TSTP Solution File: KLE084-10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE084-10 : 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 : n007.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 05:35:49 EDT 2023
% Result : Unsatisfiable 2.73s 0.73s
% Output : Proof 3.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE084-10 : TPTP v8.1.2. Released v7.5.0.
% 0.06/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 11:15:43 EDT 2023
% 0.13/0.33 % CPUTime :
% 2.73/0.73 Command-line arguments: --ground-connectedness --complete-subsets
% 2.73/0.73
% 2.73/0.73 % SZS status Unsatisfiable
% 2.73/0.73
% 2.73/0.75 % SZS output start Proof
% 2.73/0.75 Axiom 1 (domain4): domain(X) = antidomain(antidomain(X)).
% 2.73/0.75 Axiom 2 (additive_idempotence): addition(X, X) = X.
% 2.73/0.75 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 2.73/0.75 Axiom 4 (additive_identity): addition(X, zero) = X.
% 2.73/0.75 Axiom 5 (multiplicative_right_identity): multiplication(X, one) = X.
% 2.73/0.75 Axiom 6 (multiplicative_left_identity): multiplication(one, X) = X.
% 2.73/0.75 Axiom 7 (left_annihilation): multiplication(zero, X) = zero.
% 2.73/0.75 Axiom 8 (domain1): multiplication(antidomain(X), X) = zero.
% 2.73/0.75 Axiom 9 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 2.73/0.75 Axiom 10 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 2.73/0.75 Axiom 11 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 2.73/0.75 Axiom 12 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 2.73/0.75 Axiom 13 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 2.73/0.75 Axiom 14 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 2.73/0.75 Axiom 15 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 2.73/0.75 Axiom 16 (order): ifeq2(addition(X, Y), Y, leq(X, Y), true) = true.
% 2.73/0.75 Axiom 17 (order_1): ifeq(leq(X, Y), true, addition(X, Y), Y) = Y.
% 2.73/0.75 Axiom 18 (domain2): addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, antidomain(antidomain(Y))))) = antidomain(multiplication(X, antidomain(antidomain(Y)))).
% 2.73/0.75
% 2.73/0.75 Lemma 19: antidomain(one) = zero.
% 2.73/0.75 Proof:
% 2.73/0.75 antidomain(one)
% 2.73/0.75 = { by axiom 5 (multiplicative_right_identity) R->L }
% 2.73/0.75 multiplication(antidomain(one), one)
% 2.73/0.75 = { by axiom 8 (domain1) }
% 2.73/0.75 zero
% 2.73/0.75
% 2.73/0.75 Lemma 20: addition(domain(X), antidomain(X)) = one.
% 2.73/0.75 Proof:
% 2.73/0.75 addition(domain(X), antidomain(X))
% 2.73/0.75 = { by axiom 1 (domain4) }
% 2.73/0.75 addition(antidomain(antidomain(X)), antidomain(X))
% 2.73/0.75 = { by axiom 13 (domain3) }
% 2.73/0.75 one
% 2.73/0.75
% 2.73/0.75 Lemma 21: multiplication(antidomain(X), addition(X, Y)) = multiplication(antidomain(X), Y).
% 2.73/0.75 Proof:
% 2.73/0.75 multiplication(antidomain(X), addition(X, Y))
% 2.73/0.75 = { by axiom 3 (additive_commutativity) R->L }
% 2.73/0.75 multiplication(antidomain(X), addition(Y, X))
% 2.73/0.75 = { by axiom 14 (right_distributivity) }
% 2.73/0.75 addition(multiplication(antidomain(X), Y), multiplication(antidomain(X), X))
% 2.73/0.75 = { by axiom 8 (domain1) }
% 2.73/0.75 addition(multiplication(antidomain(X), Y), zero)
% 2.73/0.75 = { by axiom 4 (additive_identity) }
% 2.73/0.75 multiplication(antidomain(X), Y)
% 2.73/0.75
% 2.73/0.75 Lemma 22: multiplication(domain(X), X) = X.
% 2.73/0.75 Proof:
% 2.73/0.75 multiplication(domain(X), X)
% 2.73/0.75 = { by axiom 4 (additive_identity) R->L }
% 2.73/0.75 addition(multiplication(domain(X), X), zero)
% 2.73/0.75 = { by axiom 8 (domain1) R->L }
% 2.73/0.75 addition(multiplication(domain(X), X), multiplication(antidomain(X), X))
% 2.73/0.75 = { by axiom 15 (left_distributivity) R->L }
% 2.73/0.75 multiplication(addition(domain(X), antidomain(X)), X)
% 2.73/0.75 = { by lemma 20 }
% 2.73/0.75 multiplication(one, X)
% 2.73/0.75 = { by axiom 6 (multiplicative_left_identity) }
% 2.73/0.75 X
% 2.73/0.75
% 2.73/0.75 Lemma 23: antidomain(domain(X)) = antidomain(X).
