%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN009-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 10:19:00 AM UTC 2026
% Result : Unsatisfiable 2.16s 0.72s
% Output : Proof 2.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-2 : 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 : n004.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 10:51:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.16/0.72 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
% 2.16/0.72
% 2.16/0.72 % SZS status Unsatisfiable
% 2.16/0.72
% 2.16/0.73 % SZS output start Proof
% 2.16/0.73 Axiom 1 (x_divde_zero_is_x): quotient(X, zero, X) = true.
% 2.16/0.73 Axiom 2 (identity_divide_idQa): quotient(identity, idQa, idQ_idQa) = true.
% 2.16/0.73 Axiom 3 (identity_divide_idQ_idQa): quotient(identity, idQ_idQa, idQ__idQ_idQa) = true.
% 2.16/0.73 Axiom 4 (identity_divide_a): quotient(identity, a, idQa) = true.
% 2.16/0.73 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.16/0.73 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 2.16/0.73 Axiom 7 (divisor_existence): ifeq(quotient(X, Y, Z), true, less_equal(Z, X), true) = true.
% 2.16/0.73 Axiom 8 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 2.16/0.73 Axiom 9 (xLEy_implies_zQyLEzQx): ifeq(quotient(X, Y, Z), true, ifeq(quotient(X, W, V), true, ifeq(less_equal(W, Y), true, less_equal(Z, V), true), true), true) = true.
% 2.16/0.73 Axiom 10 (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.
% 2.16/0.73
% 2.16/0.73 Goal 1 (prove_one_inversion_equals_three): idQa = idQ__idQ_idQa.
% 2.16/0.73 Proof:
% 2.16/0.73 idQa
% 2.16/0.73 = { by axiom 6 (ifeq_axiom) R->L }
% 2.16/0.73 ifeq2(true, true, idQa, idQ__idQ_idQa)
% 2.16/0.73 = { by axiom 9 (xLEy_implies_zQyLEzQx) R->L }
% 2.16/0.73 ifeq2(ifeq(quotient(identity, a, idQa), true, ifeq(quotient(identity, idQ_idQa, idQ__idQ_idQa), true, ifeq(less_equal(idQ_idQa, a), true, less_equal(idQa, idQ__idQ_idQa), true), true), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.73 = { by axiom 3 (identity_divide_idQ_idQa) }
% 2.16/0.73 ifeq2(ifeq(quotient(identity, a, idQa), true, ifeq(true, true, ifeq(less_equal(idQ_idQa, a), true, less_equal(idQa, idQ__idQ_idQa), true), true), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.73 = { by axiom 5 (ifeq_axiom) }
% 2.16/0.73 ifeq2(ifeq(quotient(identity, a, idQa), true, ifeq(less_equal(idQ_idQa, a), true, less_equal(idQa, idQ__idQ_idQa), true), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.73 = { by axiom 4 (identity_divide_a) }
% 2.16/0.73 ifeq2(ifeq(true, true, ifeq(less_equal(idQ_idQa, a), true, less_equal(idQa, idQ__idQ_idQa), true), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.73 = { by axiom 5 (ifeq_axiom) }
% 2.16/0.73 ifeq2(ifeq(less_equal(idQ_idQa, a), true, less_equal(idQa, idQ__idQ_idQa), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.73 = { by axiom 5 (ifeq_axiom) R->L }
% 2.16/0.73 ifeq2(ifeq(ifeq(true, true, less_equal(idQ_idQa, a), true), true, less_equal(idQa, idQ__idQ_idQa), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.73 = { by axiom 7 (divisor_existence) R->L }
% 2.16/0.73 ifeq2(ifeq(ifeq(ifeq(quotient(idQa, zero, idQa), true, less_equal(idQa, idQa), true), true, less_equal(idQ_idQa, a), true), true, less_equal(idQa, idQ__idQ_idQa), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.73 = { by axiom 1 (x_divde_zero_is_x) }
% 2.16/0.73 ifeq2(ifeq(ifeq(ifeq(true, true, less_equal(idQa, idQa), true), true, less_equal(idQ_idQa, a), true), true, less_equal(idQa, idQ__idQ_idQa), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.73 = { by axiom 5 (ifeq_axiom) }
% 2.16/0.73 ifeq2(ifeq(ifeq(less_equal(idQa, idQa), true, less_equal(idQ_idQa, a), true), true, less_equal(idQa, idQ__idQ_idQa), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.73 = { by axiom 5 (ifeq_axiom) R->L }
% 2.16/0.74 ifeq2(ifeq(ifeq(true, true, ifeq(less_equal(idQa, idQa), true, less_equal(idQ_idQa, a), true), true), true, less_equal(idQa, idQ__idQ_idQa), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 4 (identity_divide_a) R->L }
