%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD010-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 07:11:26 AM UTC 2026
% Result : Unsatisfiable 0.24s 10.85s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 8 !; 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(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_identity,axiom,
defined(multiplicative_identity),
file('theBenchmark.p',well_definedness_of_multiplicative_identity) ).
cnf(c_14,plain,
defined(multiplicative_identity),
inference(clausify,[status(thm)],[well_definedness_of_multiplicative_identity]) ).
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(different_identities,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('theBenchmark.p',different_identities) ).
cnf(c_27,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(clausify,[status(thm)],[different_identities]) ).
fof(multiplicative_inv_not_equal_to_multiplicative_id_2,axiom,
~ equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('theBenchmark.p',multiplicative_inv_not_equal_to_multiplicative_id_2) ).
cnf(c_28,plain,
~ equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(clausify,[status(thm)],[multiplicative_inv_not_equal_to_multiplicative_id_2]) ).
cnf(c_89,plain,
( equalish(multiplicative_identity,additive_identity)
| equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_110,plain,
( equalish(multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_118,plain,
~ equalish(multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_22,c_27]) ).
cnf(c_119,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(resolve,[status(thm)],[c_118,c_110]) ).
cnf(c_120,plain,
equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity),
inference(resolve,[status(thm)],[c_118,c_89]) ).
cnf(c_361,plain,
equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)),
inference(resolve,[status(thm)],[c_119,c_6]) ).
cnf(c_1910,plain,
( ~ equalish(A,multiplicative_identity)
| ~ equalish(multiplicative_inverse(multiplicative_identity),A) ),
inference(resolve,[status(thm)],[c_23,c_28]) ).
cnf(c_1901,plain,
~ equalish(multiplicative_inverse(multiplicative_identity),multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity))),
inference(resolve,[status(thm)],[c_1910,c_120]) ).
cnf(c_1911,plain,
~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity)),
inference(resolve,[status(thm)],[c_22,c_1901]) ).
cnf(c_1909,plain,
$false,
inference(resolve,[status(thm)],[c_361,c_1911]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD010-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/10.68 % Computer : n010.cluster.edu
% 0.19/10.68 % Model : x86_64 x86_64
% 0.19/10.68 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/10.68 % Memory : 8046.5625MB
% 0.19/10.68 % OS : Linux 6.8.0-71-generic
% 0.19/10.68 % CPULimit : 300
% 0.19/10.68 % WCLimit : 300
% 0.19/10.68 % DateTime : Sun Sep 27 02:21:43 UTC 2026
% 0.19/10.68 % CPUTime :
% 0.19/10.68 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/10.68 % Process 526655 was started by sandbox2 on n010,
% 0.19/10.68 % Sun Sep 27 02:21:43 2026
% 0.19/10.68 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/10.69
% 0.19/10.69 % From the command line: assign(max_seconds, 300).
% 0.24/10.85
% 0.24/10.85 % SZS status Unsatisfiable for theBenchmark
% 0.24/10.85
% 0.24/10.85 % Proof 1 at 0.10 (+ 0.05) seconds.
% 0.24/10.85 % Length of proof is 16.
% 0.24/10.85 % Level of proof is 4.
% 0.24/10.85 % Maximum clause weight is 26.000.
% 0.24/10.85 % Given clauses 248.
% 0.24/10.85
% 0.24/10.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------