% 2.73/0.75 Proof:
% 2.73/0.75 antidomain(domain(X))
% 2.73/0.75 = { by axiom 5 (multiplicative_right_identity) R->L }
% 2.73/0.75 multiplication(antidomain(domain(X)), one)
% 2.73/0.75 = { by lemma 20 R->L }
% 2.73/0.75 multiplication(antidomain(domain(X)), addition(domain(X), antidomain(X)))
% 2.73/0.75 = { by lemma 21 }
% 2.73/0.75 multiplication(antidomain(domain(X)), antidomain(X))
% 2.73/0.75 = { by axiom 1 (domain4) }
% 2.73/0.75 multiplication(antidomain(antidomain(antidomain(X))), antidomain(X))
% 2.73/0.75 = { by axiom 1 (domain4) R->L }
% 2.73/0.75 multiplication(domain(antidomain(X)), antidomain(X))
% 2.73/0.75 = { by lemma 22 }
% 2.73/0.75 antidomain(X)
% 2.73/0.75
% 2.73/0.75 Lemma 24: domain(domain(X)) = domain(X).
% 2.73/0.75 Proof:
% 2.73/0.75 domain(domain(X))
% 2.73/0.75 = { by axiom 1 (domain4) }
% 2.73/0.75 antidomain(antidomain(domain(X)))
% 2.73/0.75 = { by lemma 23 }
% 2.73/0.75 antidomain(antidomain(X))
% 2.73/0.75 = { by axiom 1 (domain4) R->L }
% 2.73/0.75 domain(X)
% 2.73/0.75
% 2.73/0.75 Lemma 25: addition(one, antidomain(X)) = one.
% 2.73/0.75 Proof:
% 2.73/0.75 addition(one, antidomain(X))
% 2.73/0.75 = { by axiom 3 (additive_commutativity) R->L }
% 2.73/0.75 addition(antidomain(X), one)
% 2.73/0.75 = { by axiom 10 (ifeq_axiom_001) R->L }
% 2.73/0.75 ifeq(true, true, addition(antidomain(X), one), one)
% 2.73/0.75 = { by axiom 16 (order) R->L }
% 2.73/0.75 ifeq(ifeq2(addition(antidomain(X), addition(antidomain(X), domain(X))), addition(antidomain(X), domain(X)), leq(antidomain(X), addition(antidomain(X), domain(X))), true), true, addition(antidomain(X), one), one)
% 2.73/0.76 = { by axiom 11 (additive_associativity) }
% 2.73/0.76 ifeq(ifeq2(addition(addition(antidomain(X), antidomain(X)), domain(X)), addition(antidomain(X), domain(X)), leq(antidomain(X), addition(antidomain(X), domain(X))), true), true, addition(antidomain(X), one), one)
% 2.73/0.76 = { by axiom 2 (additive_idempotence) }
% 2.73/0.76 ifeq(ifeq2(addition(antidomain(X), domain(X)), addition(antidomain(X), domain(X)), leq(antidomain(X), addition(antidomain(X), domain(X))), true), true, addition(antidomain(X), one), one)
% 2.73/0.76 = { by axiom 9 (ifeq_axiom) }
% 2.73/0.76 ifeq(leq(antidomain(X), addition(antidomain(X), domain(X))), true, addition(antidomain(X), one), one)
% 2.73/0.76 = { by axiom 3 (additive_commutativity) }
% 2.73/0.76 ifeq(leq(antidomain(X), addition(domain(X), antidomain(X))), true, addition(antidomain(X), one), one)
% 2.73/0.76 = { by lemma 20 }
% 2.73/0.76 ifeq(leq(antidomain(X), one), true, addition(antidomain(X), one), one)
% 2.73/0.76 = { by axiom 17 (order_1) }
% 2.73/0.76 one
% 2.73/0.76
% 2.73/0.76 Lemma 26: addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, domain(Y)))) = antidomain(multiplication(X, domain(Y))).
