TSTP Solution File: KLE145-10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE145-10 : 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 : n002.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 05:36:02 EDT 2023
% Result : Unsatisfiable 14.50s 2.23s
% Output : Proof 14.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE145-10 : TPTP v8.1.2. Released v7.3.0.
% 0.12/0.13 % 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 : n002.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 11:53:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 14.50/2.23 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 14.50/2.23
% 14.50/2.23 % SZS status Unsatisfiable
% 14.50/2.23
% 14.50/2.24 % SZS output start Proof
% 14.50/2.24 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 14.50/2.25 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 14.50/2.25 Axiom 3 (idempotence): addition(X, X) = X.
% 14.50/2.25 Axiom 4 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 14.50/2.25 Axiom 5 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 14.50/2.25 Axiom 6 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 14.50/2.25 Axiom 7 (ifeq_axiom_002): ifeq(X, X, Y, Z) = Y.
% 14.50/2.25 Axiom 8 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 14.50/2.25 Axiom 9 (ifeq_axiom_001): ifeq2(X, X, Y, Z) = Y.
% 14.50/2.25 Axiom 10 (star_unfold1): addition(one, multiplication(X, star(X))) = star(X).
% 14.50/2.25 Axiom 11 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
% 14.50/2.25 Axiom 12 (distributivity1): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 14.50/2.25 Axiom 13 (distributivity2): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 14.50/2.25 Axiom 14 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 14.50/2.25 Axiom 15 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
% 14.50/2.25 Axiom 16 (infty_coinduction): ifeq(leq(X, addition(multiplication(Y, X), Z)), true, leq(X, multiplication(strong_iteration(Y), Z)), true) = true.
% 14.50/2.25 Axiom 17 (star_induction2): ifeq(leq(addition(multiplication(X, Y), Z), X), true, leq(multiplication(Z, star(Y)), X), true) = true.
% 14.50/2.25
% 14.50/2.25 Lemma 18: leq(X, X) = true.
% 14.50/2.25 Proof:
% 14.50/2.25 leq(X, X)
% 14.50/2.25 = { by axiom 8 (ifeq_axiom) R->L }
% 14.50/2.25 ifeq3(X, X, leq(X, X), true)
% 14.50/2.25 = { by axiom 3 (idempotence) R->L }
% 14.50/2.25 ifeq3(addition(X, X), X, leq(X, X), true)
% 14.50/2.25 = { by axiom 14 (order) }
% 14.50/2.25 true
% 14.50/2.25
% 14.50/2.25 Lemma 19: addition(X, multiplication(X, Y)) = multiplication(X, addition(Y, one)).
% 14.50/2.25 Proof:
% 14.50/2.25 addition(X, multiplication(X, Y))
% 14.50/2.25 = { by axiom 1 (multiplicative_right_identity) R->L }
% 14.50/2.25 addition(multiplication(X, one), multiplication(X, Y))
% 14.50/2.25 = { by axiom 12 (distributivity1) R->L }
% 14.50/2.25 multiplication(X, addition(one, Y))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) }
% 14.50/2.25 multiplication(X, addition(Y, one))
% 14.50/2.25
% 14.50/2.25 Lemma 20: addition(X, addition(X, Y)) = addition(X, Y).
% 14.50/2.25 Proof:
% 14.50/2.25 addition(X, addition(X, Y))
% 14.50/2.25 = { by axiom 6 (additive_associativity) }
% 14.50/2.25 addition(addition(X, X), Y)
% 14.50/2.25 = { by axiom 3 (idempotence) }
% 14.50/2.25 addition(X, Y)
% 14.50/2.25
% 14.50/2.25 Lemma 21: addition(one, star(X)) = star(X).
% 14.50/2.25 Proof:
% 14.50/2.25 addition(one, star(X))
% 14.50/2.25 = { by axiom 10 (star_unfold1) R->L }
% 14.50/2.25 addition(one, addition(one, multiplication(X, star(X))))
% 14.50/2.25 = { by lemma 20 }
% 14.50/2.25 addition(one, multiplication(X, star(X)))
% 14.50/2.25 = { by axiom 10 (star_unfold1) }
% 14.50/2.25 star(X)
% 14.50/2.25
% 14.50/2.25 Lemma 22: addition(X, star(X)) = star(X).
