%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 : Tue Sep 29 10:08:52 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.44s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:13:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.44 Command-line arguments: --no-flatten-goal
% 0.09/0.44
% 0.09/0.44 % SZS status Unsatisfiable
% 0.09/0.44
% 0.09/0.45 % SZS output start Proof
% 0.09/0.45 Axiom 1 (element_of_set): an_element(the_element) = true.
% 0.09/0.45 Axiom 2 (left_identity): product(identity, X, X) = true.
% 0.09/0.45 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.09/0.45 Axiom 4 (right_inverse): product(X, inverse(X), identity) = true.
% 0.09/0.45 Axiom 5 (condition): ifeq(an_element(X), true, ifeq(an_element(Y), true, ifeq(product(Y, inverse(X), Z), true, an_element(Z), true), true), true) = true.
% 0.09/0.45
% 0.09/0.45 Goal 1 (prove_b_inverse_is_in_set): an_element(inverse(the_element)) = true.
% 0.09/0.45 Proof:
% 0.09/0.45 an_element(inverse(the_element))
% 0.09/0.45 = { by axiom 3 (ifeq_axiom) R->L }
% 0.09/0.45 ifeq(true, true, an_element(inverse(the_element)), true)
% 0.09/0.45 = { by axiom 1 (element_of_set) R->L }
% 0.09/0.45 ifeq(an_element(the_element), true, an_element(inverse(the_element)), true)
% 0.09/0.45 = { by axiom 3 (ifeq_axiom) R->L }
% 0.09/0.45 ifeq(an_element(the_element), true, ifeq(true, true, an_element(inverse(the_element)), true), true)
% 0.09/0.45 = { by axiom 3 (ifeq_axiom) R->L }
% 0.09/0.45 ifeq(an_element(the_element), true, ifeq(true, true, ifeq(true, true, an_element(inverse(the_element)), true), true), true)
% 0.09/0.45 = { by axiom 5 (condition) R->L }
% 0.09/0.45 ifeq(an_element(the_element), true, ifeq(ifeq(an_element(the_element), true, ifeq(an_element(the_element), true, ifeq(product(the_element, inverse(the_element), identity), true, an_element(identity), true), true), true), true, ifeq(true, true, an_element(inverse(the_element)), true), true), true)
% 0.09/0.45 = { by axiom 4 (right_inverse) }
% 0.09/0.45 ifeq(an_element(the_element), true, ifeq(ifeq(an_element(the_element), true, ifeq(an_element(the_element), true, ifeq(true, true, an_element(identity), true), true), true), true, ifeq(true, true, an_element(inverse(the_element)), true), true), true)
% 0.09/0.45 = { by axiom 3 (ifeq_axiom) }
% 0.09/0.45 ifeq(an_element(the_element), true, ifeq(ifeq(an_element(the_element), true, ifeq(an_element(the_element), true, an_element(identity), true), true), true, ifeq(true, true, an_element(inverse(the_element)), true), true), true)
% 0.09/0.45 = { by axiom 1 (element_of_set) }
% 0.09/0.45 ifeq(an_element(the_element), true, ifeq(ifeq(true, true, ifeq(an_element(the_element), true, an_element(identity), true), true), true, ifeq(true, true, an_element(inverse(the_element)), true), true), true)
% 0.09/0.45 = { by axiom 3 (ifeq_axiom) }
% 0.09/0.45 ifeq(an_element(the_element), true, ifeq(ifeq(an_element(the_element), true, an_element(identity), true), true, ifeq(true, true, an_element(inverse(the_element)), true), true), true)
% 0.09/0.45 = { by axiom 1 (element_of_set) }
% 0.09/0.45 ifeq(an_element(the_element), true, ifeq(ifeq(true, true, an_element(identity), true), true, ifeq(true, true, an_element(inverse(the_element)), true), true), true)
% 0.09/0.45 = { by axiom 3 (ifeq_axiom) }
% 0.09/0.45 ifeq(an_element(the_element), true, ifeq(an_element(identity), true, ifeq(true, true, an_element(inverse(the_element)), true), true), true)
% 0.09/0.45 = { by axiom 2 (left_identity) R->L }
% 0.09/0.45 ifeq(an_element(the_element), true, ifeq(an_element(identity), true, ifeq(product(identity, inverse(the_element), inverse(the_element)), true, an_element(inverse(the_element)), true), true), true)
% 0.09/0.45 = { by axiom 5 (condition) }
% 0.09/0.45 true
% 0.09/0.45 % SZS output end Proof
% 0.09/0.45
% 0.09/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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