
inference(quant_inst,[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)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B)
| leq(F,B) )
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| leq(sk10,sk5) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
( ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| leq(sk10,sk5) ),
inference(unit_resolution,[status(thm)],[105,99,26,20,17,14,89,85,77]) ).
tff(107,plain,
leq(sk10,sk5),
inference(unit_resolution,[status(thm)],[106,66]) ).
tff(108,plain,
leq(sk10,sk6),
inference(modus_ponens,[status(thm)],[107,79]) ).
tff(109,plain,
( ( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) )
<=> ( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ( ~ leq(sk10,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk5,sk6) )
<=> ( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,axiom,
( ~ leq(sk10,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk5,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
tff(112,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[112,109]) ).
tff(114,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[113,109]) ).
tff(115,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[114,109]) ).
tff(116,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(modus_ponens,[status(thm)],[115,109]) ).
tff(117,plain,
~ leq(sk5,sk10),
inference(unit_resolution,[status(thm)],[116,108,43]) ).
tff(118,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)
| ( 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) != sk3 )
| ~ ssItem(B) ) )),
inference(bind,[status(th)],[]) ).
tff(119,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(quant_intro,[status(thm)],[118]) ).
tff(120,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(121,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(122,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)],[121]) ).
tff(123,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(124,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)],[123,122]) ).
tff(125,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)],[124,120]) ).
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)
| ( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3 )
| ~ ssItem(B) ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,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)],[126,119]) ).
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) )
| leq(sk5,sk10)
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 ) )
<=> ( ~ ! [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) )
| leq(sk5,sk10)
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
( ( ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| leq(sk5,sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| ~ ssItem(sk5) )
<=> ( leq(sk5,sk10)
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,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) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| leq(sk5,sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| ~ ssItem(sk5) )
<=> ( ~ ! [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) )
| leq(sk5,sk10)
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 ) ) ),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,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) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| leq(sk5,sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| ~ ssItem(sk5) )
<=> ( ~ ! [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) )
| leq(sk5,sk10)
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 ) ) ),
inference(transitivity,[status(thm)],[130,128]) ).
tff(132,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) )
| ~ ssList(sk7)
| ~ ssItem(sk10)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| leq(sk5,sk10)
| ~ memberP(sk8,sk10)
| ~ leq(sk5,sk5)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 )
| ~ ssItem(sk5) ),
inference(quant_inst,[status(thm)],[]) ).
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) )
| leq(sk5,sk10)
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ leq(sk5,sk5)
| ~ ssItem(sk10)
| ~ memberP(sk8,sk10)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9) != sk3 ) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
$false,
inference(unit_resolution,[status(thm)],[133,127,26,20,17,14,89,85,117,77,66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SWC153-1 : TPTP v9.0.0. Released v2.4.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.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 : Fri Jun 20 08:27:10 EDT 2025
% 0.13/0.36 % CPUTime :
% 6.66/6.83 % SZS status Unsatisfiable
% 6.66/6.83 % SZS output start Proof
% See solution above
% 6.66/6.88 % E exiting
%------------------------------------------------------------------------------