%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD025-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /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 : Thu Sep 24 08:38:51 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.63s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 31 ( 23 unt; 0 nHn; 31 RR)
% Number of literals : 47 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 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 : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_multiplication,axiom,
( ~ defined(Y)
| ~ defined(X)
| equalish(multiply(X,Y),multiply(Y,X)) ),
file('FLD001-0.ax',commutativity_multiplication) ).
cnf(transitivity_of_equality,axiom,
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
file('FLD001-0.ax',transitivity_of_equality) ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
file('FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(a_equals_b_5,negated_conjecture,
equalish(a,b),
file('theBenchmark.p',a_equals_b_5) ).
cnf(c_equals_d_6,negated_conjecture,
equalish(c,d),
file('theBenchmark.p',c_equals_d_6) ).
cnf(multiply_not_equal_to_multiply_7,negated_conjecture,
~ equalish(multiply(a,c),multiply(d,b)),
file('theBenchmark.p',multiply_not_equal_to_multiply_7) ).
cnf(t1,plain,
~ equalish(multiply(a,c),multiply(d,b)),
inference(start,[status(thm),parent(0:0)],[multiply_not_equal_to_multiply_7]) ).
cnf(t2,plain,
( ~ equalish(multiply(a,c),multiply(c,b))
| ~ equalish(multiply(c,b),multiply(d,b))
| equalish(multiply(a,c),multiply(d,b)) ),
inference(extension,[status(thm),parent(t1:1)],[transitivity_of_equality]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ defined(b)
| ~ equalish(c,d)
| equalish(multiply(c,b),multiply(d,b)) ),
inference(extension,[status(thm),parent(t2:2)],[compatibility_of_equality_and_multiplication]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
equalish(c,d),
inference(extension,[status(thm),parent(t4:2)],[c_equals_d_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
defined(b),
inference(extension,[status(thm),parent(t4:3)],[b_is_defined]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ equalish(multiply(a,c),multiply(b,c))
| ~ equalish(multiply(b,c),multiply(c,b))
| equalish(multiply(a,c),multiply(c,b)) ),
inference(extension,[status(thm),parent(t2:3)],[transitivity_of_equality]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( ~ defined(b)
| ~ defined(c)
| equalish(multiply(b,c),multiply(c,b)) ),
inference(extension,[status(thm),parent(t10:2)],[commutativity_multiplication]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
defined(c),
inference(extension,[status(thm),parent(t12:2)],[c_is_defined]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
defined(b),
inference(extension,[status(thm),parent(t12:3)],[b_is_defined]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
( ~ defined(c)
| ~ equalish(a,b)
| equalish(multiply(a,c),multiply(b,c)) ),
inference(extension,[status(thm),parent(t10:3)],[compatibility_of_equality_and_multiplication]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t10:3]) ).
cnf(t20,plain,
equalish(a,b),
inference(extension,[status(thm),parent(t18:2)],[a_equals_b_5]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
defined(c),
inference(extension,[status(thm),parent(t18:3)],[c_is_defined]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD025-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.53 % Computer : n010.cluster.edu
% 0.09/10.53 % Model : x86_64 x86_64
% 0.09/10.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.53 % Memory : 8046.5625MB
% 0.09/10.53 % OS : Linux 6.8.0-71-generic
% 0.09/10.53 % CPULimit : 300
% 0.09/10.53 % WCLimit : 300
% 0.09/10.53 % DateTime : Sun Sep 20 18:50:37 UTC 2026
% 0.09/10.53 % CPUTime :
% 0.14/10.63 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.63 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------