%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC408-1 : 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 : n003.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 08:57:44 AM UTC 2026
% Result : Unsatisfiable 16.03s 2.48s
% Output : CNFRefutation 16.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 18 unt; 0 def)
% Number of atoms : 40 ( 6 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 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_161,plain,
( memberP(app(A,C),B)
| ~ ssItem(B)
| ~ ssList(A)
| ~ ssList(C)
| ~ memberP(A,B) ),
inference(clausify,[status(thm)],[clause140]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_201,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_5,axiom,
app(sk4,sk4) = sk3,
file('theBenchmark.p',co1_5) ).
cnf(c_202,plain,
app(sk4,sk4) = sk3,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_6,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_6) ).
cnf(c_203,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_7,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_7) ).
cnf(c_204,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_8,axiom,
ssItem(sk5),
file('theBenchmark.p',co1_8) ).
cnf(c_205,plain,
ssItem(sk5),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_9,axiom,
memberP(sk2,sk5),
file('theBenchmark.p',co1_9) ).
cnf(c_206,plain,
memberP(sk2,sk5),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_207,plain,
memberP(sk4,sk5),
inference(paramod,[status(thm)],[c_203,c_206]) ).
fof(co1_10,axiom,
~ memberP(sk1,sk5),
file('theBenchmark.p',co1_10) ).
cnf(c_208,plain,
~ memberP(sk1,sk5),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_209,plain,
~ memberP(sk3,sk5),
inference(paramod,[status(thm)],[c_204,c_208]) ).
cnf(c_309,plain,
( memberP(app(A,A),B)
| ~ ssItem(B)
| ~ ssList(A)
| ~ memberP(A,B) ),
inference(factor,[status(thm)],[c_161]) ).
cnf(c_8812,plain,
( memberP(app(sk4,sk4),sk5)
| ~ ssItem(sk5)
| ~ ssList(sk4) ),
inference(resolve,[status(thm)],[c_309,c_207]) ).
cnf(c_8813,plain,
( memberP(sk3,sk5)
| ~ ssItem(sk5)
| ~ ssList(sk4) ),
inference(paramod,[status(thm)],[c_202,c_8812]) ).
cnf(c_8814,plain,
( memberP(sk3,sk5)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_201,c_8813]) ).
cnf(c_8815,plain,
memberP(sk3,sk5),
inference(resolve,[status(thm)],[c_205,c_8814]) ).
cnf(c_8811,plain,
$false,
inference(resolve,[status(thm)],[c_209,c_8815]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC408-1 : 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 : n003.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 13:00:54 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 2938347 was started by sandbox on n003,
% 0.12/0.36 % Sat Sep 26 13:00:54 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 16.03/2.48
% 16.03/2.48 % SZS status Unsatisfiable for theBenchmark
% 16.03/2.48
% 16.03/2.48 % Proof 1 at 1.68 (+ 0.37) seconds.
% 16.03/2.48 % Length of proof is 12.
% 16.03/2.48 % Level of proof is 2.
% 16.03/2.48 % Maximum clause weight is 18.000.
% 16.03/2.48 % Given clauses 253.
% 16.03/2.48
% 16.03/2.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------