%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : BOO018-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n013.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 08:13:59 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 14 unt; 0 nHn; 16 RR)
% Number of literals : 27 ( 21 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_multiply,axiom,
multiply(X,Y) = multiply(Y,X),
file('BOO004-0.ax',commutativity_of_multiply) ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X,
file('BOO004-0.ax',multiplicative_id1) ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity,
file('BOO004-0.ax',multiplicative_inverse1) ).
cnf(prove_inverse_of_1_is_0,negated_conjecture,
inverse(multiplicative_identity) != additive_identity,
file('theBenchmark.p',prove_inverse_of_1_is_0) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(t1,plain,
inverse(multiplicative_identity) != additive_identity,
inference(start,[status(thm),parent(0:0)],[prove_inverse_of_1_is_0]) ).
cnf(t2,plain,
( multiply(inverse(multiplicative_identity),multiplicative_identity) != additive_identity
| inverse(multiplicative_identity) != multiply(inverse(multiplicative_identity),multiplicative_identity)
| inverse(multiplicative_identity) = additive_identity ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( multiply(inverse(multiplicative_identity),multiplicative_identity) != inverse(multiplicative_identity)
| inverse(multiplicative_identity) = multiply(inverse(multiplicative_identity),multiplicative_identity) ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
multiply(inverse(multiplicative_identity),multiplicative_identity) = inverse(multiplicative_identity),
inference(extension,[status(thm),parent(t4:2)],[multiplicative_id1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( multiply(multiplicative_identity,inverse(multiplicative_identity)) != additive_identity
| multiply(inverse(multiplicative_identity),multiplicative_identity) != multiply(multiplicative_identity,inverse(multiplicative_identity))
| multiply(inverse(multiplicative_identity),multiplicative_identity) = additive_identity ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
multiply(inverse(multiplicative_identity),multiplicative_identity) = multiply(multiplicative_identity,inverse(multiplicative_identity)),
inference(extension,[status(thm),parent(t8:2)],[commutativity_of_multiply]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
multiply(multiplicative_identity,inverse(multiplicative_identity)) = additive_identity,
inference(extension,[status(thm),parent(t8:3)],[multiplicative_inverse1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO018-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_UEQ 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
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 13:38:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------