TSTP Solution File: NUM395+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM395+1 : TPTP v8.1.2. Released v3.2.0.
% 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 11:56:07 EDT 2023
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% 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 : NUM395+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 14:45:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.40 Command-line arguments: --no-flatten-goal
% 0.20/0.40
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Take the following subset of the input axioms:
% 0.20/0.41 fof(cc2_ordinal1, axiom, ![A2]: ((epsilon_transitive(A2) & epsilon_connected(A2)) => ordinal(A2))).
% 0.20/0.41 fof(l18_ordinal1, axiom, epsilon_transitive(empty_set) & epsilon_connected(empty_set)).
% 0.20/0.41 fof(t27_ordinal1, conjecture, ordinal(empty_set)).
% 0.20/0.41
% 0.20/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.41 fresh(y, y, x1...xn) = u
% 0.20/0.41 C => fresh(s, t, x1...xn) = v
% 0.20/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.41 variables of u and v.
% 0.20/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.41 input problem has no model of domain size 1).
% 0.20/0.41
% 0.20/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.41
% 0.20/0.41 Axiom 1 (l18_ordinal1): epsilon_transitive(empty_set) = true2.
% 0.20/0.41 Axiom 2 (l18_ordinal1_1): epsilon_connected(empty_set) = true2.
% 0.20/0.41 Axiom 3 (cc2_ordinal1): fresh10(X, X, Y) = ordinal(Y).
% 0.20/0.41 Axiom 4 (cc2_ordinal1): fresh9(X, X, Y) = true2.
% 0.20/0.41 Axiom 5 (cc2_ordinal1): fresh10(epsilon_connected(X), true2, X) = fresh9(epsilon_transitive(X), true2, X).
% 0.20/0.41
% 0.20/0.41 Goal 1 (t27_ordinal1): ordinal(empty_set) = true2.
% 0.20/0.41 Proof:
% 0.20/0.41 ordinal(empty_set)
% 0.20/0.41 = { by axiom 3 (cc2_ordinal1) R->L }
% 0.20/0.41 fresh10(true2, true2, empty_set)
% 0.20/0.41 = { by axiom 2 (l18_ordinal1_1) R->L }
% 0.20/0.41 fresh10(epsilon_connected(empty_set), true2, empty_set)
% 0.20/0.41 = { by axiom 5 (cc2_ordinal1) }
% 0.20/0.41 fresh9(epsilon_transitive(empty_set), true2, empty_set)
% 0.20/0.41 = { by axiom 1 (l18_ordinal1) }
% 0.20/0.41 fresh9(true2, true2, empty_set)
% 0.20/0.41 = { by axiom 4 (cc2_ordinal1) }
% 0.20/0.41 true2
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Theorem (the conjecture is true).
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