%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD066-3 : 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 : n012.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 08:39:02 AM UTC 2026
% Result : Unsatisfiable 36.44s 36.75s
% Output : Proof 36.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of clauses : 49 ( 33 unt; 0 nHn; 49 RR)
% Number of literals : 75 ( 0 equ; 28 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 : 7 ( 7 usr; 6 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(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(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_6,negated_conjecture,
sum(a,c,u),
file('theBenchmark.p',sum_6) ).
cnf(sum_7,negated_conjecture,
sum(b,c,v),
file('theBenchmark.p',sum_7) ).
cnf(less_or_equal_8,negated_conjecture,
less_or_equal(u,v),
file('theBenchmark.p',less_or_equal_8) ).
cnf(not_less_or_equal_9,negated_conjecture,
~ less_or_equal(a,b),
file('theBenchmark.p',not_less_or_equal_9) ).
cnf(t1,plain,
less_or_equal(u,v),
inference(start,[status(thm),parent(0:0)],[less_or_equal_8]) ).
cnf(t2,plain,
( ~ sum(v,additive_inverse(c),b)
| ~ sum(u,additive_inverse(c),a)
| less_or_equal(a,b)
| ~ less_or_equal(u,v) ),
inference(extension,[status(thm),parent(t1:1)],[compatibility_of_order_relation_and_addition]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
~ less_or_equal(a,b),
inference(extension,[status(thm),parent(t2:2)],[not_less_or_equal_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ sum(additive_inverse(c),u,a)
| sum(u,additive_inverse(c),a) ),
inference(extension,[status(thm),parent(t2:3)],[commutativity_addition]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ sum(additive_inverse(c),c,additive_identity)
| ~ sum(c,a,u)
| ~ sum(additive_identity,a,a)
| sum(additive_inverse(c),u,a) ),
inference(extension,[status(thm),parent(t6:2)],[associativity_addition_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ defined(a)
| sum(additive_identity,a,a) ),
inference(extension,[status(thm),parent(t8:2)],[existence_of_identity_addition]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
defined(a),
inference(extension,[status(thm),parent(t10:2)],[a_is_defined]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ sum(a,c,u)
| sum(c,a,u) ),
inference(extension,[status(thm),parent(t8:3)],[commutativity_addition]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:3]) ).
cnf(t16,plain,
sum(a,c,u),
inference(extension,[status(thm),parent(t14:2)],[sum_6]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ defined(c)
| sum(additive_inverse(c),c,additive_identity) ),
inference(extension,[status(thm),parent(t8:4)],[existence_of_inverse_addition]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t8:4]) ).
cnf(t20,plain,
defined(c),
inference(extension,[status(thm),parent(t18:2)],[c_is_defined]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ sum(additive_inverse(c),v,b)
| sum(v,additive_inverse(c),b) ),
inference(extension,[status(thm),parent(t2:4)],[commutativity_addition]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:4]) ).
cnf(t24,plain,
( ~ sum(additive_inverse(c),c,additive_identity)
| ~ sum(c,b,v)
| ~ sum(additive_identity,b,b)
| sum(additive_inverse(c),v,b) ),
inference(extension,[status(thm),parent(t22:2)],[associativity_addition_1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ defined(b)
| sum(additive_identity,b,b) ),
inference(extension,[status(thm),parent(t24:2)],[existence_of_identity_addition]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
defined(b),
inference(extension,[status(thm),parent(t26:2)],[b_is_defined]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( ~ sum(b,c,v)
| sum(c,b,v) ),
inference(extension,[status(thm),parent(t24:3)],[commutativity_addition]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t24:3]) ).
cnf(t32,plain,
sum(b,c,v),
inference(extension,[status(thm),parent(t30:2)],[sum_7]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( ~ defined(c)
| sum(additive_inverse(c),c,additive_identity) ),
inference(extension,[status(thm),parent(t24:4)],[existence_of_inverse_addition]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t24:4]) ).
cnf(t36,plain,
defined(c),
inference(extension,[status(thm),parent(t34:2)],[c_is_defined]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : FLD066-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 20 19:07:22 UTC 2026
% 0.04/0.32 % CPUTime :
% 36.44/36.75 % SZS status Unsatisfiable for theBenchmark
% 36.44/36.75 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------