%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD025-3 : 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 : n007.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 08:38:51 AM UTC 2026
% Result : Unsatisfiable 2.56s 2.84s
% Output : Proof 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of clauses : 38 ( 26 unt; 0 nHn; 38 RR)
% Number of literals : 60 ( 0 equ; 24 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 18 ( 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(commutativity_multiplication,axiom,
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('FLD002-0.ax',commutativity_multiplication) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(totality_of_multiplication,axiom,
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
file('FLD002-0.ax',totality_of_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(product_5,negated_conjecture,
product(multiplicative_identity,a,b),
file('theBenchmark.p',product_5) ).
cnf(product_6,negated_conjecture,
product(multiplicative_identity,c,d),
file('theBenchmark.p',product_6) ).
cnf(not_product_7,negated_conjecture,
~ product(d,b,multiply(a,c)),
file('theBenchmark.p',not_product_7) ).
cnf(t1,plain,
~ product(d,b,multiply(a,c)),
inference(start,[status(thm),parent(0:0)],[not_product_7]) ).
cnf(t2,plain,
( ~ product(b,d,multiply(a,c))
| product(d,b,multiply(a,c)) ),
inference(extension,[status(thm),parent(t1:1)],[commutativity_multiplication]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ product(a,multiplicative_identity,b)
| ~ product(multiplicative_identity,d,c)
| ~ product(a,c,multiply(a,c))
| product(b,d,multiply(a,c)) ),
inference(extension,[status(thm),parent(t2:2)],[associativity_multiplication_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ defined(a)
| ~ defined(c)
| product(a,c,multiply(a,c)) ),
inference(extension,[status(thm),parent(t4:2)],[totality_of_multiplication]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
defined(c),
inference(extension,[status(thm),parent(t6:2)],[c_is_defined]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
defined(a),
inference(extension,[status(thm),parent(t6:3)],[a_is_defined]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,c,d)
| ~ product(multiplicative_identity,c,c)
| product(multiplicative_identity,d,c) ),
inference(extension,[status(thm),parent(t4:3)],[associativity_multiplication_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
( ~ defined(c)
| product(multiplicative_identity,c,c) ),
inference(extension,[status(thm),parent(t12:2)],[existence_of_identity_multiplication]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
defined(c),
inference(extension,[status(thm),parent(t14:2)],[c_is_defined]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
product(multiplicative_identity,c,d),
inference(extension,[status(thm),parent(t12:3)],[product_6]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:3]) ).
cnf(t20,plain,
( ~ defined(multiplicative_identity)
| product(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(extension,[status(thm),parent(t12:4)],[existence_of_identity_multiplication]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t12:4]) ).
cnf(t22,plain,
defined(multiplicative_identity),
inference(extension,[status(thm),parent(t20:2)],[well_definedness_of_multiplicative_identity]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( ~ product(multiplicative_identity,a,b)
| product(a,multiplicative_identity,b) ),
inference(extension,[status(thm),parent(t4:4)],[commutativity_multiplication]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t4:4]) ).
cnf(t26,plain,
product(multiplicative_identity,a,b),
inference(extension,[status(thm),parent(t24:2)],[product_5]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD025-3 : 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
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 18:47:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 2.56/2.84 % SZS status Unsatisfiable for theBenchmark
% 2.56/2.84 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------