%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC002-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:29:53 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 54
% Syntax : Number of formulae : 130 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 1791 ( 533 equ)
% Maximal formula atoms : 28 ( 13 avg)
% Number of connectives : 3072 (1529 ~;1430 |; 0 &)
% ( 113 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 118 ( 118 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 273 ( 247 !; 0 ?; 273 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: ( $i * $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(geq_type,type,
geq: ( $i * $i ) > $o ).
tff(1,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(3,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( memberP(sk4,sk5(sk8,sk7,sk6))
<=> memberP(sk2,sk5(sk8,sk7,sk6)) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( memberP(sk2,sk5(sk8,sk7,sk6))
<=> memberP(sk4,sk5(sk8,sk7,sk6)) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(8,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(11,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[11,8]) ).
tff(13,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[12,7]) ).
tff(14,plain,
( ( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) )
<=> ( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ( ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
( ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_26) ).
tff(17,plain,
( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) ),
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
app(app(sk7,cons(sk6,nil)),sk8) = sk4,
inference(unit_resolution,[status(thm)],[18,13]) ).
tff(20,plain,
app(app(sk7,cons(sk6,nil)),sk8) = sk2,
inference(transitivity,[status(thm)],[19,4]) ).
tff(21,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(23,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) )
<=> ( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( ( app(sk7,sk8) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
( ( app(sk7,sk8) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_27) ).
tff(28,plain,
( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) ),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
app(sk7,sk8) = sk3,
inference(unit_resolution,[status(thm)],[29,13]) ).
tff(31,plain,
app(sk7,sk8) = sk1,
inference(transitivity,[status(thm)],[30,24]) ).
tff(32,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_20) ).
tff(38,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ssList(sk8)
| ~ neq(sk4,nil) )
<=> ( ssList(sk8)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
( ssList(sk8)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_25) ).
tff(44,plain,
( ssList(sk8)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
ssList(sk8),
inference(unit_resolution,[status(thm)],[44,13]) ).
tff(46,plain,
( ( ssList(sk7)
| ~ neq(sk4,nil) )
<=> ( ssList(sk7)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
( ssList(sk7)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_24) ).
tff(48,plain,
( ssList(sk7)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
ssList(sk7),
inference(unit_resolution,[status(thm)],[48,13]) ).
tff(50,plain,
( ( ssItem(sk6)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk6)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
( ssItem(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_23) ).
tff(52,plain,
( ssItem(sk6)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
ssItem(sk6),
inference(unit_resolution,[status(thm)],[52,13]) ).
tff(54,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| memberP(sk2,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| memberP(sk2,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| memberP(sk2,sk5(sk8,sk7,sk6)) )
<=> ( ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| memberP(sk2,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| memberP(sk2,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| memberP(sk2,sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| memberP(sk2,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| memberP(sk2,sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| memberP(sk2,sk5(sk8,sk7,sk6)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| memberP(sk2,sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
memberP(sk2,sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[59,13,53,49,45,41,31,20]) ).
tff(61,plain,
memberP(sk4,sk5(sk8,sk7,sk6)),
inference(modus_ponens,[status(thm)],[60,6]) ).
tff(62,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ssItem(sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ~ neq(sk4,nil) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A))
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
tff(68,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ssItem(sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 ) )
<=> ( ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ssItem(sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
ssItem(sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[77,13,53,49,45,71,31,20]) ).
tff(79,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_21) ).
tff(85,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ),
inference(modus_ponens,[status(thm)],[87,80]) ).
tff(89,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| geq(sk5(sk8,sk7,sk6),sk6) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| geq(sk5(sk8,sk7,sk6),sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ( ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| geq(sk5(sk8,sk7,sk6),sk6) )
<=> ( ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| geq(sk5(sk8,sk7,sk6),sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| geq(sk5(sk8,sk7,sk6),sk6) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| geq(sk5(sk8,sk7,sk6),sk6) ) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| geq(sk5(sk8,sk7,sk6),sk6) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| geq(sk5(sk8,sk7,sk6),sk6) ) ),
inference(transitivity,[status(thm)],[91,89]) ).
tff(93,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| geq(sk5(sk8,sk7,sk6),sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| geq(sk5(sk8,sk7,sk6),sk6) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
geq(sk5(sk8,sk7,sk6),sk6),
inference(unit_resolution,[status(thm)],[94,13,53,49,45,88,31,20]) ).
tff(96,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_22) ).
tff(102,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ( sk6 != sk5(sk8,sk7,sk6) ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ( sk6 != sk5(sk8,sk7,sk6) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ( ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ( sk6 != sk5(sk8,sk7,sk6) ) )
<=> ( ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ( sk6 != sk5(sk8,sk7,sk6) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ( sk6 != sk5(sk8,sk7,sk6) ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ( sk6 != sk5(sk8,sk7,sk6) ) ) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ( sk6 != sk5(sk8,sk7,sk6) ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ( sk6 != sk5(sk8,sk7,sk6) ) ) ),
inference(transitivity,[status(thm)],[108,106]) ).
tff(110,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
| ~ ssList(sk8)
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ( sk6 != sk5(sk8,sk7,sk6) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
| ~ neq(sk4,nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(sk7,sk8) != sk1 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk2 )
| ( sk6 != sk5(sk8,sk7,sk6) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
sk6 != sk5(sk8,sk7,sk6),
inference(unit_resolution,[status(thm)],[111,13,53,49,45,105,31,20]) ).
tff(113,plain,
^ [A: $i] :
refl(( ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
<=> ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
^ [A: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A) )
<=> ( ~ ssItem(A)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
( ( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6) )
<=> ( ~ ssItem(A)
| ~ memberP(sk4,A)
| ( sk6 = A )
| ~ geq(A,sk6) ) )),
rewrite(( ( ~ ssItem(A)
| ~ memberP(sk4,A)
| ( sk6 = A )
| ~ geq(A,sk6) )
<=> ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
( ( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6) )
<=> ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
( ( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6)
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A )
| ~ neq(sk4,nil) ) )),
rewrite(( ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A )
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
( ( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6)
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6)
| ~ neq(sk4,nil) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,axiom,
! [A: $i] :
( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_28) ).
tff(119,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ),
inference(modus_ponens,[status(thm)],[121,114]) ).
tff(123,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ neq(sk4,nil)
| ( sk6 = sk5(sk8,sk7,sk6) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ neq(sk4,nil)
| ( sk6 = sk5(sk8,sk7,sk6) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
( ( ~ ssItem(sk5(sk8,sk7,sk6))
| ~ neq(sk4,nil)
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6))
| ( sk6 = sk5(sk8,sk7,sk6) ) )
<=> ( ~ neq(sk4,nil)
| ( sk6 = sk5(sk8,sk7,sk6) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ neq(sk4,nil)
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6))
| ( sk6 = sk5(sk8,sk7,sk6) ) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ neq(sk4,nil)
| ( sk6 = sk5(sk8,sk7,sk6) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ neq(sk4,nil)
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6))
| ( sk6 = sk5(sk8,sk7,sk6) ) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ neq(sk4,nil)
| ( sk6 = sk5(sk8,sk7,sk6) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[125,123]) ).
tff(127,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ neq(sk4,nil)
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6))
| ( sk6 = sk5(sk8,sk7,sk6) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ neq(sk4,nil)
| ( sk6 = sk5(sk8,sk7,sk6) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
~ memberP(sk4,sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[128,13,122,112,95,78]) ).
tff(130,plain,
$false,
inference(unit_resolution,[status(thm)],[129,61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC002-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 07:59:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------