%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN010-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10:19:01 AM UTC 2026
% Result : Unsatisfiable 0.64s 0.53s
% Output : Proof 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN010-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.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 10:51:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.53 Command-line arguments: --no-flatten-goal
% 0.64/0.53
% 0.64/0.53 % SZS status Unsatisfiable
% 0.64/0.53
% 0.64/0.54 % SZS output start Proof
% 0.64/0.54 Axiom 1 (identity_is_largest): divide(X, identity) = zero.
% 0.64/0.54 Axiom 2 (zero_is_smallest): divide(zero, X) = zero.
% 0.64/0.54 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.64/0.55 Axiom 4 (quotient_smaller_than_numerator): divide(divide(X, Y), X) = zero.
% 0.64/0.55 Axiom 5 (divide_and_equal): ifeq(divide(X, Y), zero, ifeq(divide(Y, X), zero, Y, X), X) = X.
% 0.64/0.55 Axiom 6 (property_of_divide3): ifeq(divide(X, Y), zero, divide(divide(X, Z), divide(Y, Z)), zero) = zero.
% 0.64/0.55 Axiom 7 (property_of_divide1): ifeq(divide(divide(X, Y), Z), zero, divide(divide(X, Z), Y), zero) = zero.
% 0.64/0.55 Axiom 8 (quotient_property): divide(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = zero.
% 0.64/0.55 Axiom 9 (transitivity_of_divide_to_zero): ifeq(divide(X, Y), zero, ifeq(divide(Z, X), zero, divide(Z, Y), zero), zero) = zero.
% 0.64/0.55
% 0.64/0.55 Lemma 10: ifeq(divide(X, zero), zero, zero, X) = X.
% 0.64/0.55 Proof:
% 0.64/0.55 ifeq(divide(X, zero), zero, zero, X)
% 0.64/0.55 = { by axiom 3 (ifeq_axiom) R->L }
% 0.64/0.55 ifeq(divide(X, zero), zero, ifeq(zero, zero, zero, X), X)
% 0.64/0.55 = { by axiom 2 (zero_is_smallest) R->L }
% 0.64/0.55 ifeq(divide(X, zero), zero, ifeq(divide(zero, X), zero, zero, X), X)
% 0.64/0.55 = { by axiom 5 (divide_and_equal) }
% 0.64/0.55 X
% 0.64/0.55
% 0.64/0.55 Lemma 11: divide(X, X) = zero.
% 0.64/0.55 Proof:
% 0.64/0.55 divide(X, X)
% 0.64/0.55 = { by lemma 10 R->L }
% 0.64/0.55 ifeq(divide(divide(X, X), zero), zero, zero, divide(X, X))
% 0.64/0.55 = { by axiom 3 (ifeq_axiom) R->L }
% 0.64/0.55 ifeq(ifeq(zero, zero, divide(divide(X, X), zero), zero), zero, zero, divide(X, X))
% 0.64/0.55 = { by axiom 4 (quotient_smaller_than_numerator) R->L }
% 0.64/0.55 ifeq(ifeq(divide(divide(X, zero), X), zero, divide(divide(X, X), zero), zero), zero, zero, divide(X, X))
% 0.64/0.55 = { by axiom 7 (property_of_divide1) }
% 0.64/0.55 ifeq(zero, zero, zero, divide(X, X))
% 0.64/0.55 = { by axiom 3 (ifeq_axiom) }
% 0.64/0.55 zero
% 0.64/0.55
% 0.64/0.55 Lemma 12: divide(X, zero) = X.