% 14.50/2.25 Proof:
% 14.50/2.25 addition(X, star(X))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) R->L }
% 14.50/2.25 addition(star(X), X)
% 14.50/2.25 = { by axiom 10 (star_unfold1) R->L }
% 14.50/2.25 addition(addition(one, multiplication(X, star(X))), X)
% 14.50/2.25 = { by axiom 6 (additive_associativity) R->L }
% 14.50/2.25 addition(one, addition(multiplication(X, star(X)), X))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) }
% 14.50/2.25 addition(one, addition(X, multiplication(X, star(X))))
% 14.50/2.25 = { by lemma 19 }
% 14.50/2.25 addition(one, multiplication(X, addition(star(X), one)))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) }
% 14.50/2.25 addition(one, multiplication(X, addition(one, star(X))))
% 14.50/2.25 = { by lemma 21 }
% 14.50/2.25 addition(one, multiplication(X, star(X)))
% 14.50/2.25 = { by axiom 10 (star_unfold1) }
% 14.50/2.25 star(X)
% 14.50/2.25
% 14.50/2.25 Lemma 23: addition(one, multiplication(X, strong_iteration(X))) = strong_iteration(X).
% 14.50/2.25 Proof:
% 14.50/2.25 addition(one, multiplication(X, strong_iteration(X)))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) R->L }
% 14.50/2.25 addition(multiplication(X, strong_iteration(X)), one)
% 14.50/2.25 = { by axiom 11 (infty_unfold1) R->L }
% 14.50/2.25 strong_iteration(X)
% 14.50/2.25
% 14.50/2.25 Lemma 24: addition(one, strong_iteration(X)) = strong_iteration(X).
% 14.50/2.25 Proof:
% 14.50/2.25 addition(one, strong_iteration(X))
% 14.50/2.25 = { by lemma 23 R->L }
% 14.50/2.25 addition(one, addition(one, multiplication(X, strong_iteration(X))))
% 14.50/2.25 = { by lemma 20 }
% 14.50/2.25 addition(one, multiplication(X, strong_iteration(X)))
% 14.50/2.25 = { by lemma 23 }
% 14.50/2.25 strong_iteration(X)
% 14.50/2.25
% 14.50/2.25 Lemma 25: multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))) = star(multiplication(X, strong_iteration(X))).
% 14.50/2.25 Proof:
% 14.50/2.25 multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X))))
% 14.50/2.25 = { by lemma 23 R->L }
% 14.50/2.25 multiplication(addition(one, multiplication(X, strong_iteration(X))), star(multiplication(X, strong_iteration(X))))
% 14.50/2.25 = { by axiom 13 (distributivity2) }
% 14.50/2.25 addition(multiplication(one, star(multiplication(X, strong_iteration(X)))), multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))))
% 14.50/2.25 = { by axiom 2 (multiplicative_left_identity) }
% 14.50/2.25 addition(star(multiplication(X, strong_iteration(X))), multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) R->L }
% 14.50/2.25 addition(multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))), star(multiplication(X, strong_iteration(X))))
% 14.50/2.25 = { by axiom 10 (star_unfold1) R->L }
% 14.50/2.25 addition(multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))), addition(one, multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X))))))
% 14.50/2.25 = { by lemma 20 R->L }
% 14.50/2.25 addition(multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))), addition(one, addition(one, multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))))))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) R->L }
% 14.50/2.25 addition(multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))), addition(one, addition(multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))), one)))
% 14.50/2.25 = { by axiom 6 (additive_associativity) }
% 14.50/2.25 addition(addition(multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))), one), addition(multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))), one))
% 14.50/2.25 = { by axiom 3 (idempotence) }
% 14.50/2.25 addition(multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))), one)
% 14.50/2.25 = { by axiom 4 (additive_commutativity) }
% 14.50/2.25 addition(one, multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))))
% 14.50/2.25 = { by axiom 10 (star_unfold1) }
% 14.50/2.25 star(multiplication(X, strong_iteration(X)))
% 14.50/2.25
% 14.50/2.25 Lemma 26: star(multiplication(X, strong_iteration(X))) = strong_iteration(X).
