%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD008-4 : 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 : 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 08:38:47 AM UTC 2026
% Result : Unsatisfiable 90.34s 90.65s
% Output : Proof 90.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 13
% Syntax : Number of clauses : 61 ( 41 unt; 2 nHn; 61 RR)
% Number of literals : 95 ( 0 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_addition_1,axiom,
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
file('FLD002-0.ax',associativity_addition_1) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('FLD002-0.ax',existence_of_identity_addition) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('FLD002-0.ax',existence_of_inverse_addition) ).
cnf(commutativity_addition,axiom,
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('FLD002-0.ax',commutativity_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('FLD002-0.ax',well_definedness_of_additive_inverse) ).
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(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(sum_5,negated_conjecture,
sum(a,b,c),
file('theBenchmark.p',sum_5) ).
cnf(sum_6,negated_conjecture,
sum(additive_inverse(a),additive_inverse(b),d),
file('theBenchmark.p',sum_6) ).
cnf(not_sum_7,negated_conjecture,
~ sum(additive_identity,additive_inverse(c),d),
file('theBenchmark.p',not_sum_7) ).
cnf(t1,plain,
~ sum(additive_identity,additive_inverse(c),d),
inference(start,[status(thm),parent(0:0)],[not_sum_7]) ).
cnf(t2,plain,
( ~ sum(additive_inverse(c),additive_identity,d)
| sum(additive_identity,additive_inverse(c),d) ),
inference(extension,[status(thm),parent(t1:1)],[commutativity_addition]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ sum(additive_inverse(c),b,additive_inverse(a))
| ~ sum(b,additive_inverse(b),additive_identity)
| ~ sum(additive_inverse(a),additive_inverse(b),d)
| sum(additive_inverse(c),additive_identity,d) ),
inference(extension,[status(thm),parent(t2:2)],[associativity_addition_1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sum(additive_inverse(a),additive_inverse(b),d),
inference(extension,[status(thm),parent(t4:2)],[sum_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ sum(additive_inverse(b),b,additive_identity)
| sum(b,additive_inverse(b),additive_identity) ),
inference(extension,[status(thm),parent(t4:3)],[commutativity_addition]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ defined(b)
| sum(additive_inverse(b),b,additive_identity) ),
inference(extension,[status(thm),parent(t8:2)],[existence_of_inverse_addition]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
defined(b),
inference(extension,[status(thm),parent(t10:2)],[b_is_defined]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ sum(additive_inverse(c),c,additive_identity)
| ~ sum(c,additive_inverse(a),b)
| ~ sum(additive_identity,additive_inverse(a),additive_inverse(a))
| sum(additive_inverse(c),b,additive_inverse(a)) ),
inference(extension,[status(thm),parent(t4:4)],[associativity_addition_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:4]) ).
cnf(t16,plain,
( ~ less_or_equal(additive_inverse(a),additive_inverse(a))
| ~ less_or_equal(additive_inverse(a),additive_inverse(a))
| sum(additive_identity,additive_inverse(a),additive_inverse(a)) ),
inference(extension,[status(thm),parent(t14:2)],[antisymmetry_of_order_relation]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ defined(additive_inverse(a))
| ~ defined(additive_inverse(a))
| less_or_equal(additive_inverse(a),additive_inverse(a))
| less_or_equal(additive_inverse(a),additive_inverse(a)) ),
inference(extension,[status(thm),parent(t16:2)],[totality_of_order_relation]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
$false,
inference(reduction,[status(thm),parent(t18:2)],[t18:2,t16:2]) ).
cnf(t21,plain,
( ~ defined(a)
| defined(additive_inverse(a)) ),
inference(extension,[status(thm),parent(t18:3)],[well_definedness_of_additive_inverse]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t18:3]) ).
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(l11,lemma,
defined(additive_inverse(a)),
inference(lemma,[status(cth),parent(t18:3),below(t16:2)],[t18:3]) ).
cnf(t25,plain,
defined(additive_inverse(a)),
inference(lemma_extension,[status(thm),parent(t18:4)],[l11:1]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t18:4]) ).
cnf(l9,lemma,
less_or_equal(additive_inverse(a),additive_inverse(a)),
inference(lemma,[status(cth),parent(t16:2),below(t14:2)],[t16:2]) ).
cnf(t27,plain,
less_or_equal(additive_inverse(a),additive_inverse(a)),
inference(lemma_extension,[status(thm),parent(t16:3)],[l9:1]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t16:3]) ).
cnf(t29,plain,
( ~ sum(additive_inverse(a),c,b)
| sum(c,additive_inverse(a),b) ),
inference(extension,[status(thm),parent(t14:3)],[commutativity_addition]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t14:3]) ).
cnf(t31,plain,
( ~ sum(additive_inverse(a),a,additive_identity)
| ~ sum(a,b,c)
| ~ sum(additive_identity,b,b)
| sum(additive_inverse(a),c,b) ),
inference(extension,[status(thm),parent(t29:2)],[associativity_addition_1]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t29:2]) ).
cnf(t33,plain,
( ~ defined(b)
| sum(additive_identity,b,b) ),
inference(extension,[status(thm),parent(t31:2)],[existence_of_identity_addition]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t31:2]) ).
cnf(t35,plain,
defined(b),
inference(extension,[status(thm),parent(t33:2)],[b_is_defined]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t33:2]) ).
cnf(t37,plain,
sum(a,b,c),
inference(extension,[status(thm),parent(t31:3)],[sum_5]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t31:3]) ).
cnf(t39,plain,
( ~ defined(a)
| sum(additive_inverse(a),a,additive_identity) ),
inference(extension,[status(thm),parent(t31:4)],[existence_of_inverse_addition]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t31:4]) ).
cnf(t41,plain,
defined(a),
inference(extension,[status(thm),parent(t39:2)],[a_is_defined]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t39:2]) ).
cnf(t43,plain,
( ~ defined(c)
| sum(additive_inverse(c),c,additive_identity) ),
inference(extension,[status(thm),parent(t14:4)],[existence_of_inverse_addition]) ).
cnf(t44,plain,
$false,
inference(connection,[status(thm),parent(t43:1)],[t43:1,t14:4]) ).
cnf(t45,plain,
defined(c),
inference(extension,[status(thm),parent(t43:2)],[c_is_defined]) ).
cnf(t46,plain,
$false,
inference(connection,[status(thm),parent(t45:1)],[t45:1,t43:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD008-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % 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 18:50:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 90.34/90.65 % SZS status Unsatisfiable for theBenchmark
% 90.34/90.65 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------