% 0.64/0.55 Proof:
% 0.64/0.55 divide(X, zero)
% 0.64/0.55 = { by axiom 3 (ifeq_axiom) R->L }
% 0.64/0.55 ifeq(zero, zero, divide(X, zero), X)
% 0.64/0.55 = { by axiom 4 (quotient_smaller_than_numerator) R->L }
% 0.64/0.55 ifeq(divide(divide(X, zero), X), zero, divide(X, zero), X)
% 0.64/0.55 = { by axiom 3 (ifeq_axiom) R->L }
% 0.64/0.55 ifeq(zero, zero, ifeq(divide(divide(X, zero), X), zero, divide(X, zero), X), X)
% 0.64/0.55 = { by axiom 3 (ifeq_axiom) R->L }
% 0.64/0.55 ifeq(ifeq(zero, zero, zero, divide(X, divide(X, zero))), zero, ifeq(divide(divide(X, zero), X), zero, divide(X, zero), X), X)
% 0.64/0.55 = { by axiom 7 (property_of_divide1) R->L }
% 0.64/0.55 ifeq(ifeq(ifeq(divide(divide(X, zero), divide(X, zero)), zero, divide(divide(X, divide(X, zero)), zero), zero), zero, zero, divide(X, divide(X, zero))), zero, ifeq(divide(divide(X, zero), X), zero, divide(X, zero), X), X)
% 0.64/0.55 = { by lemma 11 }
% 0.64/0.55 ifeq(ifeq(ifeq(zero, zero, divide(divide(X, divide(X, zero)), zero), zero), zero, zero, divide(X, divide(X, zero))), zero, ifeq(divide(divide(X, zero), X), zero, divide(X, zero), X), X)
% 0.64/0.55 = { by axiom 3 (ifeq_axiom) }
% 0.64/0.55 ifeq(ifeq(divide(divide(X, divide(X, zero)), zero), zero, zero, divide(X, divide(X, zero))), zero, ifeq(divide(divide(X, zero), X), zero, divide(X, zero), X), X)
% 0.64/0.55 = { by lemma 10 }
% 0.64/0.55 ifeq(divide(X, divide(X, zero)), zero, ifeq(divide(divide(X, zero), X), zero, divide(X, zero), X), X)
% 0.64/0.55 = { by axiom 5 (divide_and_equal) }
% 0.64/0.55 X
% 0.64/0.55
% 0.64/0.55 Lemma 13: divide(divide(X, divide(identity, Y)), Y) = zero.
% 0.64/0.55 Proof:
% 0.64/0.55 divide(divide(X, divide(identity, Y)), Y)
% 0.64/0.55 = { by axiom 3 (ifeq_axiom) R->L }
% 0.64/0.55 ifeq(zero, zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.64/0.55 = { by axiom 6 (property_of_divide3) R->L }
% 0.64/0.55 ifeq(ifeq(divide(X, identity), zero, divide(divide(X, Y), divide(identity, Y)), zero), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.64/0.55 = { by axiom 1 (identity_is_largest) }
% 0.64/0.55 ifeq(ifeq(zero, zero, divide(divide(X, Y), divide(identity, Y)), zero), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.64/0.55 = { by axiom 3 (ifeq_axiom) }
% 0.64/0.55 ifeq(divide(divide(X, Y), divide(identity, Y)), zero, divide(divide(X, divide(identity, Y)), Y), zero)
% 0.64/0.55 = { by axiom 7 (property_of_divide1) }
% 0.64/0.55 zero
% 0.64/0.55
% 0.64/0.55 Lemma 14: divide(identity, divide(identity, divide(identity, X))) = divide(identity, X).
% 0.64/0.55 Proof:
% 0.64/0.55 divide(identity, divide(identity, divide(identity, X)))
% 0.64/0.55 = { by axiom 3 (ifeq_axiom) R->L }
% 0.64/0.55 ifeq(zero, zero, divide(identity, divide(identity, divide(identity, X))), divide(identity, X))
% 0.64/0.55 = { by axiom 9 (transitivity_of_divide_to_zero) R->L }
% 0.64/0.55 ifeq(ifeq(divide(divide(divide(identity, divide(identity, divide(identity, X))), X), divide(identity, divide(identity, divide(identity, X)))), zero, ifeq(divide(divide(divide(identity, X), divide(divide(identity, divide(identity, X)), X)), divide(divide(identity, divide(identity, divide(identity, X))), X)), zero, divide(divide(divide(identity, X), divide(divide(identity, divide(identity, X)), X)), divide(identity, divide(identity, divide(identity, X)))), zero), zero), zero, divide(identity, divide(identity, divide(identity, X))), divide(identity, X))
% 0.64/0.55 = { by axiom 4 (quotient_smaller_than_numerator) }
% 0.64/0.55 ifeq(ifeq(zero, zero, ifeq(divide(divide(divide(identity, X), divide(divide(identity, divide(identity, X)), X)), divide(divide(identity, divide(identity, divide(identity, X))), X)), zero, divide(divide(divide(identity, X), divide(divide(identity, divide(identity, X)), X)), divide(identity, divide(identity, divide(identity, X)))), zero), zero), zero, divide(identity, divide(identity, divide(identity, X))), divide(identity, X))
% 0.64/0.55 = { by axiom 3 (ifeq_axiom) }
% 0.64/0.55 ifeq(ifeq(divide(divide(divide(identity, X), divide(divide(identity, divide(identity, X)), X)), divide(divide(identity, divide(identity, divide(identity, X))), X)), zero, divide(divide(divide(identity, X), divide(divide(identity, divide(identity, X)), X)), divide(identity, divide(identity, divide(identity, X)))), zero), zero, divide(identity, divide(identity, divide(identity, X))), divide(identity, X))
