%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD027-3 : 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 : n019.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 08:38:52 AM UTC 2026
% Result : Unsatisfiable 18.13s 23.46s
% Output : Proof 18.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 15
% Syntax : Number of clauses : 82 ( 58 unt; 6 nHn; 82 RR)
% Number of literals : 132 ( 0 equ; 50 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_multiplication_1,axiom,
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
file('FLD002-0.ax',associativity_multiplication_1) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(U,Z,W) ),
file('FLD002-0.ax',associativity_multiplication_2) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
file('FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
file('FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('FLD002-0.ax',commutativity_multiplication) ).
cnf(distributivity_2,axiom,
( ~ sum(C,D,B)
| ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ sum(X,Y,A)
| product(A,Z,B) ),
file('FLD002-0.ax',distributivity_2) ).
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(b_is_defined,hypothesis,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('theBenchmark.p',not_sum_3) ).
cnf(not_sum_4,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('theBenchmark.p',not_sum_4) ).
cnf(product_5,negated_conjecture,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('theBenchmark.p',product_5) ).
cnf(not_product_6,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('theBenchmark.p',not_product_6) ).
cnf(t1,plain,
~ product(multiplicative_identity,a,b),
inference(start,[status(thm),parent(0:0)],[not_product_6]) ).
cnf(t2,plain,
( ~ product(b,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(b,multiplicative_identity,b)
| product(multiplicative_identity,a,b) ),
inference(extension,[status(thm),parent(t1:1)],[associativity_multiplication_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ sum(additive_identity,b,b)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(b,multiplicative_identity,b)
| ~ sum(additive_identity,b,b)
| product(b,multiplicative_identity,b) ),
inference(extension,[status(thm),parent(t2:2)],[distributivity_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ less_or_equal(b,b)
| ~ less_or_equal(b,b)
| sum(additive_identity,b,b) ),
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,
( ~ defined(b)
| ~ defined(b)
| less_or_equal(b,b)
| less_or_equal(b,b) ),
inference(extension,[status(thm),parent(t6:2)],[totality_of_order_relation]) ).
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,t6:2]) ).
cnf(t11,plain,
defined(b),
inference(extension,[status(thm),parent(t8:3)],[b_is_defined]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t8:3]) ).
cnf(l6,lemma,
defined(b),
inference(lemma,[status(cth),parent(t8:3),below(t6:2)],[t8:3]) ).
cnf(t13,plain,
defined(b),
inference(lemma_extension,[status(thm),parent(t8:4)],[l6:1]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t8:4]) ).
cnf(l4,lemma,
less_or_equal(b,b),
inference(lemma,[status(cth),parent(t6:2),below(t4:2)],[t6:2]) ).
cnf(t15,plain,
less_or_equal(b,b),
inference(lemma_extension,[status(thm),parent(t6:3)],[l4:1]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t6:3]) ).
cnf(t17,plain,
( ~ product(multiplicative_identity,b,b)
| product(b,multiplicative_identity,b) ),
inference(extension,[status(thm),parent(t4:3)],[commutativity_multiplication]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t4:3]) ).
cnf(t19,plain,
( ~ defined(b)
| product(multiplicative_identity,b,b) ),
inference(extension,[status(thm),parent(t17:2)],[existence_of_identity_multiplication]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t17:2]) ).
cnf(t21,plain,
defined(b),
inference(extension,[status(thm),parent(t19:2)],[b_is_defined]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
( ~ product(multiplicative_identity,additive_identity,additive_identity)
| product(additive_identity,multiplicative_identity,additive_identity) ),
inference(extension,[status(thm),parent(t4:4)],[commutativity_multiplication]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t4:4]) ).
cnf(t25,plain,
( ~ defined(additive_identity)
| product(multiplicative_identity,additive_identity,additive_identity) ),
inference(extension,[status(thm),parent(t23:2)],[existence_of_identity_multiplication]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t23:2]) ).
cnf(t27,plain,
defined(additive_identity),
inference(extension,[status(thm),parent(t25:2)],[well_definedness_of_additive_identity]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t25:2]) ).
