TSTP Solution File: KLE148+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KLE148+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n015.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 05:36:04 EDT 2023
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% 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 : KLE148+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n015.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 12:52:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.42 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.42
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 Take the following subset of the input axioms:
% 0.19/0.42 fof(additive_commutativity, axiom, ![A, B]: addition(A, B)=addition(B, A)).
% 0.19/0.42 fof(additive_identity, axiom, ![A2]: addition(A2, zero)=A2).
% 0.19/0.42 fof(distributivity1, axiom, ![C, A2, B2]: multiplication(A2, addition(B2, C))=addition(multiplication(A2, B2), multiplication(A2, C))).
% 0.19/0.42 fof(goals, conjecture, ![X0, X1]: (multiplication(X0, X1)=zero => multiplication(X0, strong_iteration(X1))=X0)).
% 0.19/0.42 fof(infty_unfold1, axiom, ![A2]: strong_iteration(A2)=addition(multiplication(A2, strong_iteration(A2)), one)).
% 0.19/0.42 fof(left_annihilation, axiom, ![A2]: multiplication(zero, A2)=zero).
% 0.19/0.42 fof(multiplicative_associativity, axiom, ![A2, B2, C2]: multiplication(A2, multiplication(B2, C2))=multiplication(multiplication(A2, B2), C2)).
% 0.19/0.42 fof(multiplicative_right_identity, axiom, ![A2]: multiplication(A2, one)=A2).
% 0.19/0.42
% 0.19/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.42 fresh(y, y, x1...xn) = u
% 0.19/0.42 C => fresh(s, t, x1...xn) = v
% 0.19/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.42 variables of u and v.
% 0.19/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.42 input problem has no model of domain size 1).
% 0.19/0.42
% 0.19/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.42
% 0.19/0.42 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 0.19/0.42 Axiom 2 (left_annihilation): multiplication(zero, X) = zero.
% 0.19/0.42 Axiom 3 (goals): multiplication(x0, x1) = zero.
% 0.19/0.42 Axiom 4 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.19/0.42 Axiom 5 (additive_identity): addition(X, zero) = X.
% 0.19/0.42 Axiom 6 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 0.19/0.42 Axiom 7 (distributivity1): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 0.19/0.42 Axiom 8 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
% 0.19/0.42
% 0.19/0.42 Goal 1 (goals_1): multiplication(x0, strong_iteration(x1)) = x0.
% 0.19/0.42 Proof:
% 0.19/0.42 multiplication(x0, strong_iteration(x1))
% 0.19/0.42 = { by axiom 8 (infty_unfold1) }
% 0.19/0.42 multiplication(x0, addition(multiplication(x1, strong_iteration(x1)), one))
% 0.19/0.42 = { by axiom 4 (additive_commutativity) R->L }
% 0.19/0.42 multiplication(x0, addition(one, multiplication(x1, strong_iteration(x1))))
% 0.19/0.42 = { by axiom 7 (distributivity1) }
% 0.19/0.42 addition(multiplication(x0, one), multiplication(x0, multiplication(x1, strong_iteration(x1))))
% 0.19/0.42 = { by axiom 1 (multiplicative_right_identity) }
% 0.19/0.42 addition(x0, multiplication(x0, multiplication(x1, strong_iteration(x1))))
% 0.19/0.42 = { by axiom 6 (multiplicative_associativity) }
% 0.19/0.42 addition(x0, multiplication(multiplication(x0, x1), strong_iteration(x1)))
% 0.19/0.42 = { by axiom 3 (goals) }
% 0.19/0.42 addition(x0, multiplication(zero, strong_iteration(x1)))
% 0.19/0.42 = { by axiom 2 (left_annihilation) }
% 0.19/0.42 addition(x0, zero)
% 0.19/0.42 = { by axiom 5 (additive_identity) }
% 0.19/0.42 x0
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Theorem (the conjecture is true).
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