%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD021-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:11:29 AM UTC 2026
% Result : Unsatisfiable 0.86s 0.53s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| equalish(add(additive_identity,VAR_0),VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_2,plain,
( ~ defined(A)
| equalish(add(additive_identity,A),A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(transitivity_of_equality,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_2,VAR_1)
| ~ equalish(VAR_0,VAR_2)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_equality) ).
cnf(c_23,plain,
( ~ equalish(C,B)
| ~ equalish(A,C)
| equalish(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_equality]) ).
fof(compatibility_of_equality_and_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_0,VAR_2)
| ~ defined(VAR_1)
| equalish(add(VAR_0,VAR_1),add(VAR_2,VAR_1)) ),
file('theBenchmark.p',compatibility_of_equality_and_addition) ).
cnf(c_24,plain,
( ~ equalish(A,C)
| ~ defined(B)
| equalish(add(A,B),add(C,B)) ),
inference(clausify,[status(thm)],[compatibility_of_equality_and_addition]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_28,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(m_equals_additive_identity_3,axiom,
equalish(m,additive_identity),
file('theBenchmark.p',m_equals_additive_identity_3) ).
cnf(c_30,plain,
equalish(m,additive_identity),
inference(clausify,[status(thm)],[m_equals_additive_identity_3]) ).
fof(add_not_equal_to_a_4,axiom,
~ equalish(add(m,a),a),
file('theBenchmark.p',add_not_equal_to_a_4) ).
cnf(c_31,plain,
~ equalish(add(m,a),a),
inference(clausify,[status(thm)],[add_not_equal_to_a_4]) ).
cnf(c_145,plain,
equalish(add(additive_identity,a),a),
inference(resolve,[status(thm)],[c_28,c_2]) ).
cnf(c_2507,plain,
( ~ equalish(A,a)
| ~ equalish(add(m,a),A) ),
inference(resolve,[status(thm)],[c_23,c_31]) ).
cnf(c_1924,plain,
~ equalish(add(m,a),add(additive_identity,a)),
inference(resolve,[status(thm)],[c_2507,c_145]) ).
cnf(c_2508,plain,
( ~ equalish(m,additive_identity)
| ~ defined(a) ),
inference(resolve,[status(thm)],[c_24,c_1924]) ).
cnf(c_2509,plain,
~ defined(a),
inference(resolve,[status(thm)],[c_2508,c_30]) ).
cnf(c_2506,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_2509]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD021-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 02:23:07 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3107924 was started by sandbox2 on n004,
% 0.11/0.37 % Sun Sep 27 02:23:07 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.86/0.53
% 0.86/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.86/0.53
% 0.86/0.53 % Proof 1 at 0.10 (+ 0.04) seconds.
% 0.86/0.53 % Length of proof is 9.
% 0.86/0.53 % Level of proof is 3.
% 0.86/0.53 % Maximum clause weight is 12.000.
% 0.86/0.53 % Given clauses 142.
% 0.86/0.53
% 0.86/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------