%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC398-1 : 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 : n013.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 08:57:42 AM UTC 2026
% Result : Unsatisfiable 87.18s 11.88s
% Output : CNFRefutation 87.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 21 unt; 0 def)
% Number of atoms : 40 ( 6 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 2 ( 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 : 9 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause140,axiom,
! [VAR_0,VAR_1,VAR_2] :
( memberP(app(VAR_0,VAR_2),VAR_1)
| ~ ssItem(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| ~ memberP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause140) ).
cnf(c_162,plain,
( memberP(app(A,C),B)
| ~ ssItem(B)
| ~ ssList(A)
| ~ ssList(C)
| ~ memberP(A,B) ),
inference(clausify,[status(thm)],[clause140]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_199,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_203,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_204,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_7,axiom,
ssList(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_205,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_8,axiom,
app(sk3,sk5) = sk4,
file('theBenchmark.p',co1_8) ).
cnf(c_206,plain,
app(sk3,sk5) = sk4,
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_11,axiom,
ssItem(sk6),
file('theBenchmark.p',co1_11) ).
cnf(c_208,plain,
ssItem(sk6),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_12,axiom,
memberP(sk1,sk6),
file('theBenchmark.p',co1_12) ).
cnf(c_209,plain,
memberP(sk1,sk6),
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_13,axiom,
~ memberP(sk2,sk6),
file('theBenchmark.p',co1_13) ).
cnf(c_210,plain,
~ memberP(sk2,sk6),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_16792,plain,
( memberP(app(sk1,A),sk6)
| ~ ssItem(sk6)
| ~ ssList(sk1)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_209,c_162]) ).
cnf(c_16793,plain,
( memberP(app(sk1,A),sk6)
| ~ ssItem(sk6)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_199,c_16792]) ).
cnf(c_3504,plain,
( memberP(app(sk1,A),sk6)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_208,c_16793]) ).
cnf(c_3507,plain,
~ memberP(sk4,sk6),
inference(paramod,[status(thm)],[c_203,c_210]) ).
cnf(c_16736,plain,
memberP(app(sk1,sk5),sk6),
inference(resolve,[status(thm)],[c_3504,c_205]) ).
cnf(c_16771,plain,
memberP(app(sk3,sk5),sk6),
inference(paramod,[status(thm)],[c_204,c_16736]) ).
cnf(c_16794,plain,
memberP(sk4,sk6),
inference(paramod,[status(thm)],[c_206,c_16771]) ).
cnf(c_16791,plain,
$false,
inference(resolve,[status(thm)],[c_3507,c_16794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC398-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 12:57:37 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2795511 was started by sandbox on n013,
% 0.09/0.37 % Sat Sep 26 12:57:37 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 87.18/11.88
% 87.18/11.88 % given #500 (I,wt=36): 562 app(A,cons(B,cons(C,cons(C,nil)))) != cons(C,nil) | -ssList(cons(C,nil)) | -ssList(A) | -ssItem(C) | -ssItem(B) | B = C. [factor(373,d,g)].
% 87.18/11.88
% 87.18/11.88 % given #1000 (T,wt=8): 3120 sk1 != nil | rearsegP(nil,sk1). [resolve(199,a,115,b),flip(a)].
% 87.18/11.88
% 87.18/11.88 % given #1500 (F,wt=13): 10709 cons(skaf44(A),skaf75(B)) != nil. [resolve(1377,b,62,a)].
% 87.18/11.88
% 87.18/11.88 % SZS status Unsatisfiable for theBenchmark
% 87.18/11.88
% 87.18/11.88 % Proof 1 at 2.68 (+ 0.72) seconds.
% 87.18/11.88 % Length of proof is 14.
% 87.18/11.88 % Level of proof is 4.
% 87.18/11.88 % Maximum clause weight is 18.000.
% 87.18/11.88 % Given clauses 1965.
% 87.18/11.88
% 87.18/11.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------