%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE002+1 : TPTP v9.3.1. Released v4.0.0.
% 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 11:39:36 AM UTC 2026
% Result : Theorem 0.22s 0.51s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE002+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 12:57:51 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.51 Command-line arguments: --flatten --complete-subsets
% 0.22/0.51
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51
% 0.22/0.51 % SZS output start Proof
% 0.22/0.51 Axiom 1 (goals): leq(x0, x1) = true.
% 0.22/0.51 Axiom 2 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.22/0.51 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.22/0.51 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.22/0.51 Axiom 5 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.22/0.51 Axiom 6 (order_1): ifeq(leq(X, Y), true, addition(X, Y), Y) = Y.
% 0.22/0.51 Axiom 7 (order): ifeq2(addition(X, Y), Y, leq(X, Y), true) = true.
% 0.22/0.51
% 0.22/0.51 Goal 1 (goals_1): leq(multiplication(x0, x2), multiplication(x1, x2)) = true.
% 0.22/0.51 Proof:
% 0.22/0.51 leq(multiplication(x0, x2), multiplication(x1, x2))
% 0.22/0.51 = { by axiom 4 (ifeq_axiom) R->L }
% 0.22/0.51 ifeq2(multiplication(x1, x2), multiplication(x1, x2), leq(multiplication(x0, x2), multiplication(x1, x2)), leq(x0, x1))
% 0.22/0.51 = { by axiom 6 (order_1) R->L }
% 0.22/0.51 ifeq2(multiplication(ifeq(leq(x0, x1), true, addition(x0, x1), x1), x2), multiplication(x1, x2), leq(multiplication(x0, x2), multiplication(x1, x2)), leq(x0, x1))
% 0.22/0.51 = { by axiom 1 (goals) R->L }
% 0.22/0.51 ifeq2(multiplication(ifeq(leq(x0, x1), leq(x0, x1), addition(x0, x1), x1), x2), multiplication(x1, x2), leq(multiplication(x0, x2), multiplication(x1, x2)), leq(x0, x1))
% 0.22/0.51 = { by axiom 3 (ifeq_axiom) }
% 0.22/0.51 ifeq2(multiplication(addition(x0, x1), x2), multiplication(x1, x2), leq(multiplication(x0, x2), multiplication(x1, x2)), leq(x0, x1))
% 0.22/0.51 = { by axiom 2 (additive_commutativity) R->L }
% 0.22/0.51 ifeq2(multiplication(addition(x1, x0), x2), multiplication(x1, x2), leq(multiplication(x0, x2), multiplication(x1, x2)), leq(x0, x1))
% 0.22/0.51 = { by axiom 5 (left_distributivity) }
% 0.22/0.51 ifeq2(addition(multiplication(x1, x2), multiplication(x0, x2)), multiplication(x1, x2), leq(multiplication(x0, x2), multiplication(x1, x2)), leq(x0, x1))
% 0.22/0.51 = { by axiom 2 (additive_commutativity) }
% 0.22/0.51 ifeq2(addition(multiplication(x0, x2), multiplication(x1, x2)), multiplication(x1, x2), leq(multiplication(x0, x2), multiplication(x1, x2)), leq(x0, x1))
% 0.22/0.51 = { by axiom 1 (goals) }
% 0.22/0.51 ifeq2(addition(multiplication(x0, x2), multiplication(x1, x2)), multiplication(x1, x2), leq(multiplication(x0, x2), multiplication(x1, x2)), true)
% 0.22/0.51 = { by axiom 7 (order) }
% 0.22/0.51 true
% 0.22/0.51 % SZS output end Proof
% 0.22/0.51
% 0.22/0.51 RESULT: Theorem (the conjecture is true).
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