TSTP Solution File: KLE044-10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE044-10 : 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 : 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 05:35:39 EDT 2023
% Result : Unsatisfiable 26.18s 3.79s
% Output : Proof 26.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : KLE044-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37 % Computer : n026.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Tue Aug 29 12:19:50 EDT 2023
% 0.15/0.37 % CPUTime :
% 26.18/3.79 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 26.18/3.79
% 26.18/3.79 % SZS status Unsatisfiable
% 26.18/3.79
% 26.18/3.81 % SZS output start Proof
% 26.18/3.81 Axiom 1 (additive_idempotence): addition(X, X) = X.
% 26.18/3.81 Axiom 2 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 26.18/3.81 Axiom 3 (multiplicative_right_identity): multiplication(X, one) = X.
% 26.18/3.81 Axiom 4 (multiplicative_left_identity): multiplication(one, X) = X.
% 26.18/3.81 Axiom 5 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 26.18/3.81 Axiom 6 (ifeq_axiom_002): ifeq(X, X, Y, Z) = Y.
% 26.18/3.81 Axiom 7 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 26.18/3.81 Axiom 8 (ifeq_axiom_001): ifeq2(X, X, Y, Z) = Y.
% 26.18/3.81 Axiom 9 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 26.18/3.81 Axiom 10 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 26.18/3.81 Axiom 11 (star_unfold_right): leq(addition(one, multiplication(X, star(X))), star(X)) = true.
% 26.18/3.81 Axiom 12 (star_unfold_left): leq(addition(one, multiplication(star(X), X)), star(X)) = true.
% 26.18/3.81 Axiom 13 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 26.18/3.81 Axiom 14 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
% 26.18/3.81 Axiom 15 (star_induction_right): ifeq(leq(addition(multiplication(X, Y), Z), X), true, leq(multiplication(Z, star(Y)), X), true) = true.
% 26.18/3.81 Axiom 16 (star_induction_left): ifeq(leq(addition(multiplication(X, Y), Z), Y), true, leq(multiplication(star(X), Z), Y), true) = true.
% 26.18/3.81
% 26.18/3.81 Lemma 17: leq(X, X) = true.
% 26.18/3.81 Proof:
% 26.18/3.81 leq(X, X)
% 26.18/3.81 = { by axiom 7 (ifeq_axiom) R->L }
% 26.18/3.81 ifeq3(X, X, leq(X, X), true)
% 26.18/3.81 = { by axiom 1 (additive_idempotence) R->L }
% 26.18/3.81 ifeq3(addition(X, X), X, leq(X, X), true)
% 26.18/3.81 = { by axiom 13 (order) }
% 26.18/3.81 true
% 26.18/3.81
% 26.18/3.81 Lemma 18: addition(X, addition(X, Y)) = addition(X, Y).
% 26.18/3.81 Proof:
% 26.18/3.81 addition(X, addition(X, Y))
% 26.18/3.81 = { by axiom 5 (additive_associativity) }
% 26.18/3.81 addition(addition(X, X), Y)
% 26.18/3.81 = { by axiom 1 (additive_idempotence) }
% 26.18/3.81 addition(X, Y)
% 26.18/3.81
% 26.18/3.81 Lemma 19: addition(X, addition(Y, X)) = addition(Y, X).
% 26.18/3.81 Proof:
% 26.18/3.81 addition(X, addition(Y, X))
% 26.18/3.81 = { by lemma 18 R->L }
% 26.18/3.81 addition(X, addition(Y, addition(Y, X)))
% 26.18/3.81 = { by axiom 2 (additive_commutativity) R->L }
% 26.18/3.81 addition(X, addition(Y, addition(X, Y)))
% 26.18/3.81 = { by axiom 5 (additive_associativity) }
% 26.18/3.81 addition(addition(X, Y), addition(X, Y))
% 26.18/3.81 = { by axiom 1 (additive_idempotence) }
% 26.18/3.81 addition(X, Y)
% 26.18/3.81 = { by axiom 2 (additive_commutativity) }
% 26.18/3.81 addition(Y, X)
% 26.18/3.81
% 26.18/3.81 Lemma 20: multiplication(X, addition(Y, one)) = addition(X, multiplication(X, Y)).
