%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC185-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:30:27 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of formulae : 54 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 478 ( 95 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 844 ( 448 ~; 360 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 126 ( 114 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk7_type,type,
sk7: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( app(app(sk6,cons(sk5,nil)),sk7) = sk1 )
<=> ( app(app(sk6,cons(sk5,nil)),sk7) = sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(6,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk3,
inference(transitivity,[status(thm)],[6,3]) ).
tff(8,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(10,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(13,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(16,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(23,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk6,sk5) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk6,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk6,sk5) )
<=> ( ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk6,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk6,sk5) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk6,sk5) ) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk6,sk5) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk6,sk5) ) ),
inference(transitivity,[status(thm)],[29,27]) ).
tff(31,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk6,sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(B,A) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk6,sk5) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
~ memberP(sk6,sk5),
inference(unit_resolution,[status(thm)],[32,26,16,13,10,7]) ).
tff(34,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(C,A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(C,A) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(C,A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(C,A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk3 )
| ~ memberP(C,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(40,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk7,sk5) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk7,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ memberP(sk7,sk5)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 ) )
<=> ( ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk7,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ memberP(sk7,sk5)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk7,sk5) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ memberP(sk7,sk5)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk7,sk5) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ memberP(sk7,sk5)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ~ memberP(C,A)
| ( app(app(B,cons(A,nil)),C) != sk3 ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != sk3 )
| ~ memberP(sk7,sk5) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
~ memberP(sk7,sk5),
inference(unit_resolution,[status(thm)],[49,43,16,13,10,7]) ).
tff(51,plain,
( ( memberP(sk6,sk5)
| memberP(sk7,sk5) )
<=> ( memberP(sk6,sk5)
| memberP(sk7,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
( memberP(sk6,sk5)
| memberP(sk7,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(53,plain,
( memberP(sk6,sk5)
| memberP(sk7,sk5) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
$false,
inference(unit_resolution,[status(thm)],[53,50,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC185-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n008.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 08:32:48 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.18/0.41 % SZS status Unsatisfiable
% 0.18/0.41 % SZS output start Proof
% See solution above
% 0.18/0.43 % E exiting
%------------------------------------------------------------------------------