TSTP Solution File: KLE089+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KLE089+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 : n028.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 05:35:50 EDT 2023
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE089+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 11:41:11 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.38 Command-line arguments: --no-flatten-goal
% 0.18/0.38
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 Take the following subset of the input axioms:
% 0.18/0.38 fof(additive_identity, axiom, ![A]: addition(A, zero)=A).
% 0.18/0.38 fof(domain1, axiom, ![X0]: multiplication(antidomain(X0), X0)=zero).
% 0.18/0.38 fof(goals, conjecture, ![X1, X0_2]: (multiplication(domain(X0_2), X1)=zero <= addition(domain(X0_2), antidomain(X1))=antidomain(X1))).
% 0.18/0.38 fof(left_distributivity, axiom, ![B, C, A2]: multiplication(addition(A2, B), C)=addition(multiplication(A2, C), multiplication(B, C))).
% 0.18/0.38
% 0.18/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.38 fresh(y, y, x1...xn) = u
% 0.18/0.38 C => fresh(s, t, x1...xn) = v
% 0.18/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.38 variables of u and v.
% 0.18/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.38 input problem has no model of domain size 1).
% 0.18/0.38
% 0.18/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.39
% 0.18/0.39 Axiom 1 (additive_identity): addition(X, zero) = X.
% 0.18/0.39 Axiom 2 (domain1): multiplication(antidomain(X), X) = zero.
% 0.18/0.39 Axiom 3 (goals): addition(domain(x0), antidomain(x1)) = antidomain(x1).
% 0.18/0.39 Axiom 4 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.18/0.39
% 0.18/0.39 Goal 1 (goals_1): multiplication(domain(x0), x1) = zero.
% 0.18/0.39 Proof:
% 0.18/0.39 multiplication(domain(x0), x1)
% 0.18/0.39 = { by axiom 1 (additive_identity) R->L }
% 0.18/0.39 addition(multiplication(domain(x0), x1), zero)
% 0.18/0.39 = { by axiom 2 (domain1) R->L }
% 0.18/0.39 addition(multiplication(domain(x0), x1), multiplication(antidomain(x1), x1))
% 0.18/0.39 = { by axiom 4 (left_distributivity) R->L }
% 0.18/0.39 multiplication(addition(domain(x0), antidomain(x1)), x1)
% 0.18/0.39 = { by axiom 3 (goals) }
% 0.18/0.39 multiplication(antidomain(x1), x1)
% 0.18/0.39 = { by axiom 2 (domain1) }
% 0.18/0.39 zero
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39
% 0.18/0.39 RESULT: Theorem (the conjecture is true).
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