% 26.18/3.81 Proof:
% 26.18/3.81 multiplication(X, addition(Y, one))
% 26.18/3.81 = { by axiom 2 (additive_commutativity) R->L }
% 26.18/3.81 multiplication(X, addition(one, Y))
% 26.18/3.81 = { by axiom 9 (right_distributivity) }
% 26.18/3.81 addition(multiplication(X, one), multiplication(X, Y))
% 26.18/3.81 = { by axiom 3 (multiplicative_right_identity) }
% 26.18/3.81 addition(X, multiplication(X, Y))
% 26.18/3.81
% 26.18/3.81 Lemma 21: multiplication(addition(one, Y), X) = addition(X, multiplication(Y, X)).
% 26.18/3.81 Proof:
% 26.18/3.81 multiplication(addition(one, Y), X)
% 26.18/3.81 = { by axiom 10 (left_distributivity) }
% 26.18/3.81 addition(multiplication(one, X), multiplication(Y, X))
% 26.18/3.81 = { by axiom 4 (multiplicative_left_identity) }
% 26.18/3.81 addition(X, multiplication(Y, X))
% 26.18/3.81
% 26.18/3.81 Lemma 22: addition(one, addition(star(X), multiplication(X, star(X)))) = star(X).
% 26.18/3.81 Proof:
% 26.18/3.81 addition(one, addition(star(X), multiplication(X, star(X))))
% 26.18/3.81 = { by axiom 2 (additive_commutativity) R->L }
% 26.18/3.81 addition(one, addition(multiplication(X, star(X)), star(X)))
% 26.18/3.81 = { by axiom 5 (additive_associativity) }
% 26.18/3.81 addition(addition(one, multiplication(X, star(X))), star(X))
% 26.18/3.81 = { by axiom 8 (ifeq_axiom_001) R->L }
% 26.18/3.81 ifeq2(true, true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
% 26.18/3.81 = { by axiom 11 (star_unfold_right) R->L }
% 26.18/3.81 ifeq2(leq(addition(one, multiplication(X, star(X))), star(X)), true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
% 26.18/3.81 = { by axiom 14 (order_1) }
% 26.18/3.81 star(X)
% 26.18/3.81
% 26.18/3.81 Lemma 23: addition(star(X), multiplication(X, star(X))) = star(X).
% 26.18/3.81 Proof:
% 26.18/3.81 addition(star(X), multiplication(X, star(X)))
% 26.18/3.81 = { by axiom 2 (additive_commutativity) R->L }
% 26.18/3.81 addition(multiplication(X, star(X)), star(X))
% 26.18/3.81 = { by lemma 19 R->L }
% 26.18/3.81 addition(star(X), addition(multiplication(X, star(X)), star(X)))
% 26.18/3.81 = { by axiom 5 (additive_associativity) }
% 26.18/3.81 addition(addition(star(X), multiplication(X, star(X))), star(X))
% 26.18/3.81 = { by lemma 22 R->L }
% 26.18/3.81 addition(addition(star(X), multiplication(X, star(X))), addition(one, addition(star(X), multiplication(X, star(X)))))
% 26.18/3.81 = { by lemma 19 }
% 26.18/3.81 addition(one, addition(star(X), multiplication(X, star(X))))
% 26.18/3.81 = { by lemma 22 }
% 26.18/3.81 star(X)
% 26.18/3.81
% 26.18/3.81 Lemma 24: multiplication(addition(one, X), star(X)) = star(X).
% 26.18/3.81 Proof:
% 26.18/3.81 multiplication(addition(one, X), star(X))
% 26.18/3.81 = { by lemma 21 }
% 26.18/3.81 addition(star(X), multiplication(X, star(X)))
% 26.18/3.81 = { by lemma 23 }
% 26.18/3.81 star(X)
% 26.18/3.81
% 26.18/3.81 Lemma 25: addition(one, addition(star(X), multiplication(star(X), X))) = star(X).