cnf(t29,plain,
( ~ less_or_equal(b,b)
| ~ less_or_equal(b,b)
| sum(additive_identity,b,b) ),
inference(extension,[status(thm),parent(t4:5)],[antisymmetry_of_order_relation]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t4:5]) ).
cnf(t31,plain,
( ~ defined(b)
| ~ defined(b)
| less_or_equal(b,b)
| less_or_equal(b,b) ),
inference(extension,[status(thm),parent(t29:2)],[totality_of_order_relation]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t29:2]) ).
cnf(t33,plain,
$false,
inference(reduction,[status(thm),parent(t31:2)],[t31:2,t29:2]) ).
cnf(t34,plain,
defined(b),
inference(extension,[status(thm),parent(t31:3)],[b_is_defined]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t31:3]) ).
cnf(l16,lemma,
defined(b),
inference(lemma,[status(cth),parent(t31:3),below(t29:2)],[t31:3]) ).
cnf(t36,plain,
defined(b),
inference(lemma_extension,[status(thm),parent(t31:4)],[l16:1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t31:4]) ).
cnf(l14,lemma,
less_or_equal(b,b),
inference(lemma,[status(cth),parent(t29:2),below(t4:5)],[t29:2]) ).
cnf(t38,plain,
less_or_equal(b,b),
inference(lemma_extension,[status(thm),parent(t29:3)],[l14:1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t29:3]) ).
cnf(t40,plain,
( sum(additive_identity,a,additive_identity)
| ~ defined(a)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(extension,[status(thm),parent(t2:3)],[existence_of_inverse_multiplication]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t2:3]) ).
cnf(t42,plain,
defined(a),
inference(extension,[status(thm),parent(t40:2)],[a_is_defined]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
~ sum(additive_identity,a,additive_identity),
inference(extension,[status(thm),parent(t40:3)],[not_sum_3]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
( ~ product(multiplicative_inverse(a),b,multiplicative_identity)
| product(b,multiplicative_inverse(a),multiplicative_identity) ),
inference(extension,[status(thm),parent(t2:4)],[commutativity_multiplication]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t2:4]) ).
cnf(t48,plain,
( ~ product(multiplicative_inverse(a),multiplicative_identity,multiplicative_inverse(b))
| ~ product(multiplicative_identity,b,b)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| product(multiplicative_inverse(a),b,multiplicative_identity) ),
inference(extension,[status(thm),parent(t46:2)],[associativity_multiplication_1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
( sum(additive_identity,b,additive_identity)
| ~ defined(b)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(extension,[status(thm),parent(t48:2)],[existence_of_inverse_multiplication]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
defined(b),
inference(extension,[status(thm),parent(t50:2)],[b_is_defined]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
~ sum(additive_identity,b,additive_identity),
inference(extension,[status(thm),parent(t50:3)],[not_sum_4]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t50:3]) ).
cnf(t56,plain,
( ~ defined(b)
| product(multiplicative_identity,b,b) ),
inference(extension,[status(thm),parent(t48:3)],[existence_of_identity_multiplication]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t48:3]) ).
cnf(t58,plain,
defined(b),
inference(extension,[status(thm),parent(t56:2)],[b_is_defined]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
( ~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b))
| product(multiplicative_inverse(a),multiplicative_identity,multiplicative_inverse(b)) ),
inference(extension,[status(thm),parent(t48:4)],[commutativity_multiplication]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t48:4]) ).
cnf(t62,plain,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
inference(extension,[status(thm),parent(t60:2)],[product_5]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD027-3 : 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
% 0.07/5.37 % Computer : n019.cluster.edu
% 0.07/5.37 % Model : x86_64 x86_64
% 0.07/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.37 % Memory : 8046.5625MB
% 0.07/5.37 % OS : Linux 6.8.0-71-generic
% 0.07/5.37 % CPULimit : 300
% 0.07/5.37 % WCLimit : 300
% 0.07/5.37 % DateTime : Sun Sep 20 18:54:15 UTC 2026
% 0.07/5.37 % CPUTime :
% 18.13/23.46 % SZS status Unsatisfiable for theBenchmark
% 18.13/23.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------