%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD002-3 : 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 : n017.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 0.39s 0.68s
% Output : Proof 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of clauses : 41 ( 28 unt; 2 nHn; 41 RR)
% Number of literals : 66 ( 0 equ; 25 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
file('FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('FLD002-0.ax',commutativity_multiplication) ).
cnf(distributivity_1,axiom,
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
file('FLD002-0.ax',distributivity_1) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
file('FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(totality_of_order_relation,axiom,
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
file('FLD002-0.ax',totality_of_order_relation) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(product_3,hypothesis,
product(multiplicative_identity,a,b),
file('theBenchmark.p',product_3) ).
cnf(not_sum_4,negated_conjecture,
~ sum(additive_identity,a,b),
file('theBenchmark.p',not_sum_4) ).
cnf(t1,plain,
~ sum(additive_identity,a,b),
inference(start,[status(thm),parent(0:0)],[not_sum_4]) ).
cnf(t2,plain,
( ~ sum(additive_identity,a,a)
| ~ product(a,multiplicative_identity,b)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(a,multiplicative_identity,a)
| sum(additive_identity,a,b) ),
inference(extension,[status(thm),parent(t1:1)],[distributivity_1]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ product(multiplicative_identity,a,a)
| product(a,multiplicative_identity,a) ),
inference(extension,[status(thm),parent(t2:2)],[commutativity_multiplication]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ defined(a)
| product(multiplicative_identity,a,a) ),
inference(extension,[status(thm),parent(t4:2)],[existence_of_identity_multiplication]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
defined(a),
inference(extension,[status(thm),parent(t6:2)],[a_is_defined]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ product(multiplicative_identity,additive_identity,additive_identity)
| product(additive_identity,multiplicative_identity,additive_identity) ),
inference(extension,[status(thm),parent(t2:3)],[commutativity_multiplication]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( ~ defined(additive_identity)
| product(multiplicative_identity,additive_identity,additive_identity) ),
inference(extension,[status(thm),parent(t10:2)],[existence_of_identity_multiplication]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
defined(additive_identity),
inference(extension,[status(thm),parent(t12:2)],[well_definedness_of_additive_identity]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ product(multiplicative_identity,a,b)
| product(a,multiplicative_identity,b) ),
inference(extension,[status(thm),parent(t2:4)],[commutativity_multiplication]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:4]) ).
cnf(t18,plain,
product(multiplicative_identity,a,b),
inference(extension,[status(thm),parent(t16:2)],[product_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ less_or_equal(a,a)
| ~ less_or_equal(a,a)
| sum(additive_identity,a,a) ),
inference(extension,[status(thm),parent(t2:5)],[antisymmetry_of_order_relation]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:5]) ).
cnf(t22,plain,
( ~ defined(a)
| ~ defined(a)
| less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(extension,[status(thm),parent(t20:2)],[totality_of_order_relation]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
$false,
inference(reduction,[status(thm),parent(t22:2)],[t22:2,t20:2]) ).
cnf(t25,plain,
defined(a),
inference(extension,[status(thm),parent(t22:3)],[a_is_defined]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t22:3]) ).
cnf(l13,lemma,
defined(a),
inference(lemma,[status(cth),parent(t22:3),below(t20:2)],[t22:3]) ).
cnf(t27,plain,
defined(a),
inference(lemma_extension,[status(thm),parent(t22:4)],[l13:1]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t22:4]) ).
cnf(l11,lemma,
less_or_equal(a,a),
inference(lemma,[status(cth),parent(t20:2),below(t2:5)],[t20:2]) ).
cnf(t29,plain,
less_or_equal(a,a),
inference(lemma_extension,[status(thm),parent(t20:3)],[l11:1]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t20:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD002-3 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.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 18:38:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.39/0.68 % SZS status Unsatisfiable for theBenchmark
% 0.39/0.68 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------