TSTP Solution File: KLE151-10 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KLE151-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:36:05 EDT 2023
% Result : Unsatisfiable 4.13s 0.92s
% Output : Proof 4.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE151-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 11:06:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.13/0.92 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 4.13/0.92
% 4.13/0.92 % SZS status Unsatisfiable
% 4.13/0.92
% 4.13/0.93 % SZS output start Proof
% 4.13/0.93 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 4.13/0.93 Axiom 2 (idempotence): addition(X, X) = X.
% 4.13/0.93 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 4.13/0.93 Axiom 4 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 4.13/0.93 Axiom 5 (ifeq_axiom_002): ifeq(X, X, Y, Z) = Y.
% 4.13/0.93 Axiom 6 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 4.13/0.93 Axiom 7 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
% 4.13/0.93 Axiom 8 (distributivity1): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 4.13/0.93 Axiom 9 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 4.13/0.93 Axiom 10 (infty_coinduction): ifeq(leq(X, addition(multiplication(Y, X), Z)), true, leq(X, multiplication(strong_iteration(Y), Z)), true) = true.
% 4.13/0.93
% 4.13/0.93 Goal 1 (goals): leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)) = true.
% 4.13/0.93 Proof:
% 4.13/0.93 leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0))
% 4.13/0.93 = { by axiom 5 (ifeq_axiom_002) R->L }
% 4.13/0.93 ifeq(true, true, leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)), true)
% 4.13/0.93 = { by axiom 9 (order) R->L }
% 4.13/0.93 ifeq(ifeq3(addition(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0)))), multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0)))), true), true, leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)), true)
% 4.13/0.93 = { by axiom 2 (idempotence) }
% 4.13/0.93 ifeq(ifeq3(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0)))), true), true, leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)), true)
% 4.13/0.93 = { by axiom 6 (ifeq_axiom) }
% 4.13/0.93 ifeq(leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0)))), true, leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)), true)
% 4.13/0.93 = { by axiom 7 (infty_unfold1) }
% 4.13/0.93 ifeq(leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(sK2_goals_X0, addition(multiplication(multiplication(sK1_goals_X1, sK2_goals_X0), strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), one))), true, leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)), true)
% 4.13/0.93 = { by axiom 3 (additive_commutativity) }
% 4.13/0.93 ifeq(leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(sK2_goals_X0, addition(one, multiplication(multiplication(sK1_goals_X1, sK2_goals_X0), strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0)))))), true, leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)), true)
% 4.13/0.93 = { by axiom 4 (multiplicative_associativity) R->L }
% 4.13/0.93 ifeq(leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(sK2_goals_X0, addition(one, multiplication(sK1_goals_X1, multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))))))), true, leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)), true)
% 4.13/0.93 = { by axiom 8 (distributivity1) }
% 4.13/0.93 ifeq(leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), addition(multiplication(sK2_goals_X0, one), multiplication(sK2_goals_X0, multiplication(sK1_goals_X1, multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))))))), true, leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)), true)
% 4.13/0.93 = { by axiom 1 (multiplicative_right_identity) }
% 4.13/0.93 ifeq(leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), addition(sK2_goals_X0, multiplication(sK2_goals_X0, multiplication(sK1_goals_X1, multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))))))), true, leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)), true)
% 4.13/0.93 = { by axiom 4 (multiplicative_associativity) }
% 4.13/0.93 ifeq(leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), addition(sK2_goals_X0, multiplication(multiplication(sK2_goals_X0, sK1_goals_X1), multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0)))))), true, leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)), true)
% 4.13/0.93 = { by axiom 3 (additive_commutativity) R->L }
% 4.13/0.93 ifeq(leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), addition(multiplication(multiplication(sK2_goals_X0, sK1_goals_X1), multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0)))), sK2_goals_X0)), true, leq(multiplication(sK2_goals_X0, strong_iteration(multiplication(sK1_goals_X1, sK2_goals_X0))), multiplication(strong_iteration(multiplication(sK2_goals_X0, sK1_goals_X1)), sK2_goals_X0)), true)
% 4.13/0.93 = { by axiom 10 (infty_coinduction) }
% 4.13/0.93 true
% 4.13/0.93 % SZS output end Proof
% 4.13/0.93
% 4.13/0.93 RESULT: Unsatisfiable (the axioms are contradictory).
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