% 26.18/3.81 Proof:
% 26.18/3.81 addition(one, addition(star(X), multiplication(star(X), X)))
% 26.18/3.81 = { by axiom 2 (additive_commutativity) R->L }
% 26.18/3.81 addition(one, addition(multiplication(star(X), X), star(X)))
% 26.18/3.81 = { by axiom 5 (additive_associativity) }
% 26.18/3.81 addition(addition(one, multiplication(star(X), X)), star(X))
% 26.18/3.81 = { by axiom 8 (ifeq_axiom_001) R->L }
% 26.18/3.81 ifeq2(true, true, addition(addition(one, multiplication(star(X), X)), star(X)), star(X))
% 26.18/3.81 = { by axiom 12 (star_unfold_left) R->L }
% 26.18/3.81 ifeq2(leq(addition(one, multiplication(star(X), X)), star(X)), true, addition(addition(one, multiplication(star(X), X)), star(X)), star(X))
% 26.18/3.81 = { by axiom 14 (order_1) }
% 26.18/3.81 star(X)
% 26.18/3.81
% 26.18/3.81 Goal 1 (goals): tuple(leq(star(addition(one, sK2_goals_X0)), star(sK2_goals_X0)), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0)))) = tuple(true, true).
% 26.18/3.81 Proof:
% 26.18/3.81 tuple(leq(star(addition(one, sK2_goals_X0)), star(sK2_goals_X0)), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 2 (additive_commutativity) R->L }
% 26.18/3.81 tuple(leq(star(addition(sK2_goals_X0, one)), star(sK2_goals_X0)), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 6 (ifeq_axiom_002) R->L }
% 26.18/3.81 tuple(ifeq(true, true, leq(star(addition(sK2_goals_X0, one)), star(sK2_goals_X0)), true), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by lemma 17 R->L }
% 26.18/3.81 tuple(ifeq(leq(star(sK2_goals_X0), star(sK2_goals_X0)), true, leq(star(addition(sK2_goals_X0, one)), star(sK2_goals_X0)), true), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 14 (order_1) R->L }
% 26.18/3.81 tuple(ifeq(leq(ifeq2(leq(addition(one, multiplication(star(sK2_goals_X0), sK2_goals_X0)), star(sK2_goals_X0)), true, addition(addition(one, multiplication(star(sK2_goals_X0), sK2_goals_X0)), star(sK2_goals_X0)), star(sK2_goals_X0)), star(sK2_goals_X0)), true, leq(star(addition(sK2_goals_X0, one)), star(sK2_goals_X0)), true), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 12 (star_unfold_left) }
% 26.18/3.81 tuple(ifeq(leq(ifeq2(true, true, addition(addition(one, multiplication(star(sK2_goals_X0), sK2_goals_X0)), star(sK2_goals_X0)), star(sK2_goals_X0)), star(sK2_goals_X0)), true, leq(star(addition(sK2_goals_X0, one)), star(sK2_goals_X0)), true), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 8 (ifeq_axiom_001) }
% 26.18/3.81 tuple(ifeq(leq(addition(addition(one, multiplication(star(sK2_goals_X0), sK2_goals_X0)), star(sK2_goals_X0)), star(sK2_goals_X0)), true, leq(star(addition(sK2_goals_X0, one)), star(sK2_goals_X0)), true), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 5 (additive_associativity) R->L }
% 26.18/3.81 tuple(ifeq(leq(addition(one, addition(multiplication(star(sK2_goals_X0), sK2_goals_X0), star(sK2_goals_X0))), star(sK2_goals_X0)), true, leq(star(addition(sK2_goals_X0, one)), star(sK2_goals_X0)), true), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 2 (additive_commutativity) }
% 26.18/3.81 tuple(ifeq(leq(addition(one, addition(star(sK2_goals_X0), multiplication(star(sK2_goals_X0), sK2_goals_X0))), star(sK2_goals_X0)), true, leq(star(addition(sK2_goals_X0, one)), star(sK2_goals_X0)), true), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by lemma 20 R->L }
% 26.18/3.81 tuple(ifeq(leq(addition(one, multiplication(star(sK2_goals_X0), addition(sK2_goals_X0, one))), star(sK2_goals_X0)), true, leq(star(addition(sK2_goals_X0, one)), star(sK2_goals_X0)), true), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 2 (additive_commutativity) R->L }
% 26.18/3.81 tuple(ifeq(leq(addition(multiplication(star(sK2_goals_X0), addition(sK2_goals_X0, one)), one), star(sK2_goals_X0)), true, leq(star(addition(sK2_goals_X0, one)), star(sK2_goals_X0)), true), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 4 (multiplicative_left_identity) R->L }
