TSTP Solution File: KLE147-10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE147-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n026.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 05:36:03 EDT 2023
% Result : Unsatisfiable 31.19s 4.40s
% Output : Proof 31.19s
% 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 : KLE147-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.35 % Computer : n026.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Aug 29 12:46:20 EDT 2023
% 0.18/0.35 % CPUTime :
% 31.19/4.40 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 31.19/4.40
% 31.19/4.40 % SZS status Unsatisfiable
% 31.19/4.40
% 31.19/4.41 % SZS output start Proof
% 31.19/4.41 Axiom 1 (multiplicative_left_identity): multiplication(one, X) = X.
% 31.19/4.41 Axiom 2 (idempotence): addition(X, X) = X.
% 31.19/4.41 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 31.19/4.41 Axiom 4 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 31.19/4.41 Axiom 5 (ifeq_axiom_002): ifeq(X, X, Y, Z) = Y.
% 31.19/4.41 Axiom 6 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 31.19/4.41 Axiom 7 (star_unfold1): addition(one, multiplication(X, star(X))) = star(X).
% 31.19/4.41 Axiom 8 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
% 31.19/4.41 Axiom 9 (distributivity2): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 31.19/4.41 Axiom 10 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 31.19/4.41 Axiom 11 (star_induction1): ifeq(leq(addition(multiplication(X, Y), Z), Y), true, leq(multiplication(star(X), Z), Y), true) = true.
% 31.19/4.41
% 31.19/4.41 Lemma 12: addition(one, star(X)) = star(X).
% 31.19/4.41 Proof:
% 31.19/4.41 addition(one, star(X))
% 31.19/4.41 = { by axiom 7 (star_unfold1) R->L }
% 31.19/4.41 addition(one, addition(one, multiplication(X, star(X))))
% 31.19/4.41 = { by axiom 4 (additive_associativity) }
% 31.19/4.41 addition(addition(one, one), multiplication(X, star(X)))
% 31.19/4.41 = { by axiom 2 (idempotence) }
% 31.19/4.41 addition(one, multiplication(X, star(X)))
% 31.19/4.41 = { by axiom 7 (star_unfold1) }
% 31.19/4.41 star(X)
% 31.19/4.41
% 31.19/4.41 Lemma 13: addition(one, multiplication(X, strong_iteration(X))) = strong_iteration(X).
% 31.19/4.41 Proof:
% 31.19/4.41 addition(one, multiplication(X, strong_iteration(X)))
% 31.19/4.41 = { by axiom 3 (additive_commutativity) R->L }
% 31.19/4.41 addition(multiplication(X, strong_iteration(X)), one)
% 31.19/4.41 = { by axiom 8 (infty_unfold1) R->L }
% 31.19/4.41 strong_iteration(X)
% 31.19/4.41
% 31.19/4.41 Lemma 14: addition(multiplication(X, Y), multiplication(Z, Y)) = multiplication(addition(Z, X), Y).
% 31.19/4.41 Proof:
% 31.19/4.41 addition(multiplication(X, Y), multiplication(Z, Y))
% 31.19/4.41 = { by axiom 9 (distributivity2) R->L }
% 31.19/4.41 multiplication(addition(X, Z), Y)
% 31.19/4.41 = { by axiom 3 (additive_commutativity) }
% 31.19/4.41 multiplication(addition(Z, X), Y)
% 31.19/4.41
% 31.19/4.41 Goal 1 (goals): tuple(leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), leq(strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1))))) = tuple(true, true).
