%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN004-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /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 : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:18:56 AM UTC 2026
% Result : Unsatisfiable 0.03s 0.44s
% Output : Proof 0.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:51:58 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.44 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.03/0.44
% 0.03/0.44 % SZS status Unsatisfiable
% 0.03/0.44
% 0.03/0.45 % SZS output start Proof
% 0.03/0.45 Axiom 1 (x_divide_x_is_zero): divide(X, X) = zero.
% 0.03/0.45 Axiom 2 (zero_is_smallest): divide(zero, X) = zero.
% 0.03/0.45 Axiom 3 (quotient_smaller_than_numerator): divide(divide(X, Y), X) = zero.
% 0.03/0.45 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.03/0.45 Axiom 5 (quotient_property): divide(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = zero.
% 0.03/0.45 Axiom 6 (divide_and_equal): ifeq(divide(X, Y), zero, ifeq(divide(Y, X), zero, Y, X), X) = X.
% 0.03/0.45
% 0.03/0.45 Goal 1 (prove_x_divide_zero_is_x): divide(a, zero) = a.
% 0.03/0.45 Proof:
% 0.03/0.45 divide(a, zero)
% 0.03/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.03/0.45 ifeq(zero, zero, divide(a, zero), a)
% 0.03/0.45 = { by axiom 3 (quotient_smaller_than_numerator) R->L }
% 0.03/0.45 ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a)
% 0.03/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.03/0.45 ifeq(zero, zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.03/0.45 ifeq(ifeq(zero, zero, zero, divide(a, divide(a, zero))), zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 2 (zero_is_smallest) R->L }
% 0.03/0.45 ifeq(ifeq(divide(zero, divide(a, divide(a, zero))), zero, zero, divide(a, divide(a, zero))), zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.03/0.45 ifeq(ifeq(zero, zero, ifeq(divide(zero, divide(a, divide(a, zero))), zero, zero, divide(a, divide(a, zero))), divide(a, divide(a, zero))), zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.03/0.45 ifeq(ifeq(ifeq(zero, zero, zero, divide(divide(a, divide(a, zero)), zero)), zero, ifeq(divide(zero, divide(a, divide(a, zero))), zero, zero, divide(a, divide(a, zero))), divide(a, divide(a, zero))), zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 2 (zero_is_smallest) R->L }
% 0.03/0.45 ifeq(ifeq(ifeq(divide(zero, divide(divide(a, divide(a, zero)), zero)), zero, zero, divide(divide(a, divide(a, zero)), zero)), zero, ifeq(divide(zero, divide(a, divide(a, zero))), zero, zero, divide(a, divide(a, zero))), divide(a, divide(a, zero))), zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.03/0.45 ifeq(ifeq(ifeq(zero, zero, ifeq(divide(zero, divide(divide(a, divide(a, zero)), zero)), zero, zero, divide(divide(a, divide(a, zero)), zero)), divide(divide(a, divide(a, zero)), zero)), zero, ifeq(divide(zero, divide(a, divide(a, zero))), zero, zero, divide(a, divide(a, zero))), divide(a, divide(a, zero))), zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 5 (quotient_property) R->L }
% 0.03/0.45 ifeq(ifeq(ifeq(divide(divide(divide(a, divide(a, zero)), divide(zero, divide(a, zero))), divide(divide(a, zero), divide(a, zero))), zero, ifeq(divide(zero, divide(divide(a, divide(a, zero)), zero)), zero, zero, divide(divide(a, divide(a, zero)), zero)), divide(divide(a, divide(a, zero)), zero)), zero, ifeq(divide(zero, divide(a, divide(a, zero))), zero, zero, divide(a, divide(a, zero))), divide(a, divide(a, zero))), zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 2 (zero_is_smallest) }
% 0.03/0.45 ifeq(ifeq(ifeq(divide(divide(divide(a, divide(a, zero)), zero), divide(divide(a, zero), divide(a, zero))), zero, ifeq(divide(zero, divide(divide(a, divide(a, zero)), zero)), zero, zero, divide(divide(a, divide(a, zero)), zero)), divide(divide(a, divide(a, zero)), zero)), zero, ifeq(divide(zero, divide(a, divide(a, zero))), zero, zero, divide(a, divide(a, zero))), divide(a, divide(a, zero))), zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 1 (x_divide_x_is_zero) }
% 0.03/0.45 ifeq(ifeq(ifeq(divide(divide(divide(a, divide(a, zero)), zero), zero), zero, ifeq(divide(zero, divide(divide(a, divide(a, zero)), zero)), zero, zero, divide(divide(a, divide(a, zero)), zero)), divide(divide(a, divide(a, zero)), zero)), zero, ifeq(divide(zero, divide(a, divide(a, zero))), zero, zero, divide(a, divide(a, zero))), divide(a, divide(a, zero))), zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 6 (divide_and_equal) }
% 0.03/0.45 ifeq(ifeq(divide(divide(a, divide(a, zero)), zero), zero, ifeq(divide(zero, divide(a, divide(a, zero))), zero, zero, divide(a, divide(a, zero))), divide(a, divide(a, zero))), zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 6 (divide_and_equal) }
% 0.03/0.45 ifeq(divide(a, divide(a, zero)), zero, ifeq(divide(divide(a, zero), a), zero, divide(a, zero), a), a)
% 0.03/0.45 = { by axiom 6 (divide_and_equal) }
% 0.03/0.45 a
% 0.03/0.45 % SZS output end Proof
% 0.03/0.45
% 0.03/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------