% 0.64/0.55 = { by axiom 8 (quotient_property) }
% 0.64/0.55 ifeq(ifeq(zero, zero, divide(divide(divide(identity, X), divide(divide(identity, divide(identity, X)), X)), divide(identity, divide(identity, divide(identity, X)))), zero), zero, divide(identity, divide(identity, divide(identity, X))), divide(identity, X))
% 0.64/0.56 = { by axiom 3 (ifeq_axiom) }
% 0.64/0.56 ifeq(divide(divide(divide(identity, X), divide(divide(identity, divide(identity, X)), X)), divide(identity, divide(identity, divide(identity, X)))), zero, divide(identity, divide(identity, divide(identity, X))), divide(identity, X))
% 0.64/0.56 = { by lemma 13 }
% 0.64/0.56 ifeq(divide(divide(divide(identity, X), zero), divide(identity, divide(identity, divide(identity, X)))), zero, divide(identity, divide(identity, divide(identity, X))), divide(identity, X))
% 0.64/0.56 = { by lemma 12 }
% 0.64/0.56 ifeq(divide(divide(identity, X), divide(identity, divide(identity, divide(identity, X)))), zero, divide(identity, divide(identity, divide(identity, X))), divide(identity, X))
% 0.64/0.56 = { by axiom 3 (ifeq_axiom) R->L }
% 0.64/0.56 ifeq(divide(divide(identity, X), divide(identity, divide(identity, divide(identity, X)))), zero, ifeq(zero, zero, divide(identity, divide(identity, divide(identity, X))), divide(identity, X)), divide(identity, X))
% 0.64/0.56 = { by lemma 13 R->L }
% 0.64/0.56 ifeq(divide(divide(identity, X), divide(identity, divide(identity, divide(identity, X)))), zero, ifeq(divide(divide(identity, divide(identity, divide(identity, X))), divide(identity, X)), zero, divide(identity, divide(identity, divide(identity, X))), divide(identity, X)), divide(identity, X))
% 0.64/0.56 = { by axiom 5 (divide_and_equal) }
% 0.64/0.56 divide(identity, X)
% 0.64/0.56
% 0.64/0.56 Goal 1 (prove_this): divide(identity, a) = divide(divide(identity, a), divide(identity, divide(identity, a))).
% 0.64/0.56 Proof:
% 0.64/0.56 divide(identity, a)
% 0.64/0.56 = { by lemma 14 R->L }
% 0.64/0.56 divide(identity, divide(identity, divide(identity, a)))
% 0.64/0.56 = { by axiom 5 (divide_and_equal) R->L }
% 0.64/0.56 ifeq(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), zero, ifeq(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.64/0.56 = { by lemma 12 R->L }
% 0.64/0.56 ifeq(divide(divide(divide(identity, divide(identity, divide(identity, a))), zero), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), zero, ifeq(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.64/0.56 = { by lemma 11 R->L }
% 0.64/0.56 ifeq(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(divide(identity, divide(identity, a)), divide(identity, divide(identity, a)))), divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))), zero, ifeq(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.64/0.56 = { by axiom 8 (quotient_property) }
% 0.64/0.56 ifeq(zero, zero, ifeq(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), divide(identity, divide(identity, divide(identity, a))))
% 0.64/0.56 = { by axiom 3 (ifeq_axiom) }
% 0.64/0.56 ifeq(divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a))))
% 0.64/0.56 = { by axiom 3 (ifeq_axiom) R->L }
% 0.64/0.56 ifeq(ifeq(zero, zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), zero), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a))))
% 0.64/0.56 = { by axiom 4 (quotient_smaller_than_numerator) R->L }
% 0.64/0.56 ifeq(ifeq(divide(divide(identity, divide(identity, divide(identity, a))), identity), zero, divide(divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a)))), zero), zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a))))
% 0.64/0.56 = { by axiom 6 (property_of_divide3) }
% 0.64/0.56 ifeq(zero, zero, divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a))), divide(identity, divide(identity, divide(identity, a))))
% 0.64/0.56 = { by axiom 3 (ifeq_axiom) }
% 0.64/0.56 divide(divide(identity, divide(identity, divide(identity, a))), divide(identity, divide(identity, a)))
% 0.64/0.56 = { by lemma 14 }
% 0.64/0.56 divide(divide(identity, a), divide(identity, divide(identity, a)))
% 0.64/0.56 % SZS output end Proof
% 0.64/0.56
% 0.64/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------