%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD025-1 : 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 : n008.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 8.50s 1.60s
% Output : CNFRefutation 8.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 24 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 31 ~; 21 |; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 8 !; 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(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_5,axiom,
equalish(a,b),
file('theBenchmark.p',a_equals_b_5) ).
cnf(c_32,plain,
equalish(a,b),
inference(clausify,[status(thm)],[a_equals_b_5]) ).
fof(c_equals_d_6,axiom,
equalish(c,d),
file('theBenchmark.p',c_equals_d_6) ).
cnf(c_33,plain,
equalish(c,d),
inference(clausify,[status(thm)],[c_equals_d_6]) ).
fof(multiply_not_equal_to_multiply_7,axiom,
~ equalish(multiply(a,c),multiply(d,b)),
file('theBenchmark.p',multiply_not_equal_to_multiply_7) ).
cnf(c_34,plain,
~ equalish(multiply(a,c),multiply(d,b)),
inference(clausify,[status(thm)],[multiply_not_equal_to_multiply_7]) ).
cnf(c_138,plain,
( ~ defined(A)
| equalish(multiply(A,a),multiply(a,A)) ),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_139,plain,
( ~ defined(A)
| equalish(multiply(a,A),multiply(A,a)) ),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_174,plain,
( ~ defined(A)
| equalish(multiply(b,A),multiply(A,b)) ),
inference(resolve,[status(thm)],[c_29,c_8]) ).
cnf(c_267,plain,
( ~ defined(A)
| equalish(multiply(a,A),multiply(b,A)) ),
inference(resolve,[status(thm)],[c_32,c_25]) ).
cnf(c_272,plain,
( ~ defined(A)
| equalish(multiply(c,A),multiply(d,A)) ),
inference(resolve,[status(thm)],[c_33,c_25]) ).
cnf(c_5045,plain,
equalish(multiply(d,a),multiply(a,d)),
inference(resolve,[status(thm)],[c_138,c_31]) ).
cnf(c_5077,plain,
equalish(multiply(a,c),multiply(c,a)),
inference(resolve,[status(thm)],[c_139,c_30]) ).
cnf(c_10545,plain,
equalish(multiply(b,d),multiply(d,b)),
inference(resolve,[status(thm)],[c_174,c_31]) ).
cnf(c_15629,plain,
equalish(multiply(a,d),multiply(b,d)),
inference(resolve,[status(thm)],[c_267,c_31]) ).
cnf(c_15826,plain,
equalish(multiply(c,a),multiply(d,a)),
inference(resolve,[status(thm)],[c_272,c_28]) ).
cnf(c_19505,plain,
( ~ equalish(A,multiply(d,b))
| ~ equalish(multiply(a,c),A) ),
inference(resolve,[status(thm)],[c_23,c_34]) ).
cnf(c_16766,plain,
~ equalish(multiply(c,a),multiply(d,b)),
inference(resolve,[status(thm)],[c_19505,c_5077]) ).
cnf(c_19506,plain,
( ~ equalish(A,multiply(d,b))
| ~ equalish(multiply(c,a),A) ),
inference(resolve,[status(thm)],[c_23,c_16766]) ).
cnf(c_17514,plain,
~ equalish(multiply(c,a),multiply(b,d)),
inference(resolve,[status(thm)],[c_19506,c_10545]) ).
cnf(c_19507,plain,
( ~ equalish(A,multiply(b,d))
| ~ equalish(multiply(c,a),A) ),
inference(resolve,[status(thm)],[c_23,c_17514]) ).
cnf(c_19496,plain,
~ equalish(multiply(c,a),multiply(a,d)),
inference(resolve,[status(thm)],[c_19507,c_15629]) ).
cnf(c_19508,plain,
( ~ equalish(A,multiply(a,d))
| ~ equalish(multiply(c,a),A) ),
inference(resolve,[status(thm)],[c_23,c_19496]) ).
cnf(c_19509,plain,
~ equalish(multiply(c,a),multiply(d,a)),
inference(resolve,[status(thm)],[c_19508,c_5045]) ).
cnf(c_19504,plain,
$false,
inference(resolve,[status(thm)],[c_15826,c_19509]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD025-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 02:24:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 822952 was started by sandbox on n008,
% 0.11/0.37 % Sun Sep 27 02:24:24 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 8.50/1.60
% 8.50/1.60 % given #500 (T,wt=14): 4742 defined(multiply(a,d)). [resolve(131,b,31,a)].
% 8.50/1.60
% 8.50/1.60 % given #1000 (W,wt=17): 11491 less_or_equal(multiplicative_identity,c) | less_or_equal(additive_identity,multiplicative_identity) | less_or_equal(c,A) | -less_or_equal(additive_identity,A). [resolve(4672,b,17,b)].
% 8.50/1.60
% 8.50/1.60 % SZS status Unsatisfiable for theBenchmark
% 8.50/1.60
% 8.50/1.60 % Proof 1 at 0.86 (+ 0.34) seconds.
% 8.50/1.60 % Length of proof is 24.
% 8.50/1.60 % Level of proof is 6.
% 8.50/1.60 % Maximum clause weight is 22.000.
% 8.50/1.60 % Given clauses 1285.
% 8.50/1.60
% 8.50/1.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------