% 26.18/3.81 tuple(ifeq(leq(addition(multiplication(star(sK2_goals_X0), addition(sK2_goals_X0, one)), one), star(sK2_goals_X0)), true, leq(multiplication(one, star(addition(sK2_goals_X0, one))), star(sK2_goals_X0)), true), leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 15 (star_induction_right) }
% 26.18/3.81 tuple(true, leq(star(sK1_goals_X0), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 14 (order_1) R->L }
% 26.18/3.81 tuple(true, leq(ifeq2(leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(sK1_goals_X0)), true, addition(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))))
% 26.18/3.81 = { by axiom 2 (additive_commutativity) }
% 26.18/3.82 tuple(true, leq(ifeq2(leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(sK1_goals_X0)), true, addition(star(sK1_goals_X0), multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0))), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))))
% 26.18/3.82 = { by lemma 24 R->L }
% 26.18/3.82 tuple(true, leq(ifeq2(leq(multiplication(star(addition(one, sK1_goals_X0)), multiplication(addition(one, sK1_goals_X0), star(sK1_goals_X0))), star(sK1_goals_X0)), true, addition(star(sK1_goals_X0), multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0))), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))))
% 26.18/3.82 = { by axiom 6 (ifeq_axiom_002) R->L }
% 26.18/3.82 tuple(true, leq(ifeq2(ifeq(true, true, leq(multiplication(star(addition(one, sK1_goals_X0)), multiplication(addition(one, sK1_goals_X0), star(sK1_goals_X0))), star(sK1_goals_X0)), true), true, addition(star(sK1_goals_X0), multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0))), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))))
% 26.18/3.82 = { by lemma 17 R->L }
% 26.18/3.82 tuple(true, leq(ifeq2(ifeq(leq(star(sK1_goals_X0), star(sK1_goals_X0)), true, leq(multiplication(star(addition(one, sK1_goals_X0)), multiplication(addition(one, sK1_goals_X0), star(sK1_goals_X0))), star(sK1_goals_X0)), true), true, addition(star(sK1_goals_X0), multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0))), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))))
% 26.18/3.82 = { by lemma 24 R->L }
% 26.18/3.82 tuple(true, leq(ifeq2(ifeq(leq(multiplication(addition(one, sK1_goals_X0), star(sK1_goals_X0)), star(sK1_goals_X0)), true, leq(multiplication(star(addition(one, sK1_goals_X0)), multiplication(addition(one, sK1_goals_X0), star(sK1_goals_X0))), star(sK1_goals_X0)), true), true, addition(star(sK1_goals_X0), multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0))), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))))
% 26.18/3.82 = { by axiom 1 (additive_idempotence) R->L }
% 26.18/3.82 tuple(true, leq(ifeq2(ifeq(leq(addition(multiplication(addition(one, sK1_goals_X0), star(sK1_goals_X0)), multiplication(addition(one, sK1_goals_X0), star(sK1_goals_X0))), star(sK1_goals_X0)), true, leq(multiplication(star(addition(one, sK1_goals_X0)), multiplication(addition(one, sK1_goals_X0), star(sK1_goals_X0))), star(sK1_goals_X0)), true), true, addition(star(sK1_goals_X0), multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0))), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))))
% 26.18/3.82 = { by axiom 16 (star_induction_left) }
% 26.18/3.82 tuple(true, leq(ifeq2(true, true, addition(star(sK1_goals_X0), multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0))), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))))
% 26.18/3.82 = { by axiom 8 (ifeq_axiom_001) }
% 26.18/3.82 tuple(true, leq(addition(star(sK1_goals_X0), multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0))), star(addition(one, sK1_goals_X0))))
% 26.18/3.82 = { by lemma 23 R->L }
% 26.18/3.82 tuple(true, leq(addition(star(sK1_goals_X0), multiplication(addition(star(addition(one, sK1_goals_X0)), multiplication(addition(one, sK1_goals_X0), star(addition(one, sK1_goals_X0)))), star(sK1_goals_X0))), star(addition(one, sK1_goals_X0))))
