%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD032-1 : 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 : 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 07:11:32 AM UTC 2026
% Result : Unsatisfiable 112.55s 15.76s
% Output : CNFRefutation 112.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 19 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 35 ~; 31 |; 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 : 32 ( 0 sgn 13 !; 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(commutativity_multiplication,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| equalish(multiply(VAR_0,VAR_1),multiply(VAR_1,VAR_0)) ),
file('theBenchmark.p',commutativity_multiplication) ).
cnf(c_8,plain,
( ~ defined(B)
| ~ defined(A)
| equalish(multiply(A,B),multiply(B,A)) ),
inference(clausify,[status(thm)],[commutativity_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_2,axiom,
~ equalish(a,additive_identity),
file('theBenchmark.p',a_not_equal_to_additive_identity_2) ).
cnf(c_29,plain,
~ equalish(a,additive_identity),
inference(clausify,[status(thm)],[a_not_equal_to_additive_identity_2]) ).
fof(multiplicative_inverses_equal,axiom,
equalish(multiplicative_inverse(a),multiplicative_identity),
file('theBenchmark.p',multiplicative_inverses_equal) ).
cnf(c_30,plain,
equalish(multiplicative_inverse(a),multiplicative_identity),
inference(clausify,[status(thm)],[multiplicative_inverses_equal]) ).
fof(a_not_equal_to_multiplicative_identity_4,axiom,
~ equalish(a,multiplicative_identity),
file('theBenchmark.p',a_not_equal_to_multiplicative_identity_4) ).
cnf(c_31,plain,
~ equalish(a,multiplicative_identity),
inference(clausify,[status(thm)],[a_not_equal_to_multiplicative_identity_4]) ).
cnf(c_130,plain,
( ~ equalish(A,B)
| equalish(multiply(A,a),multiply(B,a)) ),
inference(resolve,[status(thm)],[c_28,c_25]) ).
cnf(c_25840,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_29,c_25840]) ).
cnf(c_144,plain,
( ~ defined(A)
| equalish(multiply(A,a),multiply(a,A)) ),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_25841,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_29,c_25841]) ).
cnf(c_147,plain,
equalish(multiply(multiplicative_identity,a),a),
inference(resolve,[status(thm)],[c_28,c_6]) ).
cnf(c_174,plain,
equalish(multiplicative_identity,multiplicative_inverse(a)),
inference(resolve,[status(thm)],[c_30,c_22]) ).
cnf(c_934,plain,
equalish(a,multiply(multiplicative_identity,a)),
inference(resolve,[status(thm)],[c_147,c_22]) ).
cnf(c_25842,plain,
( ~ equalish(A,multiplicative_identity)
| ~ equalish(a,A) ),
inference(resolve,[status(thm)],[c_23,c_31]) ).
cnf(c_1037,plain,
~ equalish(multiply(multiplicative_identity,a),multiplicative_identity),
inference(resolve,[status(thm)],[c_25842,c_934]) ).
cnf(c_3163,plain,
equalish(multiply(multiplicative_inverse(a),a),multiply(a,multiplicative_inverse(a))),
inference(resolve,[status(thm)],[c_144,c_135]) ).
cnf(c_4428,plain,
equalish(multiply(multiplicative_identity,a),multiply(multiplicative_inverse(a),a)),
inference(resolve,[status(thm)],[c_130,c_174]) ).
cnf(c_25843,plain,
( ~ equalish(A,multiplicative_identity)
| ~ equalish(multiply(multiplicative_identity,a),A) ),
inference(resolve,[status(thm)],[c_23,c_1037]) ).
cnf(c_14994,plain,
~ equalish(multiply(multiplicative_identity,a),multiply(a,multiplicative_inverse(a))),
inference(resolve,[status(thm)],[c_25843,c_146]) ).
cnf(c_25844,plain,
( ~ equalish(A,multiply(a,multiplicative_inverse(a)))
| ~ equalish(multiply(multiplicative_identity,a),A) ),
inference(resolve,[status(thm)],[c_23,c_14994]) ).
cnf(c_25845,plain,
~ equalish(multiply(multiplicative_inverse(a),a),multiply(a,multiplicative_inverse(a))),
inference(resolve,[status(thm)],[c_25844,c_4428]) ).
cnf(c_25839,plain,
$false,
inference(resolve,[status(thm)],[c_3163,c_25845]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD032-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 02:25:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 536422 was started by sandbox2 on n010,
% 0.14/0.37 % Sun Sep 27 02:25:30 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 112.55/15.76
% 112.55/15.76 % given #500 (W,wt=18): 2744 equalish(add(multiplicative_identity,additive_identity),A) | -equalish(multiplicative_identity,A). [resolve(2724,a,23,b)].
% 112.55/15.76
% 112.55/15.76 % given #1000 (T,wt=20): 2836 less_or_equal(A,add(a,additive_identity)) | -equalish(multiply(multiplicative_identity,a),A). [resolve(2829,a,26,b)].
% 112.55/15.76
% 112.55/15.76 % given #1500 (T,wt=21): 1999 defined(add(multiply(a,multiplicative_identity),a)). [resolve(139,b,1630,a)].
% 112.55/15.76
% 112.55/15.76 % given #2000 (W,wt=21): 18445 defined(add(additive_inverse(additive_identity),multiplicative_inverse(a))). [resolve(279,b,135,a)].
% 112.55/15.76
% 112.55/15.76 % given #2500 (W,wt=21): 20203 less_or_equal(a,multiplicative_identity) | less_or_equal(A,a) | -equalish(add(additive_identity,multiplicative_identity),A). [resolve(20137,b,26,b)].
% 112.55/15.76
% 112.55/15.76 % given #3000 (T,wt=22): 13683 less_or_equal(additive_identity,multiply(multiplicative_identity,multiplicative_identity)) | less_or_equal(add(multiplicative_identity,additive_identity),multiply(additive_identity,additive_identity)). [resolve(5320,b,954,b)].
% 112.55/15.76
% 112.55/15.76 % given #3500 (T,wt=22): 19647 less_or_equal(multiply(multiplicative_identity,additive_identity),additive_inverse(multiplicative_identity)) | less_or_equal(additive_inverse(multiplicative_identity),add(additive_identity,additive_identity)). [resolve(4687,b,2365,b)].
% 112.55/15.76
% 112.55/15.76 % given #4000 (W,wt=22): 24290 less_or_equal(a,multiply(additive_identity,additive_identity)) | -less_or_equal(add(a,additive_identity),multiply(additive_identity,multiplicative_identity)). [resolve(14640,b,16,c),unit_del(b,2711)].
% 112.55/15.76
% 112.55/15.76 % SZS status Unsatisfiable for theBenchmark
% 112.55/15.76
% 112.55/15.76 % Proof 1 at 5.10 (+ 2.11) seconds.
% 112.55/15.76 % Length of proof is 23.
% 112.55/15.76 % Level of proof is 5.
% 112.55/15.76 % Maximum clause weight is 26.000.
% 112.55/15.76 % Given clauses 4396.
% 112.55/15.76
% 112.55/15.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------