%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC189-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:28 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 21
% Syntax : Number of formulae : 39 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 323 ( 93 equ)
% Maximal formula atoms : 24 ( 8 avg)
% Number of connectives : 515 ( 251 ~; 239 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 84 ( 76 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk8_type,type,
sk8: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk7_type,type,
sk7: $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(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1 )
<=> ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(6,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk3,
inference(transitivity,[status(thm)],[6,3]) ).
tff(8,plain,
( ( sk5 != sk6 )
<=> ( sk5 != sk6 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
sk5 != sk6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(10,plain,
sk5 != sk6,
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ssList(sk8)
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(13,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(16,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(19,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(22,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
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)
| ( A = B ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( A = B ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ~ ssItem(B)
| ( A = B ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ( A = B ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ( A = B )
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ) )),
( ( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ( A = B )
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ( A = B )
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssItem(B)
| ~ ssList(C)
| ~ ssList(D)
| ( A = B )
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(29,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
| ( sk5 = sk6 )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
| ( sk5 = sk6 )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ( sk5 = sk6 )
| ~ ssItem(sk6)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ( sk5 = sk6 )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ( sk5 = sk6 )
| ~ ssItem(sk6)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
| ( sk5 = sk6 )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != sk3 ) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ( sk5 = sk6 )
| ~ ssItem(sk6)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != sk3 ) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
| ( sk5 = sk6 )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != sk3 ) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ( sk5 = sk6 )
| ~ ssItem(sk6)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(D)
| ( A = B )
| ~ ssItem(B)
| ( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3 ) )
| ( sk5 = sk6 )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != sk3 ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,32,22,19,16,13,10,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC189-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.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 08:34:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% See solution above
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------