%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD025-2 : 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 : n005.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 07:11:30 AM UTC 2026
% Result : Unsatisfiable 34.18s 4.78s
% Output : CNFRefutation 34.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 53 ( 35 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 40 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_29,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(c_is_defined,axiom,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(c_30,plain,
defined(c),
inference(clausify,[status(thm)],[c_is_defined]) ).
fof(d_is_defined,axiom,
defined(d),
file('theBenchmark.p',d_is_defined) ).
cnf(c_31,plain,
defined(d),
inference(clausify,[status(thm)],[d_is_defined]) ).
fof(a_equals_b_7,axiom,
equalish(a,b),
file('theBenchmark.p',a_equals_b_7) ).
cnf(c_34,plain,
equalish(a,b),
inference(clausify,[status(thm)],[a_equals_b_7]) ).
fof(c_equals_d_8,axiom,
equalish(c,d),
file('theBenchmark.p',c_equals_d_8) ).
cnf(c_35,plain,
equalish(c,d),
inference(clausify,[status(thm)],[c_equals_d_8]) ).
fof(multiply_equals_u_9,axiom,
equalish(multiply(a,c),u),
file('theBenchmark.p',multiply_equals_u_9) ).
cnf(c_36,plain,
equalish(multiply(a,c),u),
inference(clausify,[status(thm)],[multiply_equals_u_9]) ).
fof(multiply_equals_v_10,axiom,
equalish(multiply(d,b),v),
file('theBenchmark.p',multiply_equals_v_10) ).
cnf(c_37,plain,
equalish(multiply(d,b),v),
inference(clausify,[status(thm)],[multiply_equals_v_10]) ).
fof(v_not_equal_to_u_11,axiom,
~ equalish(v,u),
file('theBenchmark.p',v_not_equal_to_u_11) ).
cnf(c_38,plain,
~ equalish(v,u),
inference(clausify,[status(thm)],[v_not_equal_to_u_11]) ).
cnf(c_137,plain,
( ~ equalish(A,B)
| equalish(multiply(A,a),multiply(B,a)) ),
inference(resolve,[status(thm)],[c_28,c_25]) ).
cnf(c_151,plain,
( ~ defined(A)
| equalish(multiply(A,a),multiply(a,A)) ),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_189,plain,
( ~ defined(A)
| equalish(multiply(A,b),multiply(b,A)) ),
inference(resolve,[status(thm)],[c_29,c_8]) ).
cnf(c_251,plain,
( ~ equalish(A,B)
| equalish(multiply(A,d),multiply(B,d)) ),
inference(resolve,[status(thm)],[c_31,c_25]) ).
cnf(c_370,plain,
equalish(b,a),
inference(resolve,[status(thm)],[c_34,c_22]) ).
cnf(c_376,plain,
equalish(d,c),
inference(resolve,[status(thm)],[c_35,c_22]) ).
cnf(c_388,plain,
equalish(v,multiply(d,b)),
inference(resolve,[status(thm)],[c_37,c_22]) ).
cnf(c_26409,plain,
( ~ equalish(A,u)
| ~ equalish(v,A) ),
inference(resolve,[status(thm)],[c_23,c_38]) ).
cnf(c_389,plain,
~ equalish(v,multiply(a,c)),
inference(resolve,[status(thm)],[c_26409,c_36]) ).
cnf(c_10283,plain,
equalish(multiply(d,a),multiply(c,a)),
inference(resolve,[status(thm)],[c_137,c_376]) ).
cnf(c_13014,plain,
equalish(multiply(d,a),multiply(a,d)),
inference(resolve,[status(thm)],[c_151,c_31]) ).
cnf(c_13015,plain,
equalish(multiply(c,a),multiply(a,c)),
inference(resolve,[status(thm)],[c_151,c_30]) ).
cnf(c_20059,plain,
equalish(multiply(d,b),multiply(b,d)),
inference(resolve,[status(thm)],[c_189,c_31]) ).
