TSTP Solution File: KRS262+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS262+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : n011.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 05:53:17 EDT 2023
% Result : Theorem 0.19s 0.64s
% 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
% 0.11/0.12 % Problem : KRS262+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 01:25:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.64 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.64
% 0.19/0.64 % SZS status Theorem
% 0.19/0.64
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 Take the following subset of the input axioms:
% 0.19/0.65 fof(mighta, axiom, ![S1, S2]: (?[Ax, C]: (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))).
% 0.19/0.65 fof(mighta_tau_thm, conjecture, mighta(tau, thm)).
% 0.19/0.65 fof(tau, axiom, ![Ax2, C2]: (![I1]: (model(I1, Ax2) & model(I1, C2)) <=> status(Ax2, C2, tau))).
% 0.19/0.65 fof(tautology, axiom, ?[F]: ![I]: model(I, F)).
% 0.19/0.65 fof(thm, axiom, ![Ax2, C2]: (![I1_2]: (model(I1_2, Ax2) => model(I1_2, C2)) <=> status(Ax2, C2, thm))).
% 0.19/0.65
% 0.19/0.65 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.65 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.65 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.65 fresh(y, y, x1...xn) = u
% 0.19/0.65 C => fresh(s, t, x1...xn) = v
% 0.19/0.65 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.65 variables of u and v.
% 0.19/0.65 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.65 input problem has no model of domain size 1).
% 0.19/0.65
% 0.19/0.65 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.65
% 0.19/0.65 Axiom 1 (tautology): model(X, f3) = true2.
% 0.19/0.65 Axiom 2 (mighta): fresh47(X, X, Y, Z) = true2.
% 0.19/0.65 Axiom 3 (tau): fresh26(X, X, Y, Z) = status(Y, Z, tau).
% 0.19/0.65 Axiom 4 (tau): fresh25(X, X, Y, Z) = true2.
% 0.19/0.65 Axiom 5 (thm_2): fresh19(X, X, Y, Z) = true2.
% 0.19/0.65 Axiom 6 (mighta): fresh48(X, X, Y, Z, W, V) = mighta(Y, Z).
% 0.19/0.65 Axiom 7 (tau): fresh26(model(i1_14(X), X), true2, Y, X) = fresh25(model(i1_15(Y), Y), true2, Y, X).
% 0.19/0.65 Axiom 8 (thm_2): fresh19(model(i1_20(X, Y), Y), true2, X, Y) = status(X, Y, thm).
% 0.19/0.65 Axiom 9 (mighta): fresh48(status(X, Y, Z), true2, W, Z, X, Y) = fresh47(status(X, Y, W), true2, W, Z).
% 0.19/0.65
% 0.19/0.65 Goal 1 (mighta_tau_thm): mighta(tau, thm) = true2.
% 0.19/0.65 Proof:
% 0.19/0.65 mighta(tau, thm)
% 0.19/0.65 = { by axiom 6 (mighta) R->L }
% 0.19/0.65 fresh48(true2, true2, tau, thm, f3, f3)
% 0.19/0.65 = { by axiom 5 (thm_2) R->L }
% 0.19/0.65 fresh48(fresh19(true2, true2, f3, f3), true2, tau, thm, f3, f3)
% 0.19/0.65 = { by axiom 1 (tautology) R->L }
% 0.19/0.65 fresh48(fresh19(model(i1_20(f3, f3), f3), true2, f3, f3), true2, tau, thm, f3, f3)
% 0.19/0.65 = { by axiom 8 (thm_2) }
% 0.19/0.65 fresh48(status(f3, f3, thm), true2, tau, thm, f3, f3)
% 0.19/0.65 = { by axiom 9 (mighta) }
% 0.19/0.65 fresh47(status(f3, f3, tau), true2, tau, thm)
% 0.19/0.65 = { by axiom 3 (tau) R->L }
% 0.19/0.65 fresh47(fresh26(true2, true2, f3, f3), true2, tau, thm)
% 0.19/0.65 = { by axiom 1 (tautology) R->L }
% 0.19/0.65 fresh47(fresh26(model(i1_14(f3), f3), true2, f3, f3), true2, tau, thm)
% 0.19/0.65 = { by axiom 7 (tau) }
% 0.19/0.65 fresh47(fresh25(model(i1_15(f3), f3), true2, f3, f3), true2, tau, thm)
% 0.19/0.65 = { by axiom 1 (tautology) }
% 0.19/0.65 fresh47(fresh25(true2, true2, f3, f3), true2, tau, thm)
% 0.19/0.65 = { by axiom 4 (tau) }
% 0.19/0.65 fresh47(true2, true2, tau, thm)
% 0.19/0.65 = { by axiom 2 (mighta) }
% 0.19/0.65 true2
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65
% 0.19/0.65 RESULT: Theorem (the conjecture is true).
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