%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD059-4 : 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 : n001.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 08:39:00 AM UTC 2026
% Result : Unsatisfiable 2.95s 3.25s
% Output : Proof 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of clauses : 41 ( 30 unt; 2 nHn; 41 RR)
% Number of literals : 66 ( 0 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_addition,axiom,
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('FLD002-0.ax',existence_of_identity_addition) ).
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(transitivity_of_order_relation,axiom,
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('FLD002-0.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('FLD002-0.ax',totality_of_order_relation) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
file('FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(less_or_equal_3,negated_conjecture,
less_or_equal(additive_identity,a),
file('theBenchmark.p',less_or_equal_3) ).
cnf(sum_4,negated_conjecture,
sum(a,a,u),
file('theBenchmark.p',sum_4) ).
cnf(not_less_or_equal_5,negated_conjecture,
~ less_or_equal(additive_identity,u),
file('theBenchmark.p',not_less_or_equal_5) ).
cnf(t1,plain,
~ less_or_equal(additive_identity,u),
inference(start,[status(thm),parent(0:0)],[not_less_or_equal_5]) ).
cnf(t2,plain,
( ~ defined(additive_identity)
| ~ defined(u)
| less_or_equal(u,additive_identity)
| less_or_equal(additive_identity,u) ),
inference(extension,[status(thm),parent(t1:1)],[totality_of_order_relation]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ less_or_equal(a,u)
| less_or_equal(a,additive_identity)
| ~ less_or_equal(u,additive_identity) ),
inference(extension,[status(thm),parent(t2:2)],[transitivity_of_order_relation]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ less_or_equal(additive_identity,a)
| sum(additive_identity,a,additive_identity)
| ~ less_or_equal(a,additive_identity) ),
inference(extension,[status(thm),parent(t4:2)],[antisymmetry_of_order_relation]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ less_or_equal(additive_identity,a)
| ~ sum(a,a,u)
| less_or_equal(additive_identity,u)
| ~ sum(additive_identity,a,additive_identity) ),
inference(extension,[status(thm),parent(t6:2)],[compatibility_of_order_relation_and_addition]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t1:1]) ).
cnf(t11,plain,
sum(a,a,u),
inference(extension,[status(thm),parent(t8:3)],[sum_4]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t8:3]) ).
cnf(t13,plain,
less_or_equal(additive_identity,a),
inference(extension,[status(thm),parent(t8:4)],[less_or_equal_3]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t8:4]) ).
cnf(t15,plain,
less_or_equal(additive_identity,a),
inference(extension,[status(thm),parent(t6:3)],[less_or_equal_3]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t6:3]) ).
cnf(t17,plain,
( ~ less_or_equal(additive_identity,a)
| ~ sum(additive_identity,a,a)
| ~ sum(a,a,u)
| less_or_equal(a,u) ),
inference(extension,[status(thm),parent(t4:3)],[compatibility_of_order_relation_and_addition]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t4:3]) ).
cnf(t19,plain,
sum(a,a,u),
inference(extension,[status(thm),parent(t17:2)],[sum_4]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t17:2]) ).
cnf(t21,plain,
( ~ defined(a)
| sum(additive_identity,a,a) ),
inference(extension,[status(thm),parent(t17:3)],[existence_of_identity_addition]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t17:3]) ).
cnf(t23,plain,
defined(a),
inference(extension,[status(thm),parent(t21:2)],[a_is_defined]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t21:2]) ).
cnf(t25,plain,
less_or_equal(additive_identity,a),
inference(extension,[status(thm),parent(t17:4)],[less_or_equal_3]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t17:4]) ).
cnf(t27,plain,
defined(u),
inference(extension,[status(thm),parent(t2:3)],[u_is_defined]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t2:3]) ).
cnf(t29,plain,
defined(additive_identity),
inference(extension,[status(thm),parent(t2:4)],[well_definedness_of_additive_identity]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD059-4 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:11:44 UTC 2026
% 0.08/0.35 % CPUTime :
% 2.95/3.25 % SZS status Unsatisfiable for theBenchmark
% 2.95/3.25 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------