%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET044-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 08:35:28 AM UTC 2026
% Result : Unsatisfiable 0.02s 0.38s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 4 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 13 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_1,axiom,
! [VAR_0] :
( element(VAR_0,VAR_0)
| ~ element(VAR_0,a) ),
file('theBenchmark.p',clause_1) ).
cnf(c_1,plain,
( element(A,A)
| ~ element(A,a) ),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_2,axiom,
! [VAR_0] :
( element(VAR_0,a)
| ~ element(VAR_0,VAR_0) ),
file('theBenchmark.p',clause_2) ).
cnf(c_2,plain,
( element(A,a)
| ~ element(A,A) ),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_3,axiom,
! [VAR_0,VAR_1] :
( ~ element(VAR_0,VAR_1)
| ~ element(VAR_0,f(VAR_1)) ),
file('theBenchmark.p',clause_3) ).
cnf(c_3,plain,
( ~ element(A,B)
| ~ element(A,f(B)) ),
inference(clausify,[status(thm)],[clause_3]) ).
fof(clause_4,axiom,
! [VAR_0,VAR_1] :
( element(VAR_0,f(VAR_1))
| element(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_4) ).
cnf(c_4,plain,
( element(A,f(B))
| element(A,B) ),
inference(clausify,[status(thm)],[clause_4]) ).
cnf(c_5,plain,
( element(f(A),a)
| element(f(A),A) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_6,plain,
element(f(a),a),
inference(factor,[status(thm)],[c_5]) ).
cnf(c_8,plain,
element(f(a),f(a)),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_10,plain,
~ element(f(a),f(a)),
inference(resolve,[status(thm)],[c_3,c_6]) ).
cnf(c_9,plain,
$false,
inference(resolve,[status(thm)],[c_8,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET044-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.36 % Computer : n011.cluster.edu
% 0.02/0.36 % Model : x86_64 x86_64
% 0.02/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.36 % Memory : 8046.5625MB
% 0.02/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sat Sep 26 06:59:13 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 4028318 was started by sandbox on n011,
% 0.02/0.36 % Sat Sep 26 06:59:13 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.36
% 0.02/0.36 % From the command line: assign(max_seconds, 300).
% 0.02/0.38
% 0.02/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.02/0.38
% 0.02/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.02/0.38 % Length of proof is 8.
% 0.02/0.38 % Level of proof is 4.
% 0.02/0.38 % Maximum clause weight is 8.000.
% 0.02/0.38 % Given clauses 6.
% 0.02/0.38
% 0.02/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------