%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD031-1 : 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 : n016.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 07:11:32 AM UTC 2026
% Result : Unsatisfiable 14.77s 2.34s
% Output : CNFRefutation 14.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 16 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 28 ~; 25 |; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 11 !; 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_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_equals_multiplicative_identity_2,axiom,
equalish(a,multiplicative_identity),
file('theBenchmark.p',a_equals_multiplicative_identity_2) ).
cnf(c_29,plain,
equalish(a,multiplicative_identity),
inference(clausify,[status(thm)],[a_equals_multiplicative_identity_2]) ).
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(multiplicative_inverses_not_equal,axiom,
~ equalish(multiplicative_inverse(a),multiplicative_identity),
file('theBenchmark.p',multiplicative_inverses_not_equal) ).
cnf(c_31,plain,
~ equalish(multiplicative_inverse(a),multiplicative_identity),
inference(clausify,[status(thm)],[multiplicative_inverses_not_equal]) ).
cnf(c_20003,plain,
( equalish(a,additive_identity)
| defined(multiplicative_inverse(a)) ),
inference(resolve,[status(thm)],[c_28,c_15]) ).
cnf(c_135,plain,
defined(multiplicative_inverse(a)),
inference(resolve,[status(thm)],[c_30,c_20003]) ).
cnf(c_20004,plain,
( equalish(a,additive_identity)
| equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity) ),
inference(resolve,[status(thm)],[c_28,c_7]) ).
cnf(c_146,plain,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(resolve,[status(thm)],[c_30,c_20004]) ).
cnf(c_169,plain,
( ~ defined(A)
| equalish(multiply(a,A),multiply(multiplicative_identity,A)) ),
inference(resolve,[status(thm)],[c_29,c_25]) ).
cnf(c_665,plain,
equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(resolve,[status(thm)],[c_135,c_6]) ).
cnf(c_20005,plain,
( ~ equalish(A,multiplicative_identity)
| ~ equalish(multiplicative_inverse(a),A) ),
inference(resolve,[status(thm)],[c_23,c_31]) ).
cnf(c_4374,plain,
~ equalish(multiplicative_inverse(a),multiply(a,multiplicative_inverse(a))),
inference(resolve,[status(thm)],[c_20005,c_146]) ).
cnf(c_5344,plain,
equalish(multiply(a,multiplicative_inverse(a)),multiply(multiplicative_identity,multiplicative_inverse(a))),
inference(resolve,[status(thm)],[c_169,c_135]) ).
cnf(c_6462,plain,
~ equalish(multiply(a,multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(resolve,[status(thm)],[c_22,c_4374]) ).
cnf(c_20006,plain,
( ~ equalish(A,multiplicative_inverse(a))
| ~ equalish(multiply(a,multiplicative_inverse(a)),A) ),
inference(resolve,[status(thm)],[c_23,c_6462]) ).
cnf(c_20007,plain,
~ equalish(multiply(a,multiplicative_inverse(a)),multiply(multiplicative_identity,multiplicative_inverse(a))),
inference(resolve,[status(thm)],[c_20006,c_665]) ).
cnf(c_20002,plain,
$false,
inference(resolve,[status(thm)],[c_5344,c_20007]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD031-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n016.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 02:30:01 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2225751 was started by sandbox2 on n016,
% 0.18/0.44 % Sun Sep 27 02:30:01 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 14.77/2.34
% 14.77/2.34 % given #500 (T,wt=18): 513 less_or_equal(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) | less_or_equal(multiplicative_inverse(multiplicative_identity),multiplicative_identity). [resolve(128,a,115,c)].
% 14.77/2.34
% 14.77/2.34 % given #1000 (F,wt=23): 10165 -equalish(multiply(multiplicative_identity,a),multiply(multiplicative_identity,additive_inverse(additive_identity))). [ur(23,a,8362,a,c,358,a)].
% 14.77/2.34
% 14.77/2.34 % given #1500 (T,wt=20): 1722 defined(multiply(additive_identity,additive_inverse(multiplicative_identity))). [resolve(80,b,84,a)].
% 14.77/2.34
% 14.77/2.34 % SZS status Unsatisfiable for theBenchmark
% 14.77/2.34
% 14.77/2.34 % Proof 1 at 1.29 (+ 0.57) seconds.
% 14.77/2.34 % Length of proof is 18.
% 14.77/2.34 % Level of proof is 4.
% 14.77/2.34 % Maximum clause weight is 26.000.
% 14.77/2.34 % Given clauses 1901.
% 14.77/2.34
% 14.77/2.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------