% 31.19/4.41 Proof:
% 31.19/4.41 tuple(leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), leq(strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)))))
% 31.19/4.41 = { by axiom 6 (ifeq_axiom) R->L }
% 31.19/4.41 tuple(leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), ifeq3(multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1))), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1))), leq(strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)))), true))
% 31.19/4.41 = { by lemma 12 R->L }
% 31.19/4.41 tuple(leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), ifeq3(multiplication(addition(one, star(sK3_goals_X1)), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1))), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1))), leq(strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)))), true))
% 31.19/4.41 = { by lemma 14 R->L }
% 31.19/4.41 tuple(leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), ifeq3(addition(multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1))), multiplication(one, strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)))), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1))), leq(strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)))), true))
% 31.19/4.41 = { by axiom 1 (multiplicative_left_identity) }
% 31.19/4.41 tuple(leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), ifeq3(addition(multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1))), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1))), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1))), leq(strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)))), true))
% 31.19/4.41 = { by axiom 3 (additive_commutativity) R->L }
% 31.19/4.41 tuple(leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), ifeq3(addition(strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)))), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1))), leq(strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)), multiplication(star(sK3_goals_X1), strong_iteration(multiplication(star(sK4_goals_X0), sK3_goals_X1)))), true))
% 31.19/4.41 = { by axiom 10 (order) }
% 31.19/4.41 tuple(leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true)
% 31.19/4.41 = { by axiom 5 (ifeq_axiom_002) R->L }
% 31.19/4.41 tuple(ifeq(true, true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.41 = { by axiom 10 (order) R->L }
% 31.19/4.41 tuple(ifeq(ifeq3(addition(strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)), leq(strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.41 = { by axiom 2 (idempotence) }
% 31.19/4.41 tuple(ifeq(ifeq3(strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)), leq(strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.41 = { by axiom 6 (ifeq_axiom) }
% 31.19/4.41 tuple(ifeq(leq(strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.41 = { by lemma 13 R->L }
% 31.19/4.42 tuple(ifeq(leq(addition(one, multiplication(multiplication(star(sK2_goals_X0), sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.42 = { by lemma 12 R->L }
% 31.19/4.42 tuple(ifeq(leq(addition(one, multiplication(multiplication(addition(one, star(sK2_goals_X0)), sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.42 = { by lemma 14 R->L }
% 31.19/4.42 tuple(ifeq(leq(addition(one, multiplication(addition(multiplication(star(sK2_goals_X0), sK1_goals_X1), multiplication(one, sK1_goals_X1)), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.42 = { by axiom 1 (multiplicative_left_identity) }
% 31.19/4.42 tuple(ifeq(leq(addition(one, multiplication(addition(multiplication(star(sK2_goals_X0), sK1_goals_X1), sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.42 = { by axiom 3 (additive_commutativity) }
% 31.19/4.42 tuple(ifeq(leq(addition(one, multiplication(addition(sK1_goals_X1, multiplication(star(sK2_goals_X0), sK1_goals_X1)), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.42 = { by axiom 3 (additive_commutativity) R->L }
% 31.19/4.42 tuple(ifeq(leq(addition(multiplication(addition(sK1_goals_X1, multiplication(star(sK2_goals_X0), sK1_goals_X1)), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), one), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.42 = { by axiom 9 (distributivity2) }
% 31.19/4.42 tuple(ifeq(leq(addition(addition(multiplication(sK1_goals_X1, strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), multiplication(multiplication(star(sK2_goals_X0), sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1)))), one), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.42 = { by axiom 4 (additive_associativity) R->L }
% 31.19/4.42 tuple(ifeq(leq(addition(multiplication(sK1_goals_X1, strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), addition(multiplication(multiplication(star(sK2_goals_X0), sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), one)), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.42 = { by axiom 3 (additive_commutativity) }
% 31.19/4.42 tuple(ifeq(leq(addition(multiplication(sK1_goals_X1, strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), addition(one, multiplication(multiplication(star(sK2_goals_X0), sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.42 = { by lemma 13 }
% 31.19/4.42 tuple(ifeq(leq(addition(multiplication(sK1_goals_X1, strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true, leq(multiplication(star(sK1_goals_X1), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), strong_iteration(multiplication(star(sK2_goals_X0), sK1_goals_X1))), true), true)
% 31.19/4.42 = { by axiom 11 (star_induction1) }
% 31.19/4.42 tuple(true, true)
% 31.19/4.42 % SZS output end Proof
% 31.19/4.42
% 31.19/4.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------