% 14.50/2.25 Proof:
% 14.50/2.25 star(multiplication(X, strong_iteration(X)))
% 14.50/2.25 = { by lemma 21 R->L }
% 14.50/2.25 addition(one, star(multiplication(X, strong_iteration(X))))
% 14.50/2.25 = { by lemma 22 R->L }
% 14.50/2.25 addition(one, addition(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))))
% 14.50/2.25 = { by axiom 6 (additive_associativity) }
% 14.50/2.25 addition(addition(one, multiplication(X, strong_iteration(X))), star(multiplication(X, strong_iteration(X))))
% 14.50/2.25 = { by lemma 23 }
% 14.50/2.25 addition(strong_iteration(X), star(multiplication(X, strong_iteration(X))))
% 14.50/2.25 = { by axiom 9 (ifeq_axiom_001) R->L }
% 14.50/2.25 ifeq2(true, true, addition(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X))
% 14.50/2.25 = { by axiom 16 (infty_coinduction) R->L }
% 14.50/2.25 ifeq2(ifeq(leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), addition(multiplication(X, multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X))))), one)), true, leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), multiplication(strong_iteration(X), one)), true), true, addition(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) }
% 14.50/2.25 ifeq2(ifeq(leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), addition(one, multiplication(X, multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X))))))), true, leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), multiplication(strong_iteration(X), one)), true), true, addition(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X))
% 14.50/2.25 = { by axiom 5 (multiplicative_associativity) }
% 14.50/2.25 ifeq2(ifeq(leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), addition(one, multiplication(multiplication(X, strong_iteration(X)), star(multiplication(X, strong_iteration(X)))))), true, leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), multiplication(strong_iteration(X), one)), true), true, addition(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X))
% 14.50/2.25 = { by axiom 10 (star_unfold1) }
% 14.50/2.25 ifeq2(ifeq(leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), star(multiplication(X, strong_iteration(X)))), true, leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), multiplication(strong_iteration(X), one)), true), true, addition(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X))
% 14.50/2.25 = { by axiom 1 (multiplicative_right_identity) }
% 14.50/2.25 ifeq2(ifeq(leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), star(multiplication(X, strong_iteration(X)))), true, leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X)), true), true, addition(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X))
% 14.50/2.25 = { by lemma 25 }
% 14.50/2.25 ifeq2(ifeq(leq(star(multiplication(X, strong_iteration(X))), star(multiplication(X, strong_iteration(X)))), true, leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X)), true), true, addition(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X))
% 14.50/2.25 = { by lemma 18 }
% 14.50/2.25 ifeq2(ifeq(true, true, leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X)), true), true, addition(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X))
% 14.50/2.25 = { by axiom 7 (ifeq_axiom_002) }
% 14.50/2.25 ifeq2(leq(multiplication(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X)), true, addition(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X))
% 14.50/2.25 = { by lemma 25 }
% 14.50/2.25 ifeq2(leq(star(multiplication(X, strong_iteration(X))), strong_iteration(X)), true, addition(strong_iteration(X), star(multiplication(X, strong_iteration(X)))), strong_iteration(X))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) R->L }
% 14.50/2.25 ifeq2(leq(star(multiplication(X, strong_iteration(X))), strong_iteration(X)), true, addition(star(multiplication(X, strong_iteration(X))), strong_iteration(X)), strong_iteration(X))
% 14.50/2.25 = { by axiom 15 (order_1) }
% 14.50/2.25 strong_iteration(X)
% 14.50/2.25
% 14.50/2.25 Goal 1 (goals): star(strong_iteration(sK1_goals_X0)) = strong_iteration(sK1_goals_X0).
