%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN007-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 10:18:58 AM UTC 2026
% Result : Unsatisfiable 0.31s 0.55s
% Output : Proof 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN007-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.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 10:53:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.55 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
% 0.31/0.55
% 0.31/0.55 % SZS status Unsatisfiable
% 0.31/0.55
% 0.31/0.56 % SZS output start Proof
% 0.31/0.56 Axiom 1 (xLEy): less_equal(x, y) = true.
% 0.31/0.56 Axiom 2 (x_divde_zero_is_x): quotient(X, zero, X) = true.
% 0.31/0.56 Axiom 3 (zQx): quotient(z, x, zQx) = true.
% 0.31/0.56 Axiom 4 (zQy): quotient(z, y, zQy) = true.
% 0.31/0.56 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.31/0.56 Axiom 6 (closure): quotient(X, Y, divide(X, Y)) = true.
% 0.31/0.56 Axiom 7 (divisor_existence): ifeq(quotient(X, Y, Z), true, less_equal(Z, X), true) = true.
% 0.31/0.56 Axiom 8 (transitivity_of_less_equal): ifeq(less_equal(X, Y), true, ifeq(less_equal(Z, X), true, less_equal(Z, Y), true), true) = true.
% 0.31/0.56 Axiom 9 (xQyLEz_implies_xQzLEy): ifeq(quotient(X, Y, Z), true, ifeq(quotient(X, W, V), true, ifeq(less_equal(V, Y), true, less_equal(Z, W), true), true), true) = true.
% 0.31/0.56
% 0.31/0.56 Goal 1 (prove_zQyLEzQx): less_equal(zQy, zQx) = true.
% 0.31/0.56 Proof:
% 0.31/0.56 less_equal(zQy, zQx)
% 0.31/0.56 = { by axiom 5 (ifeq_axiom) R->L }
% 0.31/0.56 ifeq(true, true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 8 (transitivity_of_less_equal) R->L }
% 0.31/0.56 ifeq(ifeq(less_equal(x, y), true, ifeq(less_equal(divide(z, zQx), x), true, less_equal(divide(z, zQx), y), true), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 1 (xLEy) }
% 0.31/0.56 ifeq(ifeq(true, true, ifeq(less_equal(divide(z, zQx), x), true, less_equal(divide(z, zQx), y), true), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.56 ifeq(ifeq(less_equal(divide(z, zQx), x), true, less_equal(divide(z, zQx), y), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 5 (ifeq_axiom) R->L }
% 0.31/0.56 ifeq(ifeq(ifeq(true, true, less_equal(divide(z, zQx), x), true), true, less_equal(divide(z, zQx), y), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 6 (closure) R->L }
% 0.31/0.56 ifeq(ifeq(ifeq(quotient(z, zQx, divide(z, zQx)), true, less_equal(divide(z, zQx), x), true), true, less_equal(divide(z, zQx), y), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 5 (ifeq_axiom) R->L }
% 0.31/0.56 ifeq(ifeq(ifeq(quotient(z, zQx, divide(z, zQx)), true, ifeq(true, true, less_equal(divide(z, zQx), x), true), true), true, less_equal(divide(z, zQx), y), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 7 (divisor_existence) R->L }
% 0.31/0.56 ifeq(ifeq(ifeq(quotient(z, zQx, divide(z, zQx)), true, ifeq(ifeq(quotient(zQx, zero, zQx), true, less_equal(zQx, zQx), true), true, less_equal(divide(z, zQx), x), true), true), true, less_equal(divide(z, zQx), y), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 2 (x_divde_zero_is_x) }
% 0.31/0.56 ifeq(ifeq(ifeq(quotient(z, zQx, divide(z, zQx)), true, ifeq(ifeq(true, true, less_equal(zQx, zQx), true), true, less_equal(divide(z, zQx), x), true), true), true, less_equal(divide(z, zQx), y), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.56 ifeq(ifeq(ifeq(quotient(z, zQx, divide(z, zQx)), true, ifeq(less_equal(zQx, zQx), true, less_equal(divide(z, zQx), x), true), true), true, less_equal(divide(z, zQx), y), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 5 (ifeq_axiom) R->L }
% 0.31/0.56 ifeq(ifeq(ifeq(quotient(z, zQx, divide(z, zQx)), true, ifeq(true, true, ifeq(less_equal(zQx, zQx), true, less_equal(divide(z, zQx), x), true), true), true), true, less_equal(divide(z, zQx), y), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 3 (zQx) R->L }
% 0.31/0.56 ifeq(ifeq(ifeq(quotient(z, zQx, divide(z, zQx)), true, ifeq(quotient(z, x, zQx), true, ifeq(less_equal(zQx, zQx), true, less_equal(divide(z, zQx), x), true), true), true), true, less_equal(divide(z, zQx), y), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 9 (xQyLEz_implies_xQzLEy) }
% 0.31/0.56 ifeq(ifeq(true, true, less_equal(divide(z, zQx), y), true), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.56 ifeq(less_equal(divide(z, zQx), y), true, less_equal(zQy, zQx), true)
% 0.31/0.56 = { by axiom 5 (ifeq_axiom) R->L }
% 0.31/0.56 ifeq(true, true, ifeq(less_equal(divide(z, zQx), y), true, less_equal(zQy, zQx), true), true)
% 0.31/0.56 = { by axiom 6 (closure) R->L }
% 0.31/0.56 ifeq(quotient(z, zQx, divide(z, zQx)), true, ifeq(less_equal(divide(z, zQx), y), true, less_equal(zQy, zQx), true), true)
% 0.31/0.56 = { by axiom 5 (ifeq_axiom) R->L }
% 0.31/0.56 ifeq(true, true, ifeq(quotient(z, zQx, divide(z, zQx)), true, ifeq(less_equal(divide(z, zQx), y), true, less_equal(zQy, zQx), true), true), true)
% 0.31/0.56 = { by axiom 4 (zQy) R->L }
% 0.31/0.56 ifeq(quotient(z, y, zQy), true, ifeq(quotient(z, zQx, divide(z, zQx)), true, ifeq(less_equal(divide(z, zQx), y), true, less_equal(zQy, zQx), true), true), true)
% 0.31/0.56 = { by axiom 9 (xQyLEz_implies_xQzLEy) }
% 0.31/0.56 true
% 0.31/0.56 % SZS output end Proof
% 0.31/0.56
% 0.31/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------