%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 10:18:55 AM UTC 2026
% Result : Unsatisfiable 1.78s 0.65s
% Output : Proof 1.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n014.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 10:49:16 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.78/0.65 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
% 1.78/0.65
% 1.78/0.65 % SZS status Unsatisfiable
% 1.78/0.65
% 1.78/0.68 % SZS output start Proof
% 1.78/0.68 Axiom 1 (zero_is_smallest): less_equal(zero, X) = true.
% 1.78/0.68 Axiom 2 (zero_divide_anything_is_zero): quotient(zero, X, zero) = true.
% 1.78/0.68 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.78/0.68 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 1.78/0.68 Axiom 5 (closure): quotient(X, Y, divide(X, Y)) = true.
% 1.78/0.68 Axiom 6 (quotient_less_equal): ifeq(less_equal(X, Y), true, quotient(X, Y, zero), true) = true.
% 1.78/0.68 Axiom 7 (divisor_existence): ifeq(quotient(X, Y, Z), true, less_equal(Z, X), true) = true.
% 1.78/0.68 Axiom 8 (less_equal_quotient): ifeq(quotient(X, Y, zero), true, less_equal(X, Y), true) = true.
% 1.78/0.68 Axiom 9 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 1.78/0.68 Axiom 10 (quotient_property): ifeq(quotient(X, Y, Z), true, ifeq(quotient(W, V, U), true, ifeq(quotient(T, V, Y), true, ifeq(quotient(S, V, X), true, ifeq(quotient(S, T, W), true, less_equal(Z, U), true), true), true), true), true) = true.
% 1.78/0.68
% 1.78/0.68 Goal 1 (prove_x_divide_x_is_zero): quotient(x, x, zero) = true.
% 1.78/0.68 Proof:
% 1.78/0.68 quotient(x, x, zero)
% 1.78/0.68 = { by axiom 4 (ifeq_axiom) R->L }
% 1.78/0.68 quotient(x, x, ifeq2(true, true, zero, divide(x, x)))
% 1.78/0.68 = { by axiom 1 (zero_is_smallest) R->L }
% 1.78/0.68 quotient(x, x, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)))
% 1.78/0.68 = { by axiom 4 (ifeq_axiom) R->L }
% 1.78/0.68 quotient(x, x, ifeq2(true, true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.68 = { by axiom 8 (less_equal_quotient) R->L }
% 1.78/0.68 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, zero), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.68 = { by axiom 4 (ifeq_axiom) R->L }
% 1.78/0.68 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(true, true, zero, divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.68 = { by axiom 1 (zero_is_smallest) R->L }
% 1.78/0.68 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.68 = { by axiom 4 (ifeq_axiom) R->L }
% 1.78/0.68 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.68 = { by axiom 10 (quotient_property) R->L }
% 1.78/0.68 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(quotient(divide(x, x), zero, divide(divide(x, x), zero)), true, ifeq(quotient(divide(x, zero), x, zero), true, ifeq(quotient(zero, x, zero), true, ifeq(quotient(x, x, divide(x, x)), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, x), zero), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.68 = { by axiom 2 (zero_divide_anything_is_zero) }
% 1.78/0.68 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(quotient(divide(x, x), zero, divide(divide(x, x), zero)), true, ifeq(quotient(divide(x, zero), x, zero), true, ifeq(true, true, ifeq(quotient(x, x, divide(x, x)), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, x), zero), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.68 = { by axiom 3 (ifeq_axiom) }
% 1.78/0.68 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(quotient(divide(x, x), zero, divide(divide(x, x), zero)), true, ifeq(quotient(divide(x, zero), x, zero), true, ifeq(quotient(x, x, divide(x, x)), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, x), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.68 = { by axiom 5 (closure) }
% 1.78/0.68 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(true, true, ifeq(quotient(divide(x, zero), x, zero), true, ifeq(quotient(x, x, divide(x, x)), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, x), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.68 = { by axiom 3 (ifeq_axiom) }
% 1.78/0.68 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(quotient(divide(x, zero), x, zero), true, ifeq(quotient(x, x, divide(x, x)), true, ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(divide(x, x), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.68 = { by axiom 5 (closure) }
% 1.78/0.68 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(quotient(divide(x, zero), x, zero), true, ifeq(quotient(x, x, divide(x, x)), true, ifeq(true, true, less_equal(divide(divide(x, x), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 3 (ifeq_axiom) }
% 1.78/0.69 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(quotient(divide(x, zero), x, zero), true, ifeq(quotient(x, x, divide(x, x)), true, less_equal(divide(divide(x, x), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 3 (ifeq_axiom) R->L }
% 1.78/0.69 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(ifeq(true, true, quotient(divide(x, zero), x, zero), true), true, ifeq(quotient(x, x, divide(x, x)), true, less_equal(divide(divide(x, x), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 7 (divisor_existence) R->L }
% 1.78/0.69 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(ifeq(ifeq(quotient(x, zero, divide(x, zero)), true, less_equal(divide(x, zero), x), true), true, quotient(divide(x, zero), x, zero), true), true, ifeq(quotient(x, x, divide(x, x)), true, less_equal(divide(divide(x, x), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 5 (closure) }
% 1.78/0.69 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(ifeq(ifeq(true, true, less_equal(divide(x, zero), x), true), true, quotient(divide(x, zero), x, zero), true), true, ifeq(quotient(x, x, divide(x, x)), true, less_equal(divide(divide(x, x), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 3 (ifeq_axiom) }
% 1.78/0.69 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(ifeq(less_equal(divide(x, zero), x), true, quotient(divide(x, zero), x, zero), true), true, ifeq(quotient(x, x, divide(x, x)), true, less_equal(divide(divide(x, x), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 6 (quotient_less_equal) }
% 1.78/0.69 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(true, true, ifeq(quotient(x, x, divide(x, x)), true, less_equal(divide(divide(x, x), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 3 (ifeq_axiom) }
% 1.78/0.69 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(quotient(x, x, divide(x, x)), true, less_equal(divide(divide(x, x), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 5 (closure) }
% 1.78/0.69 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(ifeq(true, true, less_equal(divide(divide(x, x), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 3 (ifeq_axiom) }
% 1.78/0.69 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, ifeq2(less_equal(divide(divide(x, x), zero), zero), true, ifeq2(less_equal(zero, divide(divide(x, x), zero)), true, zero, divide(divide(x, x), zero)), divide(divide(x, x), zero))), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 9 (less_equal_and_equal) }
% 1.78/0.69 quotient(x, x, ifeq2(ifeq(quotient(divide(x, x), zero, divide(divide(x, x), zero)), true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 5 (closure) }
% 1.78/0.69 quotient(x, x, ifeq2(ifeq(true, true, less_equal(divide(x, x), zero), true), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 3 (ifeq_axiom) }
% 1.78/0.69 quotient(x, x, ifeq2(less_equal(divide(x, x), zero), true, ifeq2(less_equal(zero, divide(x, x)), true, zero, divide(x, x)), divide(x, x)))
% 1.78/0.69 = { by axiom 9 (less_equal_and_equal) }
% 1.78/0.69 quotient(x, x, divide(x, x))
% 1.78/0.69 = { by axiom 5 (closure) }
% 1.78/0.69 true
% 1.78/0.69 % SZS output end Proof
% 1.78/0.69
% 1.78/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------