%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD005-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 08:38:46 AM UTC 2026
% Result : Unsatisfiable 20.88s 21.27s
% Output : Proof 20.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of clauses : 66 ( 43 unt; 0 nHn; 66 RR)
% Number of literals : 106 ( 0 equ; 42 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_addition,axiom,
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ),
file('FLD001-0.ax',associativity_addition) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
file('FLD001-0.ax',existence_of_identity_addition) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
file('FLD001-0.ax',existence_of_inverse_addition) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
file('FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(commutativity_multiplication,axiom,
( ~ defined(Y)
| ~ defined(X)
| equalish(multiply(X,Y),multiply(Y,X)) ),
file('FLD001-0.ax',commutativity_multiplication) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(well_definedness_of_multiplication,axiom,
( ~ defined(Y)
| ~ defined(X)
| defined(multiply(X,Y)) ),
file('FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
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_addition,axiom,
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(add(X,Z),add(Y,Z)) ),
file('FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(add_not_equal_to_b_3,negated_conjecture,
~ equalish(add(a,X),b),
file('theBenchmark.p',add_not_equal_to_b_3) ).
cnf(t1,plain,
~ equalish(add(a,add(additive_inverse(a),multiply(b,multiplicative_identity))),b),
inference(start,[status(thm),parent(0:0)],[add_not_equal_to_b_3]) ).
cnf(t2,plain,
( ~ equalish(add(a,add(additive_inverse(a),multiply(b,multiplicative_identity))),add(additive_identity,multiply(b,multiplicative_identity)))
| ~ equalish(add(additive_identity,multiply(b,multiplicative_identity)),b)
| equalish(add(a,add(additive_inverse(a),multiply(b,multiplicative_identity))),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,
( ~ equalish(add(additive_identity,multiply(b,multiplicative_identity)),multiply(b,multiplicative_identity))
| ~ equalish(multiply(b,multiplicative_identity),b)
| equalish(add(additive_identity,multiply(b,multiplicative_identity)),b) ),
inference(extension,[status(thm),parent(t2:2)],[transitivity_of_equality]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ equalish(multiply(b,multiplicative_identity),multiply(multiplicative_identity,b))
| ~ equalish(multiply(multiplicative_identity,b),b)
| equalish(multiply(b,multiplicative_identity),b) ),
inference(extension,[status(thm),parent(t4:2)],[transitivity_of_equality]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ defined(b)
| equalish(multiply(multiplicative_identity,b),b) ),
inference(extension,[status(thm),parent(t6:2)],[existence_of_identity_multiplication]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
defined(b),
inference(extension,[status(thm),parent(t8:2)],[b_is_defined]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ defined(b)
| ~ defined(multiplicative_identity)
| equalish(multiply(b,multiplicative_identity),multiply(multiplicative_identity,b)) ),
inference(extension,[status(thm),parent(t6:3)],[commutativity_multiplication]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t6:3]) ).
cnf(t14,plain,
defined(multiplicative_identity),
inference(extension,[status(thm),parent(t12:2)],[well_definedness_of_multiplicative_identity]) ).
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(multiply(b,multiplicative_identity))
| equalish(add(additive_identity,multiply(b,multiplicative_identity)),multiply(b,multiplicative_identity)) ),
inference(extension,[status(thm),parent(t4:3)],[existence_of_identity_addition]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t4:3]) ).
cnf(t20,plain,
( ~ defined(b)
| ~ defined(multiplicative_identity)
| defined(multiply(b,multiplicative_identity)) ),
inference(extension,[status(thm),parent(t18:2)],[well_definedness_of_multiplication]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
defined(multiplicative_identity),
inference(extension,[status(thm),parent(t20:2)],[well_definedness_of_multiplicative_identity]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
defined(b),
inference(extension,[status(thm),parent(t20:3)],[b_is_defined]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
( ~ equalish(add(a,add(additive_inverse(a),multiply(b,multiplicative_identity))),add(add(a,additive_inverse(a)),multiply(b,multiplicative_identity)))
| ~ equalish(add(add(a,additive_inverse(a)),multiply(b,multiplicative_identity)),add(additive_identity,multiply(b,multiplicative_identity)))
| equalish(add(a,add(additive_inverse(a),multiply(b,multiplicative_identity))),add(additive_identity,multiply(b,multiplicative_identity))) ),
inference(extension,[status(thm),parent(t2:3)],[transitivity_of_equality]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t2:3]) ).
cnf(t28,plain,
( ~ defined(multiply(b,multiplicative_identity))
| ~ equalish(add(a,additive_inverse(a)),additive_identity)
| equalish(add(add(a,additive_inverse(a)),multiply(b,multiplicative_identity)),add(additive_identity,multiply(b,multiplicative_identity))) ),
inference(extension,[status(thm),parent(t26:2)],[compatibility_of_equality_and_addition]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( ~ defined(a)
| equalish(add(a,additive_inverse(a)),additive_identity) ),
inference(extension,[status(thm),parent(t28:2)],[existence_of_inverse_addition]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
defined(a),
inference(extension,[status(thm),parent(t30:2)],[a_is_defined]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( ~ defined(b)
| ~ defined(multiplicative_identity)
| defined(multiply(b,multiplicative_identity)) ),
inference(extension,[status(thm),parent(t28:3)],[well_definedness_of_multiplication]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t28:3]) ).
cnf(t36,plain,
defined(multiplicative_identity),
inference(extension,[status(thm),parent(t34:2)],[well_definedness_of_multiplicative_identity]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
defined(b),
inference(extension,[status(thm),parent(t34:3)],[b_is_defined]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
cnf(t40,plain,
( ~ defined(a)
| ~ defined(additive_inverse(a))
| ~ defined(multiply(b,multiplicative_identity))
| equalish(add(a,add(additive_inverse(a),multiply(b,multiplicative_identity))),add(add(a,additive_inverse(a)),multiply(b,multiplicative_identity))) ),
inference(extension,[status(thm),parent(t26:3)],[associativity_addition]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t26:3]) ).
cnf(t42,plain,
( ~ defined(b)
| ~ defined(multiplicative_identity)
| defined(multiply(b,multiplicative_identity)) ),
inference(extension,[status(thm),parent(t40:2)],[well_definedness_of_multiplication]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
defined(multiplicative_identity),
inference(extension,[status(thm),parent(t42:2)],[well_definedness_of_multiplicative_identity]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
defined(b),
inference(extension,[status(thm),parent(t42:3)],[b_is_defined]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
( ~ defined(a)
| defined(additive_inverse(a)) ),
inference(extension,[status(thm),parent(t40:3)],[well_definedness_of_additive_inverse]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t40:3]) ).
cnf(t50,plain,
defined(a),
inference(extension,[status(thm),parent(t48:2)],[a_is_defined]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
defined(a),
inference(extension,[status(thm),parent(t40:4)],[a_is_defined]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t40:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD005-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n026.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 20 18:48:51 UTC 2026
% 0.15/0.42 % CPUTime :
% 20.88/21.27 % SZS status Unsatisfiable for theBenchmark
% 20.88/21.27 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------