% 2.73/0.76 Proof:
% 2.73/0.76 addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, domain(Y))))
% 2.73/0.76 = { by axiom 1 (domain4) }
% 2.73/0.76 addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, antidomain(antidomain(Y)))))
% 2.73/0.76 = { by axiom 18 (domain2) }
% 2.73/0.76 antidomain(multiplication(X, antidomain(antidomain(Y))))
% 2.73/0.76 = { by axiom 1 (domain4) R->L }
% 2.73/0.76 antidomain(multiplication(X, domain(Y)))
% 2.73/0.76
% 2.73/0.76 Goal 1 (goals): domain(multiplication(sK2_goals_X0, sK1_goals_X1)) = domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))).
% 2.73/0.76 Proof:
% 2.73/0.76 domain(multiplication(sK2_goals_X0, sK1_goals_X1))
% 2.73/0.76 = { by axiom 6 (multiplicative_left_identity) R->L }
% 2.73/0.76 multiplication(one, domain(multiplication(sK2_goals_X0, sK1_goals_X1)))
% 2.73/0.76 = { by lemma 20 R->L }
% 2.73/0.76 multiplication(addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))
% 2.73/0.76 = { by axiom 15 (left_distributivity) }
% 2.73/0.76 addition(multiplication(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by lemma 24 R->L }
% 2.73/0.76 addition(multiplication(domain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by axiom 1 (domain4) }
% 2.73/0.76 addition(multiplication(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by lemma 21 R->L }
% 2.73/0.76 addition(multiplication(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), addition(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by axiom 3 (additive_commutativity) }
% 2.73/0.76 addition(multiplication(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), addition(domain(multiplication(sK2_goals_X0, sK1_goals_X1)), antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by lemma 23 }
% 2.73/0.76 addition(multiplication(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), addition(domain(multiplication(sK2_goals_X0, sK1_goals_X1)), antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by lemma 26 R->L }
% 2.73/0.76 addition(multiplication(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), addition(domain(multiplication(sK2_goals_X0, sK1_goals_X1)), addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by axiom 11 (additive_associativity) }
% 2.73/0.76 addition(multiplication(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), addition(addition(domain(multiplication(sK2_goals_X0, sK1_goals_X1)), antidomain(multiplication(sK2_goals_X0, sK1_goals_X1))), antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by lemma 20 }
% 2.73/0.76 addition(multiplication(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), addition(one, antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by axiom 3 (additive_commutativity) }
% 2.73/0.76 addition(multiplication(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), addition(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), one)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by lemma 23 R->L }
% 2.73/0.76 addition(multiplication(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), addition(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), one)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by axiom 3 (additive_commutativity) }
% 2.73/0.76 addition(multiplication(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), addition(one, antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by lemma 25 }
% 2.73/0.76 addition(multiplication(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), one), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by axiom 5 (multiplicative_right_identity) }
% 2.73/0.76 addition(antidomain(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by axiom 1 (domain4) R->L }
% 2.73/0.76 addition(domain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by lemma 24 }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by lemma 23 R->L }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))
% 2.73/0.76 = { by axiom 6 (multiplicative_left_identity) R->L }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(one, multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by lemma 25 R->L }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(one, antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by lemma 20 R->L }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(addition(domain(one), antidomain(one)), antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by lemma 19 }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(addition(domain(one), zero), antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by axiom 4 (additive_identity) }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(domain(one), antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by axiom 1 (domain4) }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(antidomain(antidomain(one)), antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by lemma 19 }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(antidomain(zero), antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by axiom 7 (left_annihilation) R->L }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(antidomain(multiplication(zero, sK1_goals_X1)), antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by axiom 8 (domain1) R->L }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(antidomain(multiplication(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(sK2_goals_X0, domain(sK1_goals_X1))), sK1_goals_X1)), antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by axiom 12 (multiplicative_associativity) R->L }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(antidomain(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(multiplication(sK2_goals_X0, domain(sK1_goals_X1)), sK1_goals_X1))), antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by axiom 12 (multiplicative_associativity) R->L }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(antidomain(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1)))), antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by lemma 22 }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(antidomain(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(sK2_goals_X0, sK1_goals_X1))), antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by lemma 23 R->L }
% 2.73/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(addition(antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), multiplication(sK2_goals_X0, sK1_goals_X1))), antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 2.73/0.76 = { by lemma 26 }
% 3.33/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(antidomain(multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))), multiplication(antidomain(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))
% 3.33/0.76 = { by axiom 8 (domain1) }
% 3.33/0.76 addition(domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), zero)
% 3.33/0.76 = { by axiom 4 (additive_identity) }
% 3.33/0.76 domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))
% 3.33/0.76 % SZS output end Proof
% 3.33/0.76
% 3.33/0.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------