TSTP Solution File: KLE075+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KLE075+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 : n021.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 05:35:47 EDT 2023
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : KLE075+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 11:41:14 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.40 Command-line arguments: --no-flatten-goal
% 0.21/0.40
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Take the following subset of the input axioms:
% 0.21/0.41 fof(domain2, axiom, ![X0, X1]: domain(multiplication(X0, X1))=domain(multiplication(X0, domain(X1)))).
% 0.21/0.41 fof(goals, conjecture, ![X0_2]: domain(multiplication(one, domain(X0_2)))=domain(X0_2)).
% 0.21/0.41 fof(multiplicative_left_identity, axiom, ![A]: multiplication(one, A)=A).
% 0.21/0.41
% 0.21/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.41 fresh(y, y, x1...xn) = u
% 0.21/0.41 C => fresh(s, t, x1...xn) = v
% 0.21/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.41 variables of u and v.
% 0.21/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.41 input problem has no model of domain size 1).
% 0.21/0.41
% 0.21/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.41
% 0.21/0.41 Axiom 1 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.21/0.41 Axiom 2 (domain2): domain(multiplication(X, Y)) = domain(multiplication(X, domain(Y))).
% 0.21/0.41
% 0.21/0.41 Goal 1 (goals): domain(multiplication(one, domain(x0))) = domain(x0).
% 0.21/0.41 Proof:
% 0.21/0.41 domain(multiplication(one, domain(x0)))
% 0.21/0.41 = { by axiom 2 (domain2) R->L }
% 0.21/0.41 domain(multiplication(one, x0))
% 0.21/0.41 = { by axiom 1 (multiplicative_left_identity) }
% 0.21/0.41 domain(x0)
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41
% 0.21/0.41 RESULT: Theorem (the conjecture is true).
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