% 26.18/3.82 = { by lemma 21 R->L }
% 26.18/3.82 tuple(true, leq(multiplication(addition(one, addition(star(addition(one, sK1_goals_X0)), multiplication(addition(one, sK1_goals_X0), star(addition(one, sK1_goals_X0))))), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))))
% 26.18/3.82 = { by lemma 22 }
% 26.18/3.82 tuple(true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))))
% 26.18/3.82 = { by axiom 6 (ifeq_axiom_002) R->L }
% 26.18/3.82 tuple(true, ifeq(true, true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by lemma 17 R->L }
% 26.18/3.82 tuple(true, ifeq(leq(star(addition(one, sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by lemma 25 R->L }
% 26.18/3.82 tuple(true, ifeq(leq(addition(one, addition(star(addition(one, sK1_goals_X0)), multiplication(star(addition(one, sK1_goals_X0)), addition(one, sK1_goals_X0)))), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by lemma 19 R->L }
% 26.18/3.82 tuple(true, ifeq(leq(addition(addition(star(addition(one, sK1_goals_X0)), multiplication(star(addition(one, sK1_goals_X0)), addition(one, sK1_goals_X0))), addition(one, addition(star(addition(one, sK1_goals_X0)), multiplication(star(addition(one, sK1_goals_X0)), addition(one, sK1_goals_X0))))), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by lemma 25 }
% 26.18/3.82 tuple(true, ifeq(leq(addition(addition(star(addition(one, sK1_goals_X0)), multiplication(star(addition(one, sK1_goals_X0)), addition(one, sK1_goals_X0))), star(addition(one, sK1_goals_X0))), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by axiom 5 (additive_associativity) R->L }
% 26.18/3.82 tuple(true, ifeq(leq(addition(star(addition(one, sK1_goals_X0)), addition(multiplication(star(addition(one, sK1_goals_X0)), addition(one, sK1_goals_X0)), star(addition(one, sK1_goals_X0)))), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by lemma 19 }
% 26.18/3.82 tuple(true, ifeq(leq(addition(multiplication(star(addition(one, sK1_goals_X0)), addition(one, sK1_goals_X0)), star(addition(one, sK1_goals_X0))), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by axiom 2 (additive_commutativity) }
% 26.18/3.82 tuple(true, ifeq(leq(addition(star(addition(one, sK1_goals_X0)), multiplication(star(addition(one, sK1_goals_X0)), addition(one, sK1_goals_X0))), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by lemma 20 R->L }
% 26.18/3.82 tuple(true, ifeq(leq(multiplication(star(addition(one, sK1_goals_X0)), addition(addition(one, sK1_goals_X0), one)), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by axiom 2 (additive_commutativity) }
% 26.18/3.82 tuple(true, ifeq(leq(multiplication(star(addition(one, sK1_goals_X0)), addition(one, addition(one, sK1_goals_X0))), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by lemma 18 }
% 26.18/3.82 tuple(true, ifeq(leq(multiplication(star(addition(one, sK1_goals_X0)), addition(one, sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by axiom 2 (additive_commutativity) R->L }
% 26.18/3.82 tuple(true, ifeq(leq(multiplication(star(addition(one, sK1_goals_X0)), addition(sK1_goals_X0, one)), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by lemma 20 }
% 26.18/3.82 tuple(true, ifeq(leq(addition(star(addition(one, sK1_goals_X0)), multiplication(star(addition(one, sK1_goals_X0)), sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by axiom 2 (additive_commutativity) R->L }
% 26.18/3.82 tuple(true, ifeq(leq(addition(multiplication(star(addition(one, sK1_goals_X0)), sK1_goals_X0), star(addition(one, sK1_goals_X0))), star(addition(one, sK1_goals_X0))), true, leq(multiplication(star(addition(one, sK1_goals_X0)), star(sK1_goals_X0)), star(addition(one, sK1_goals_X0))), true))
% 26.18/3.82 = { by axiom 15 (star_induction_right) }
% 26.18/3.82 tuple(true, true)
% 26.18/3.82 % SZS output end Proof
% 26.18/3.82
% 26.18/3.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------