%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : ALG002-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Jul 24 09:45:41 AM UTC 2025
% Result : Unsatisfiable 151.19s 19.37s
% Output : CNFRefutation 151.72s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_a_inverse_greater_than_0)
% Comments :
%------------------------------------------------------------------------------
cnf(13,plain,
~ greater_than_0(multiplicative_inverse(a)),
inference(cnf,[status(esa)],[prove_a_inverse_greater_than_0]) ).
cnf(l0,plain,
~ greater_than_0(multiplicative_inverse(a)),
inference(instantiation,[status(thm)],[13]) ).
cnf(9,plain,
( product(X0,X0,additive_identity)
| greater_than_0(X0)
| greater_than_0(additive_inverse(X0)) ),
inference(cnf,[status(esa)],[product_and_inverse]) ).
cnf(l1,plain,
( product(multiplicative_inverse(a),multiplicative_inverse(a),additive_identity)
| greater_than_0(multiplicative_inverse(a))
| greater_than_0(additive_inverse(multiplicative_inverse(a))) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(10,plain,
( ~ product(X0,X0,additive_identity)
| ~ product(X0,X1,X2)
| product(X2,X2,additive_identity) ),
inference(cnf,[status(esa)],[square_to_0]) ).
cnf(l2,plain,
( ~ product(multiplicative_inverse(a),multiplicative_inverse(a),additive_identity)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(multiplicative_identity,multiplicative_identity,additive_identity) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(11,plain,
( ~ product(X0,X1,X2)
| ~ greater_than_0(X0)
| ~ greater_than_0(X1)
| greater_than_0(X2) ),
inference(cnf,[status(esa)],[product_and_greater_than_0]) ).
cnf(l3,plain,
( ~ product(a,additive_inverse(multiplicative_inverse(a)),additive_inverse(multiplicative_identity))
| ~ greater_than_0(a)
| ~ greater_than_0(additive_inverse(multiplicative_inverse(a)))
| greater_than_0(additive_inverse(multiplicative_identity)) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(4,plain,
( ~ product(X0,X1,X2)
| product(X0,additive_inverse(X1),additive_inverse(X2)) ),
inference(cnf,[status(esa)],[product_to_inverse]) ).
cnf(l8,plain,
( ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| product(a,additive_inverse(multiplicative_inverse(a)),additive_inverse(multiplicative_identity)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(6,plain,
( ~ greater_than_0(X0)
| ~ greater_than_0(additive_inverse(X0)) ),
inference(cnf,[status(esa)],[inverse_greater_than_0]) ).
cnf(l415,plain,
( ~ greater_than_0(additive_inverse(multiplicative_identity))
| ~ greater_than_0(additive_inverse(additive_inverse(multiplicative_identity))) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l417,plain,
( ~ product(additive_inverse(multiplicative_identity),additive_inverse(multiplicative_identity),additive_inverse(additive_inverse(multiplicative_identity)))
| ~ greater_than_0(additive_inverse(multiplicative_identity))
| ~ greater_than_0(additive_inverse(multiplicative_identity))
| greater_than_0(additive_inverse(additive_inverse(multiplicative_identity))) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(12,plain,
greater_than_0(a),
inference(cnf,[status(esa)],[a_greater_than_0]) ).
cnf(l17,plain,
greater_than_0(a),
inference(instantiation,[status(thm)],[12]) ).
cnf(8,plain,
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
inference(cnf,[status(esa)],[commutativity_of_product]) ).
cnf(l136,plain,
( ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(1,plain,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
inference(cnf,[status(esa)],[not_abelian]) ).
cnf(l124,plain,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
inference(instantiation,[status(thm)],[1]) ).
cnf(5,plain,
( product(X0,X0,additive_identity)
| product(X0,multiplicative_inverse(X0),multiplicative_identity) ),
inference(cnf,[status(esa)],[inverse_and_identity]) ).
cnf(l12,plain,
( product(a,a,additive_identity)
| product(a,multiplicative_inverse(a),multiplicative_identity) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l137,plain,
( product(a,a,additive_identity)
| product(a,multiplicative_inverse(a),multiplicative_identity) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(7,plain,
( ~ product(X0,X0,additive_identity)
| ~ greater_than_0(X0) ),
inference(cnf,[status(esa)],[greater_than_0_square]) ).
cnf(l15,plain,
( ~ product(a,a,additive_identity)
| ~ greater_than_0(a) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l419,plain,
( ~ product(additive_inverse(multiplicative_identity),multiplicative_identity,additive_inverse(multiplicative_identity))
| product(additive_inverse(multiplicative_identity),additive_inverse(multiplicative_identity),additive_inverse(additive_inverse(multiplicative_identity))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(0,plain,
product(X0,multiplicative_identity,X0),
inference(cnf,[status(esa)],[right_identity]) ).
cnf(l425,plain,
product(additive_inverse(multiplicative_identity),multiplicative_identity,additive_inverse(multiplicative_identity)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l452,plain,
greater_than_0(a),
inference(instantiation,[status(thm)],[12]) ).
cnf(l138,plain,
( ~ product(a,a,additive_identity)
| ~ greater_than_0(a) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l139,plain,
greater_than_0(a),
inference(instantiation,[status(thm)],[12]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l8,l415,l417,l17,l136,l124,l12,l137,l15,l419,l425,l452,l138,l139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG002-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Jul 20 01:53:49 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.34 % launching worker at depth: 10
% 0.13/0.34 % launching worker at depth: 11
% 0.19/0.42 % launching worker at depth: 12
% 14.63/2.22 % launching worker at depth: 13
% 151.19/19.37 % SZS status Theorem for theBenchmark
% 151.72/19.37 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------