%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : 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 08:11:33 AM UTC 2026
% Result : Unsatisfiable 0.14s 15.45s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
product(X,multiplicative_identity,X),
file('theBenchmark.p',right_identity) ).
cnf(not_abelian,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('theBenchmark.p',not_abelian) ).
cnf(product_of_inverses1,axiom,
( product(additive_inverse(X),additive_inverse(Y),Z)
| ~ product(X,Y,Z) ),
file('theBenchmark.p',product_of_inverses1) ).
cnf(product_of_inverses2,axiom,
( ~ product(additive_inverse(X),additive_inverse(Y),Z)
| product(X,Y,Z) ),
file('theBenchmark.p',product_of_inverses2) ).
cnf(product_to_inverse,axiom,
( product(X,additive_inverse(Y),additive_inverse(Z))
| ~ product(X,Y,Z) ),
file('theBenchmark.p',product_to_inverse) ).
cnf(inverse_and_identity,axiom,
( product(X,X,additive_identity)
| product(X,multiplicative_inverse(X),multiplicative_identity) ),
file('theBenchmark.p',inverse_and_identity) ).
cnf(inverse_greater_than_0,axiom,
( ~ greater_than_0(additive_inverse(X))
| ~ greater_than_0(X) ),
file('theBenchmark.p',inverse_greater_than_0) ).
cnf(greater_than_0_square,axiom,
( ~ product(X,X,additive_identity)
| ~ greater_than_0(X) ),
file('theBenchmark.p',greater_than_0_square) ).
cnf(commutativity_of_product,axiom,
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('theBenchmark.p',commutativity_of_product) ).
cnf(product_and_inverse,axiom,
( greater_than_0(additive_inverse(X))
| product(X,X,additive_identity)
| greater_than_0(X) ),
file('theBenchmark.p',product_and_inverse) ).
cnf(square_to_0,axiom,
( product(X,X,additive_identity)
| ~ product(Y,Y,additive_identity)
| ~ product(Y,Z,X) ),
file('theBenchmark.p',square_to_0) ).
cnf(product_and_greater_than_0,axiom,
( greater_than_0(X)
| ~ greater_than_0(Z)
| ~ greater_than_0(Y)
| ~ product(Y,Z,X) ),
file('theBenchmark.p',product_and_greater_than_0) ).
cnf(a_greater_than_0,hypothesis,
greater_than_0(a),
file('theBenchmark.p',a_greater_than_0) ).
cnf(prove_a_inverse_greater_than_0,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
file('theBenchmark.p',prove_a_inverse_greater_than_0) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.11/15.39 % Computer : n013.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Sun Sep 20 08:38:30 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.14/15.45 % SZS status Unsatisfiable for theBenchmark
% 0.14/15.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------