%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD037-1 : 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 : 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 07:11:33 AM UTC 2026
% Result : Unsatisfiable 6.29s 1.79s
% Output : CNFRefutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 15 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 25 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_inverse_multiplication,axiom,
! [VAR_0] :
( equalish(VAR_0,additive_identity)
| ~ defined(VAR_0)
| equalish(multiply(VAR_0,multiplicative_inverse(VAR_0)),multiplicative_identity) ),
file('theBenchmark.p',existence_of_inverse_multiplication) ).
cnf(c_7,plain,
( equalish(A,additive_identity)
| ~ defined(A)
| equalish(multiply(A,multiplicative_inverse(A)),multiplicative_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_multiplication]) ).
fof(well_definedness_of_multiplicative_inverse,axiom,
! [VAR_0] :
( equalish(VAR_0,additive_identity)
| ~ defined(VAR_0)
| defined(multiplicative_inverse(VAR_0)) ),
file('theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
cnf(c_15,plain,
( equalish(A,additive_identity)
| ~ defined(A)
| defined(multiplicative_inverse(A)) ),
inference(clausify,[status(thm)],[well_definedness_of_multiplicative_inverse]) ).
fof(symmetry_of_equality,axiom,
! [VAR_0,VAR_1] :
( ~ equalish(VAR_1,VAR_0)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry_of_equality) ).
cnf(c_22,plain,
( ~ equalish(B,A)
| equalish(A,B) ),
inference(clausify,[status(thm)],[symmetry_of_equality]) ).
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(a_not_equal_to_additive_identity_3,axiom,
~ equalish(a,additive_identity),
file('theBenchmark.p',a_not_equal_to_additive_identity_3) ).
cnf(c_30,plain,
~ equalish(a,additive_identity),
inference(clausify,[status(thm)],[a_not_equal_to_additive_identity_3]) ).
fof(a_equals_b_4,axiom,
equalish(a,b),
file('theBenchmark.p',a_equals_b_4) ).
cnf(c_31,plain,
equalish(a,b),
inference(clausify,[status(thm)],[a_equals_b_4]) ).
fof(multiplicative_identity_not_equal_to_multiply_5,axiom,
~ equalish(multiplicative_identity,multiply(b,multiplicative_inverse(a))),
file('theBenchmark.p',multiplicative_identity_not_equal_to_multiply_5) ).
cnf(c_32,plain,
~ equalish(multiplicative_identity,multiply(b,multiplicative_inverse(a))),
inference(clausify,[status(thm)],[multiplicative_identity_not_equal_to_multiply_5]) ).
cnf(c_8874,plain,
( equalish(a,additive_identity)
| defined(multiplicative_inverse(a)) ),
inference(resolve,[status(thm)],[c_28,c_15]) ).
cnf(c_136,plain,
defined(multiplicative_inverse(a)),
inference(resolve,[status(thm)],[c_30,c_8874]) ).
cnf(c_8875,plain,
( equalish(a,additive_identity)
| equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity) ),
inference(resolve,[status(thm)],[c_28,c_7]) ).
cnf(c_147,plain,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(resolve,[status(thm)],[c_30,c_8875]) ).
cnf(c_213,plain,
equalish(b,a),
inference(resolve,[status(thm)],[c_31,c_22]) ).
cnf(c_217,plain,
~ equalish(multiply(b,multiplicative_inverse(a)),multiplicative_identity),
inference(resolve,[status(thm)],[c_22,c_32]) ).
cnf(c_8876,plain,
( ~ equalish(A,multiplicative_identity)
| ~ equalish(multiply(b,multiplicative_inverse(a)),A) ),
inference(resolve,[status(thm)],[c_23,c_217]) ).
cnf(c_8620,plain,
~ equalish(multiply(b,multiplicative_inverse(a)),multiply(a,multiplicative_inverse(a))),
inference(resolve,[status(thm)],[c_8876,c_147]) ).
cnf(c_8877,plain,
( ~ equalish(b,a)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolve,[status(thm)],[c_25,c_8620]) ).
cnf(c_8878,plain,
~ defined(multiplicative_inverse(a)),
inference(resolve,[status(thm)],[c_8877,c_213]) ).
cnf(c_8873,plain,
$false,
inference(resolve,[status(thm)],[c_136,c_8878]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD037-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 02:27:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 79791 was started by sandbox on n003,
% 0.10/0.36 % Sun Sep 27 02:27:40 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 6.29/1.79
% 6.29/1.79 % given #500 (F,wt=15): 6287 -equalish(multiply(a,multiplicative_identity),additive_identity). [ur(22,a,6270,a)].
% 6.29/1.79
% 6.29/1.79 % SZS status Unsatisfiable for theBenchmark
% 6.29/1.79
% 6.29/1.79 % Proof 1 at 0.57 (+ 0.18) seconds.
% 6.29/1.79 % Length of proof is 15.
% 6.29/1.79 % Level of proof is 3.
% 6.29/1.79 % Maximum clause weight is 26.000.
% 6.29/1.79 % Given clauses 708.
% 6.29/1.79
% 6.29/1.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------