%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD028-3 : 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 : 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 08:38:52 AM UTC 2026
% Result : Unsatisfiable 1.06s 1.33s
% Output : Proof 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 22 unt; 2 nHn; 30 RR)
% Number of literals : 48 ( 0 equ; 20 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 : 14 ( 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(a_is_defined,hypothesis,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(v_is_defined,hypothesis,
defined(v),
file('theBenchmark.p',v_is_defined) ).
cnf(not_sum_5,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('theBenchmark.p',not_sum_5) ).
cnf(product_6,negated_conjecture,
product(a,u,b),
file('theBenchmark.p',product_6) ).
cnf(product_7,negated_conjecture,
product(a,v,b),
file('theBenchmark.p',product_7) ).
cnf(not_product_8,negated_conjecture,
~ product(multiplicative_identity,u,v),
file('theBenchmark.p',not_product_8) ).
cnf(t1,plain,
~ sum(additive_identity,a,additive_identity),
inference(start,[status(thm),parent(0:0)],[not_sum_5]) ).
cnf(t2,plain,
( ~ defined(a)
| product(multiplicative_inverse(a),a,multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(extension,[status(thm),parent(t1:1)],[existence_of_inverse_multiplication]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ product(multiplicative_identity,v,v)
| ~ product(a,v,b)
| product(multiplicative_inverse(a),b,v)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(extension,[status(thm),parent(t2:2)],[associativity_multiplication_1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(a,u,b)
| product(multiplicative_identity,u,v)
| ~ product(multiplicative_inverse(a),b,v) ),
inference(extension,[status(thm),parent(t4:2)],[associativity_multiplication_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
~ product(multiplicative_identity,u,v),
inference(extension,[status(thm),parent(t6:2)],[not_product_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
product(a,u,b),
inference(extension,[status(thm),parent(t6:3)],[product_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
$false,
inference(reduction,[status(thm),parent(t6:4)],[t6:4,t2:2]) ).
cnf(t13,plain,
product(a,v,b),
inference(extension,[status(thm),parent(t4:3)],[product_7]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t4:3]) ).
cnf(t15,plain,
( ~ defined(v)
| product(multiplicative_identity,v,v) ),
inference(extension,[status(thm),parent(t4:4)],[existence_of_identity_multiplication]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t4:4]) ).
cnf(t17,plain,
defined(v),
inference(extension,[status(thm),parent(t15:2)],[v_is_defined]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
cnf(t19,plain,
defined(a),
inference(extension,[status(thm),parent(t2:3)],[a_is_defined]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD028-3 : 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/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 : n017.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 18:46:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 1.06/1.33 % SZS status Unsatisfiable for theBenchmark
% 1.06/1.33 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------