%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN007-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 10:18:59 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:50:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48 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
% 0.19/0.48
% 0.19/0.48 % SZS status Unsatisfiable
% 0.19/0.48
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 Axiom 1 (x_divide_x_is_zero): divide(X, X) = zero.
% 0.19/0.48 Axiom 2 (a_LE_b): less_equal(a, b) = true.
% 0.19/0.48 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.48 Axiom 4 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.19/0.48 Axiom 5 (quotient_less_equal2): ifeq3(divide(X, Y), zero, less_equal(X, Y), true) = true.
% 0.19/0.48 Axiom 6 (property_of_divide1): ifeq(less_equal(divide(X, Y), Z), true, less_equal(divide(X, Z), Y), true) = true.
% 0.19/0.48 Axiom 7 (transitivity_of_less_equal): ifeq(less_equal(X, Y), true, ifeq(less_equal(Z, X), true, less_equal(Z, Y), true), true) = true.
% 0.19/0.48
% 0.19/0.48 Goal 1 (prove_c_divide_b_LE_c_divide_a): less_equal(divide(c, b), divide(c, a)) = true.
% 0.19/0.48 Proof:
% 0.19/0.48 less_equal(divide(c, b), divide(c, a))
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.48 ifeq(true, true, less_equal(divide(c, b), divide(c, a)), true)
% 0.19/0.48 = { by axiom 7 (transitivity_of_less_equal) R->L }
% 0.19/0.48 ifeq(ifeq(less_equal(a, b), true, ifeq(less_equal(divide(c, divide(c, a)), a), true, less_equal(divide(c, divide(c, a)), b), true), true), true, less_equal(divide(c, b), divide(c, a)), true)
% 0.19/0.48 = { by axiom 2 (a_LE_b) }
% 0.19/0.48 ifeq(ifeq(true, true, ifeq(less_equal(divide(c, divide(c, a)), a), true, less_equal(divide(c, divide(c, a)), b), true), true), true, less_equal(divide(c, b), divide(c, a)), true)
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.48 ifeq(ifeq(less_equal(divide(c, divide(c, a)), a), true, less_equal(divide(c, divide(c, a)), b), true), true, less_equal(divide(c, b), divide(c, a)), true)
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.48 ifeq(ifeq(ifeq(true, true, less_equal(divide(c, divide(c, a)), a), true), true, less_equal(divide(c, divide(c, a)), b), true), true, less_equal(divide(c, b), divide(c, a)), true)
% 0.19/0.48 = { by axiom 5 (quotient_less_equal2) R->L }
% 0.19/0.48 ifeq(ifeq(ifeq(ifeq3(divide(divide(c, a), divide(c, a)), zero, less_equal(divide(c, a), divide(c, a)), true), true, less_equal(divide(c, divide(c, a)), a), true), true, less_equal(divide(c, divide(c, a)), b), true), true, less_equal(divide(c, b), divide(c, a)), true)
% 0.19/0.48 = { by axiom 1 (x_divide_x_is_zero) }
% 0.19/0.48 ifeq(ifeq(ifeq(ifeq3(zero, zero, less_equal(divide(c, a), divide(c, a)), true), true, less_equal(divide(c, divide(c, a)), a), true), true, less_equal(divide(c, divide(c, a)), b), true), true, less_equal(divide(c, b), divide(c, a)), true)
% 0.19/0.48 = { by axiom 4 (ifeq_axiom) }
% 0.19/0.48 ifeq(ifeq(ifeq(less_equal(divide(c, a), divide(c, a)), true, less_equal(divide(c, divide(c, a)), a), true), true, less_equal(divide(c, divide(c, a)), b), true), true, less_equal(divide(c, b), divide(c, a)), true)
% 0.19/0.48 = { by axiom 6 (property_of_divide1) }
% 0.19/0.48 ifeq(ifeq(true, true, less_equal(divide(c, divide(c, a)), b), true), true, less_equal(divide(c, b), divide(c, a)), true)
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.48 ifeq(less_equal(divide(c, divide(c, a)), b), true, less_equal(divide(c, b), divide(c, a)), true)
% 0.19/0.48 = { by axiom 6 (property_of_divide1) }
% 0.19/0.48 true
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48
% 0.19/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
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