%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD034-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 07:11:33 AM UTC 2026
% Result : Unsatisfiable 0.93s 0.61s
% Output : CNFRefutation 0.93s
% 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_multiplication,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| equalish(multiply(multiplicative_identity,VAR_0),VAR_0) ),
file('theBenchmark.p',existence_of_identity_multiplication) ).
cnf(c_6,plain,
( ~ defined(A)
| equalish(multiply(multiplicative_identity,A),A) ),
inference(clausify,[status(thm)],[existence_of_identity_multiplication]) ).
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_multiplication,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_0,VAR_2)
| ~ defined(VAR_1)
| equalish(multiply(VAR_0,VAR_1),multiply(VAR_2,VAR_1)) ),
file('theBenchmark.p',compatibility_of_equality_and_multiplication) ).
cnf(c_25,plain,
( ~ equalish(A,C)
| ~ defined(B)
| equalish(multiply(A,B),multiply(C,B)) ),
inference(clausify,[status(thm)],[compatibility_of_equality_and_multiplication]) ).
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_multiplicative_identity_3,axiom,
equalish(m,multiplicative_identity),
file('theBenchmark.p',m_equals_multiplicative_identity_3) ).
cnf(c_30,plain,
equalish(m,multiplicative_identity),
inference(clausify,[status(thm)],[m_equals_multiplicative_identity_3]) ).
fof(multiply_not_equal_to_a_4,axiom,
~ equalish(multiply(m,a),a),
file('theBenchmark.p',multiply_not_equal_to_a_4) ).
cnf(c_31,plain,
~ equalish(multiply(m,a),a),
inference(clausify,[status(thm)],[multiply_not_equal_to_a_4]) ).
cnf(c_138,plain,
equalish(multiply(multiplicative_identity,a),a),
inference(resolve,[status(thm)],[c_28,c_6]) ).
cnf(c_4957,plain,
( ~ equalish(A,a)
| ~ equalish(multiply(m,a),A) ),
inference(resolve,[status(thm)],[c_23,c_31]) ).
cnf(c_4712,plain,
~ equalish(multiply(m,a),multiply(multiplicative_identity,a)),
inference(resolve,[status(thm)],[c_4957,c_138]) ).
cnf(c_4958,plain,
( ~ equalish(m,multiplicative_identity)
| ~ defined(a) ),
inference(resolve,[status(thm)],[c_25,c_4712]) ).
cnf(c_4959,plain,
~ defined(a),
inference(resolve,[status(thm)],[c_4958,c_30]) ).
cnf(c_4956,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_4959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD034-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n017.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 02:20:48 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2132904 was started by sandbox on n017,
% 0.08/0.35 % Sun Sep 27 02:20:48 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.93/0.61
% 0.93/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.93/0.61
% 0.93/0.61 % Proof 1 at 0.18 (+ 0.06) seconds.
% 0.93/0.61 % Length of proof is 9.
% 0.93/0.61 % Level of proof is 3.
% 0.93/0.61 % Maximum clause weight is 22.000.
% 0.93/0.61 % Given clauses 269.
% 0.93/0.61
% 0.93/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------