% 2.16/0.74 ifeq2(ifeq(ifeq(quotient(identity, a, idQa), true, ifeq(less_equal(idQa, idQa), true, less_equal(idQ_idQa, a), true), true), true, less_equal(idQa, idQ__idQ_idQa), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 5 (ifeq_axiom) R->L }
% 2.16/0.74 ifeq2(ifeq(ifeq(true, true, ifeq(quotient(identity, a, idQa), true, ifeq(less_equal(idQa, idQa), true, less_equal(idQ_idQa, a), true), true), true), true, less_equal(idQa, idQ__idQ_idQa), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 2 (identity_divide_idQa) R->L }
% 2.16/0.74 ifeq2(ifeq(ifeq(quotient(identity, idQa, idQ_idQa), true, ifeq(quotient(identity, a, idQa), true, ifeq(less_equal(idQa, idQa), true, less_equal(idQ_idQa, a), true), true), true), true, less_equal(idQa, idQ__idQ_idQa), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 10 (xQyLEz_implies_xQzLEy) }
% 2.16/0.74 ifeq2(ifeq(true, true, less_equal(idQa, idQ__idQ_idQa), true), true, idQa, idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 5 (ifeq_axiom) }
% 2.16/0.74 ifeq2(less_equal(idQa, idQ__idQ_idQa), true, idQa, idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 6 (ifeq_axiom) R->L }
% 2.16/0.74 ifeq2(true, true, ifeq2(less_equal(idQa, idQ__idQ_idQa), true, idQa, idQ__idQ_idQa), idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 10 (xQyLEz_implies_xQzLEy) R->L }
% 2.16/0.74 ifeq2(ifeq(quotient(identity, idQ_idQa, idQ__idQ_idQa), true, ifeq(quotient(identity, idQa, idQ_idQa), true, ifeq(less_equal(idQ_idQa, idQ_idQa), true, less_equal(idQ__idQ_idQa, idQa), true), true), true), true, ifeq2(less_equal(idQa, idQ__idQ_idQa), true, idQa, idQ__idQ_idQa), idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 2 (identity_divide_idQa) }
% 2.16/0.74 ifeq2(ifeq(quotient(identity, idQ_idQa, idQ__idQ_idQa), true, ifeq(true, true, ifeq(less_equal(idQ_idQa, idQ_idQa), true, less_equal(idQ__idQ_idQa, idQa), true), true), true), true, ifeq2(less_equal(idQa, idQ__idQ_idQa), true, idQa, idQ__idQ_idQa), idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 5 (ifeq_axiom) }
% 2.16/0.74 ifeq2(ifeq(quotient(identity, idQ_idQa, idQ__idQ_idQa), true, ifeq(less_equal(idQ_idQa, idQ_idQa), true, less_equal(idQ__idQ_idQa, idQa), true), true), true, ifeq2(less_equal(idQa, idQ__idQ_idQa), true, idQa, idQ__idQ_idQa), idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 3 (identity_divide_idQ_idQa) }
% 2.16/0.74 ifeq2(ifeq(true, true, ifeq(less_equal(idQ_idQa, idQ_idQa), true, less_equal(idQ__idQ_idQa, idQa), true), true), true, ifeq2(less_equal(idQa, idQ__idQ_idQa), true, idQa, idQ__idQ_idQa), idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 5 (ifeq_axiom) }
% 2.16/0.74 ifeq2(ifeq(less_equal(idQ_idQa, idQ_idQa), true, less_equal(idQ__idQ_idQa, idQa), true), true, ifeq2(less_equal(idQa, idQ__idQ_idQa), true, idQa, idQ__idQ_idQa), idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 5 (ifeq_axiom) R->L }
% 2.16/0.74 ifeq2(ifeq(ifeq(true, true, less_equal(idQ_idQa, idQ_idQa), true), true, less_equal(idQ__idQ_idQa, idQa), true), true, ifeq2(less_equal(idQa, idQ__idQ_idQa), true, idQa, idQ__idQ_idQa), idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 1 (x_divde_zero_is_x) R->L }
% 2.16/0.74 ifeq2(ifeq(ifeq(quotient(idQ_idQa, zero, idQ_idQa), true, less_equal(idQ_idQa, idQ_idQa), true), true, less_equal(idQ__idQ_idQa, idQa), true), true, ifeq2(less_equal(idQa, idQ__idQ_idQa), true, idQa, idQ__idQ_idQa), idQ__idQ_idQa)
% 2.16/0.74 = { by axiom 7 (divisor_existence) }
% 2.16/0.75 ifeq2(ifeq(true, true, less_equal(idQ__idQ_idQa, idQa), true), true, ifeq2(less_equal(idQa, idQ__idQ_idQa), true, idQa, idQ__idQ_idQa), idQ__idQ_idQa)
% 2.16/0.75 = { by axiom 5 (ifeq_axiom) }
% 2.16/0.75 ifeq2(less_equal(idQ__idQ_idQa, idQa), true, ifeq2(less_equal(idQa, idQ__idQ_idQa), true, idQa, idQ__idQ_idQa), idQ__idQ_idQa)
% 2.16/0.75 = { by axiom 8 (less_equal_and_equal) }
% 2.16/0.75 idQ__idQ_idQa
% 2.16/0.75 % SZS output end Proof
% 2.16/0.75
% 2.16/0.75 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------