%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD013-2 : 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 : n016.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 08:38:48 AM UTC 2026
% Result : Unsatisfiable 0.67s 0.90s
% Output : Proof 0.67s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(commutativity_addition,axiom,
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ),
file('FLD001-0.ax',commutativity_addition) ).
cnf(associativity_multiplication,axiom,
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)) ),
file('FLD001-0.ax',associativity_multiplication) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
file('FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( equalish(X,additive_identity)
| ~ defined(X)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ),
file('FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(commutativity_multiplication,axiom,
( ~ defined(Y)
| ~ defined(X)
| equalish(multiply(X,Y),multiply(Y,X)) ),
file('FLD001-0.ax',commutativity_multiplication) ).
cnf(distributivity,axiom,
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(multiply(X,Z),multiply(Y,Z)),multiply(add(X,Y),Z)) ),
file('FLD001-0.ax',distributivity) ).
cnf(well_definedness_of_addition,axiom,
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
file('FLD001-0.ax',well_definedness_of_addition) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('FLD001-0.ax',well_definedness_of_additive_identity) ).
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(well_definedness_of_multiplicative_inverse,axiom,
( equalish(X,additive_identity)
| ~ defined(X)
| defined(multiplicative_inverse(X)) ),
file('FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| equalish(X,Y) ),
file('FLD001-0.ax',antisymmetry_of_order_relation) ).
cnf(transitivity_of_order_relation,axiom,
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('FLD001-0.ax',transitivity_of_order_relation) ).
cnf(totality_of_order_relation,axiom,
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
file('FLD001-0.ax',totality_of_order_relation) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ less_or_equal(X,Y)
| ~ defined(Z)
| less_or_equal(add(X,Z),add(Y,Z)) ),
file('FLD001-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(compatibility_of_order_relation_and_multiplication,axiom,
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
file('FLD001-0.ax',compatibility_of_order_relation_and_multiplication) ).
cnf(reflexivity_of_equality,axiom,
( ~ defined(X)
| equalish(X,X) ),
file('FLD001-0.ax',reflexivity_of_equality) ).
cnf(symmetry_of_equality,axiom,
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('FLD001-0.ax',symmetry_of_equality) ).
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(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(compatibility_of_equality_and_order_relation,axiom,
( ~ equalish(X,Y)
| ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ),
file('FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
cnf(different_identities,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('FLD001-0.ax',different_identities) ).
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(c_is_defined,hypothesis,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('theBenchmark.p',d_is_defined) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(a_equals_b_6,negated_conjecture,
equalish(a,b),
file('theBenchmark.p',a_equals_b_6) ).
cnf(c_equals_d_7,negated_conjecture,
equalish(c,d),
file('theBenchmark.p',c_equals_d_7) ).
cnf(add_equals_u_8,negated_conjecture,
equalish(add(a,c),u),
file('theBenchmark.p',add_equals_u_8) ).
cnf(add_not_equal_to_u_9,negated_conjecture,
~ equalish(add(d,b),u),
file('theBenchmark.p',add_not_equal_to_u_9) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 18:52:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.67/0.90 % SZS status Unsatisfiable for theBenchmark
% 0.67/0.90 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------