%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC331-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:57:30 AM UTC 2026
% Result : Unsatisfiable 50.04s 6.79s
% Output : CNFRefutation 50.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 34 ( 20 unt; 0 def)
% Number of atoms : 65 ( 16 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 70 ( 39 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_12,axiom,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
file('theBenchmark.p',co1_12) ).
cnf(c_42,plain,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_9,axiom,
equalelemsP(sk3),
file('theBenchmark.p',co1_9) ).
cnf(c_46,plain,
equalelemsP(sk3),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
app(sk3,sk5) = sk4,
file('theBenchmark.p',co1_8) ).
cnf(c_47,plain,
app(sk3,sk5) = sk4,
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
ssList(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_48,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_49,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_50,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_51,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_52,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(clause173,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( segmentP(VAR_3,VAR_1)
| ~ ssList(VAR_3)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| app(app(VAR_0,VAR_1),VAR_2) != VAR_3 ),
file('theBenchmark.p',clause173) ).
cnf(c_63,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_146,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_207,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_14058,plain,
( ~ equalelemsP(sk1)
| ~ segmentP(sk4,sk1) ),
inference(paramod,[status(thm)],[c_50,c_42]) ).
cnf(c_14059,plain,
( ~ equalelemsP(sk1)
| ~ segmentP(sk4,sk3) ),
inference(paramod,[status(thm)],[c_49,c_14058]) ).
cnf(c_14060,plain,
( ~ equalelemsP(sk3)
| ~ segmentP(sk4,sk3) ),
inference(paramod,[status(thm)],[c_49,c_14059]) ).
cnf(c_287,plain,
~ segmentP(sk4,sk3),
inference(resolve,[status(thm)],[c_46,c_14060]) ).
cnf(c_859,plain,
( segmentP(sk4,B)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != sk4 ),
inference(resolve,[status(thm)],[c_63,c_51]) ).
cnf(c_1325,plain,
app(nil,sk3) = sk3,
inference(resolve,[status(thm)],[c_146,c_52]) ).
cnf(c_14061,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(paramod,[status(thm)],[c_1325,c_859]) ).
cnf(c_14062,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_207,c_14061]) ).
cnf(c_14063,plain,
( segmentP(sk4,sk3)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_52,c_14062]) ).
cnf(c_14055,plain,
( ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_287,c_14063]) ).
cnf(c_14064,plain,
~ ssList(sk5),
inference(resolve,[status(thm)],[c_14055,c_47]) ).
cnf(c_14057,plain,
$false,
inference(resolve,[status(thm)],[c_48,c_14064]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC331-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 12:51:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1024937 was started by sandbox on n026,
% 0.09/0.36 % Sat Sep 26 12:51:40 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 50.04/6.79
% 50.04/6.79 % given #500 (I,wt=40): 548 -lt(skaf59(A),skaf60(A)) | -ssList(A) | app(app(A,cons(B,C)),cons(D,A)) != A | -ssList(C) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B). [factor(365,b,e)].
% 50.04/6.79
% 50.04/6.79 % given #1000 (F,wt=12): 11297 -gt(skaf65(A),skac2) | -gt(skac2,skaf65(A)). [resolve(7326,c,185,a)].
% 50.04/6.79
% 50.04/6.79 % SZS status Unsatisfiable for theBenchmark
% 50.04/6.79
% 50.04/6.79 % Proof 1 at 4.76 (+ 1.53) seconds.
% 50.04/6.79 % Length of proof is 16.
% 50.04/6.79 % Level of proof is 3.
% 50.04/6.79 % Maximum clause weight is 26.000.
% 50.04/6.79 % Given clauses 1154.
% 50.04/6.79
% 50.04/6.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------