% 14.50/2.25 Proof:
% 14.50/2.25 star(strong_iteration(sK1_goals_X0))
% 14.50/2.25 = { by lemma 22 R->L }
% 14.50/2.25 addition(strong_iteration(sK1_goals_X0), star(strong_iteration(sK1_goals_X0)))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) }
% 14.50/2.25 addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.25 = { by axiom 9 (ifeq_axiom_001) R->L }
% 14.50/2.25 ifeq2(true, true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.25 = { by axiom 17 (star_induction2) R->L }
% 14.50/2.25 ifeq2(ifeq(leq(addition(multiplication(strong_iteration(sK1_goals_X0), strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true, leq(multiplication(one, star(strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.25 = { by axiom 2 (multiplicative_left_identity) }
% 14.50/2.25 ifeq2(ifeq(leq(addition(multiplication(strong_iteration(sK1_goals_X0), strong_iteration(sK1_goals_X0)), one), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) }
% 14.50/2.25 ifeq2(ifeq(leq(addition(one, multiplication(strong_iteration(sK1_goals_X0), strong_iteration(sK1_goals_X0))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.25 = { by lemma 24 R->L }
% 14.50/2.25 ifeq2(ifeq(leq(addition(one, multiplication(strong_iteration(sK1_goals_X0), addition(one, strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.25 = { by axiom 4 (additive_commutativity) R->L }
% 14.50/2.25 ifeq2(ifeq(leq(addition(one, multiplication(strong_iteration(sK1_goals_X0), addition(strong_iteration(sK1_goals_X0), one))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.25 = { by lemma 26 R->L }
% 14.50/2.25 ifeq2(ifeq(leq(addition(one, multiplication(strong_iteration(sK1_goals_X0), addition(star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), one))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.25 = { by axiom 9 (ifeq_axiom_001) R->L }
% 14.50/2.25 ifeq2(ifeq(leq(addition(one, ifeq2(true, true, multiplication(strong_iteration(sK1_goals_X0), addition(star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), one)), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.25 = { by axiom 14 (order) R->L }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, ifeq2(ifeq3(addition(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), addition(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), addition(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))), leq(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), addition(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), true), true, multiplication(strong_iteration(sK1_goals_X0), addition(star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), one)), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by lemma 20 }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, ifeq2(ifeq3(addition(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))), addition(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))), leq(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), addition(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), true), true, multiplication(strong_iteration(sK1_goals_X0), addition(star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), one)), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by axiom 8 (ifeq_axiom) }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, ifeq2(leq(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), addition(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), true, multiplication(strong_iteration(sK1_goals_X0), addition(star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), one)), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by axiom 6 (additive_associativity) R->L }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, ifeq2(leq(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), addition(one, addition(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), true, multiplication(strong_iteration(sK1_goals_X0), addition(star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), one)), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by lemma 22 }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, ifeq2(leq(addition(one, multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), addition(one, star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), true, multiplication(strong_iteration(sK1_goals_X0), addition(star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), one)), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by lemma 23 }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, ifeq2(leq(strong_iteration(sK1_goals_X0), addition(one, star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), true, multiplication(strong_iteration(sK1_goals_X0), addition(star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), one)), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by lemma 21 }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, ifeq2(leq(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))), true, multiplication(strong_iteration(sK1_goals_X0), addition(star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), one)), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by lemma 25 R->L }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, ifeq2(leq(strong_iteration(sK1_goals_X0), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), true, multiplication(strong_iteration(sK1_goals_X0), addition(star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))), one)), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by lemma 19 R->L }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, ifeq2(leq(strong_iteration(sK1_goals_X0), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), true, addition(strong_iteration(sK1_goals_X0), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by axiom 15 (order_1) }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, multiplication(strong_iteration(sK1_goals_X0), star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0))))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by lemma 25 }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, star(multiplication(sK1_goals_X0, strong_iteration(sK1_goals_X0)))), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by lemma 26 }
% 14.50/2.26 ifeq2(ifeq(leq(addition(one, strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by lemma 24 }
% 14.50/2.26 ifeq2(ifeq(leq(strong_iteration(sK1_goals_X0), strong_iteration(sK1_goals_X0)), true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by lemma 18 }
% 14.50/2.26 ifeq2(ifeq(true, true, leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by axiom 7 (ifeq_axiom_002) }
% 14.50/2.26 ifeq2(leq(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), true, addition(star(strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0)), strong_iteration(sK1_goals_X0))
% 14.50/2.26 = { by axiom 15 (order_1) }
% 14.50/2.26 strong_iteration(sK1_goals_X0)
% 14.50/2.26 % SZS output end Proof
% 14.50/2.26
% 14.50/2.26 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------