%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET046-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 08:35:29 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 4 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 13 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 9 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_1,axiom,
! [VAR_0,VAR_1] :
( ~ element(VAR_1,VAR_0)
| ~ element(VAR_0,VAR_1)
| ~ element(VAR_0,a) ),
file('theBenchmark.p',clause_1) ).
cnf(c_1,plain,
( ~ element(B,A)
| ~ element(A,B)
| ~ element(A,a) ),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_2,axiom,
! [VAR_0] :
( element(VAR_0,a)
| element(VAR_0,f(VAR_0)) ),
file('theBenchmark.p',clause_2) ).
cnf(c_2,plain,
( element(A,a)
| element(A,f(A)) ),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_3,axiom,
! [VAR_0] :
( element(VAR_0,a)
| element(f(VAR_0),VAR_0) ),
file('theBenchmark.p',clause_3) ).
cnf(c_3,plain,
( element(A,a)
| element(f(A),A) ),
inference(clausify,[status(thm)],[clause_3]) ).
cnf(c_15,plain,
( ~ element(a,a)
| ~ element(a,a) ),
inference(factor,[status(thm)],[c_1]) ).
cnf(c_5,plain,
~ element(a,a),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_7,plain,
( ~ element(f(A),A)
| ~ element(f(A),a)
| element(A,a) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_16,plain,
( ~ element(f(a),a)
| element(a,a) ),
inference(factor,[status(thm)],[c_7]) ).
cnf(c_8,plain,
~ element(f(a),a),
inference(resolve,[status(thm)],[c_5,c_16]) ).
cnf(c_17,plain,
element(a,a),
inference(resolve,[status(thm)],[c_8,c_3]) ).
cnf(c_14,plain,
$false,
inference(resolve,[status(thm)],[c_5,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET046-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 07:00:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3024242 was started by sandbox2 on n008,
% 0.10/0.37 % Sat Sep 26 07:00:26 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 7.
% 0.10/0.39 % Level of proof is 3.
% 0.10/0.39 % Maximum clause weight is 11.000.
% 0.10/0.39 % Given clauses 8.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------