%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : BOO012-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/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 10:39:58 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_inverse_is_an_involution)
% Comments :
%------------------------------------------------------------------------------
cnf(22,plain,
inverse(inverse(x)) != x,
inference(cnf,[status(esa)],[prove_inverse_is_an_involution]) ).
cnf(l0,plain,
inverse(inverse(x)) != x,
inference(instantiation,[status(thm)],[22]) ).
cnf(20,plain,
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf,[status(esa)],[addition_is_well_defined]) ).
cnf(l1,plain,
( ~ sum(multiply(x,inverse(inverse(x))),additive_identity,inverse(inverse(x)))
| ~ sum(multiply(x,inverse(inverse(x))),additive_identity,x)
| inverse(inverse(x)) = x ),
inference(instantiation,[status(thm)],[20]) ).
cnf(10,plain,
( ~ sum(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X1,X3,X5)
| ~ product(X2,X3,X6)
| sum(X4,X5,X6) ),
inference(cnf,[status(esa)],[distributivity3]) ).
cnf(l2,plain,
( ~ sum(x,inverse(x),multiplicative_identity)
| ~ product(x,inverse(inverse(x)),multiply(x,inverse(inverse(x))))
| ~ product(inverse(x),inverse(inverse(x)),additive_identity)
| ~ product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x)))
| sum(multiply(x,inverse(inverse(x))),additive_identity,inverse(inverse(x))) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(6,plain,
product(multiplicative_identity,X0,X0),
inference(cnf,[status(esa)],[multiplicative_identity1]) ).
cnf(l6,plain,
product(multiplicative_identity,inverse(inverse(x)),inverse(inverse(x))),
inference(instantiation,[status(thm)],[6]) ).
cnf(1,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf,[status(esa)],[closure_of_multiplication]) ).
cnf(l5,plain,
product(x,inverse(inverse(x)),multiply(x,inverse(inverse(x)))),
inference(instantiation,[status(thm)],[1]) ).
cnf(19,plain,
product(X0,inverse(X0),additive_identity),
inference(cnf,[status(esa)],[multiplicative_inverse2]) ).
cnf(l10,plain,
product(inverse(x),inverse(inverse(x)),additive_identity),
inference(instantiation,[status(thm)],[19]) ).
cnf(8,plain,
( ~ sum(X0,X1,X2)
| ~ product(X3,X0,X4)
| ~ product(X3,X1,X5)
| ~ product(X3,X2,X6)
| sum(X4,X5,X6) ),
inference(cnf,[status(esa)],[distributivity1]) ).
cnf(l4,plain,
( ~ sum(inverse(inverse(x)),inverse(x),multiplicative_identity)
| ~ product(x,inverse(inverse(x)),multiply(x,inverse(inverse(x))))
| ~ product(x,inverse(x),additive_identity)
| ~ product(x,multiplicative_identity,x)
| sum(multiply(x,inverse(inverse(x))),additive_identity,x) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l8,plain,
product(x,inverse(inverse(x)),multiply(x,inverse(inverse(x)))),
inference(instantiation,[status(thm)],[1]) ).
cnf(16,plain,
sum(inverse(X0),X0,multiplicative_identity),
inference(cnf,[status(esa)],[additive_inverse1]) ).
cnf(l11,plain,
sum(inverse(inverse(x)),inverse(x),multiplicative_identity),
inference(instantiation,[status(thm)],[16]) ).
cnf(17,plain,
sum(X0,inverse(X0),multiplicative_identity),
inference(cnf,[status(esa)],[additive_inverse2]) ).
cnf(l3,plain,
sum(x,inverse(x),multiplicative_identity),
inference(instantiation,[status(thm)],[17]) ).
cnf(l9,plain,
product(x,inverse(x),additive_identity),
inference(instantiation,[status(thm)],[19]) ).
cnf(7,plain,
product(X0,multiplicative_identity,X0),
inference(cnf,[status(esa)],[multiplicative_identity2]) ).
cnf(l7,plain,
product(x,multiplicative_identity,x),
inference(instantiation,[status(thm)],[7]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l6,l5,l10,l4,l8,l11,l3,l9,l7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : BOO012-1 : TPTP v9.0.0. Released v1.0.0.
% 0.08/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jul 20 04:41:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.33 % launching worker at depth: 3
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 6
% 0.12/0.33 % launching worker at depth: 7
% 0.12/0.33 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------