cnf(c_23981,plain,
equalish(multiply(b,d),multiply(a,d)),
inference(resolve,[status(thm)],[c_251,c_370]) ).
cnf(c_26410,plain,
( ~ equalish(A,multiply(a,c))
| ~ equalish(v,A) ),
inference(resolve,[status(thm)],[c_23,c_389]) ).
cnf(c_25939,plain,
~ equalish(v,multiply(c,a)),
inference(resolve,[status(thm)],[c_26410,c_13015]) ).
cnf(c_26411,plain,
( ~ equalish(A,multiply(c,a))
| ~ equalish(v,A) ),
inference(resolve,[status(thm)],[c_23,c_25939]) ).
cnf(c_25940,plain,
~ equalish(v,multiply(d,a)),
inference(resolve,[status(thm)],[c_26411,c_10283]) ).
cnf(c_25945,plain,
~ equalish(multiply(d,a),v),
inference(resolve,[status(thm)],[c_22,c_25940]) ).
cnf(c_26412,plain,
( ~ equalish(A,v)
| ~ equalish(multiply(d,a),A) ),
inference(resolve,[status(thm)],[c_23,c_25945]) ).
cnf(c_25952,plain,
~ equalish(multiply(a,d),v),
inference(resolve,[status(thm)],[c_26412,c_13014]) ).
cnf(c_25956,plain,
~ equalish(v,multiply(a,d)),
inference(resolve,[status(thm)],[c_22,c_25952]) ).
cnf(c_26413,plain,
( ~ equalish(A,multiply(a,d))
| ~ equalish(v,A) ),
inference(resolve,[status(thm)],[c_23,c_25956]) ).
cnf(c_25968,plain,
~ equalish(multiply(d,b),multiply(a,d)),
inference(resolve,[status(thm)],[c_26413,c_388]) ).
cnf(c_26414,plain,
( ~ equalish(A,multiply(a,d))
| ~ equalish(multiply(d,b),A) ),
inference(resolve,[status(thm)],[c_23,c_25968]) ).
cnf(c_26415,plain,
~ equalish(multiply(b,d),multiply(a,d)),
inference(resolve,[status(thm)],[c_26414,c_20059]) ).
cnf(c_26408,plain,
$false,
inference(resolve,[status(thm)],[c_23981,c_26415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD025-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.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 02:23:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 3593520 was started by sandbox on n005,
% 0.10/0.38 % Sun Sep 27 02:23:31 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 34.18/4.78
% 34.18/4.78 % given #500 (A,wt=20): 126 less_or_equal(add(A,multiplicative_identity),add(B,multiplicative_identity)) | -less_or_equal(A,B). [resolve(19,b,14,a)].
% 34.18/4.78
% 34.18/4.78 % given #1000 (W,wt=15): 23282 -equalish(additive_identity,add(multiplicative_identity,additive_identity)). [ur(23,a,5931,a,c,922,a)].
% 34.18/4.78
% 34.18/4.78 % given #1500 (A,wt=32): 301 equalish(add(multiply(A,B),multiply(u,B)),multiply(add(A,u),B)) | -defined(A) | -defined(B). [resolve(32,a,9,c)].
% 34.18/4.78
% 34.18/4.78 % given #2000 (T,wt=17): 17124 less_or_equal(multiply(u,b),multiply(u,b)). [resolve(16956,a,53,b)].
% 34.18/4.78
% 34.18/4.78 % SZS status Unsatisfiable for theBenchmark
% 34.18/4.78
% 34.18/4.78 % Proof 1 at 3.10 (+ 1.24) seconds.
% 34.18/4.78 % Length of proof is 33.
% 34.18/4.78 % Level of proof is 9.
% 34.18/4.78 % Maximum clause weight is 22.000.
% 34.18/4.78 % Given clauses 2081.
% 34.18/4.78
% 34.18/4.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------