TSTP Solution File: KRS063+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS063+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n018.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 05:52:46 EDT 2023
% Result : Unsatisfiable 0.18s 0.37s
% 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
% 0.06/0.12 % Problem : KRS063+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.13 % 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 : n018.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 : Mon Aug 28 02:03:01 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.37 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.18/0.37
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37
% 0.18/0.37 % SZS output start Proof
% 0.18/0.38 Take the following subset of the input axioms:
% 0.18/0.38 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.18/0.38 fof(axiom_10, axiom, ~cEuroMP(iKinnock)).
% 0.18/0.38 fof(axiom_14, axiom, rhasEuroMP(iUK, iKinnock)).
% 0.18/0.38 fof(axiom_3, axiom, ![X2]: (cEuroMP(X2) <=> ?[Y]: (risEuroMPFrom(X2, Y) & cowlThing(Y)))).
% 0.18/0.38 fof(axiom_5, axiom, ![X2, Y2]: (risEuroMPFrom(X2, Y2) <=> rhasEuroMP(Y2, X2))).
% 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:
% 0.18/0.38
% 0.18/0.38 Axiom 1 (axiom_0): cowlThing(X) = true2.
% 0.18/0.38 Axiom 2 (axiom_14): rhasEuroMP(iUK, iKinnock) = true2.
% 0.18/0.38 Axiom 3 (axiom_3_2): fresh4(X, X, Y) = true2.
% 0.18/0.38 Axiom 4 (axiom_3_2): fresh5(X, X, Y, Z) = cEuroMP(Y).
% 0.18/0.38 Axiom 5 (axiom_5): fresh2(X, X, Y, Z) = true2.
% 0.18/0.38 Axiom 6 (axiom_3_2): fresh5(risEuroMPFrom(X, Y), true2, X, Y) = fresh4(cowlThing(Y), true2, X).
% 0.18/0.38 Axiom 7 (axiom_5): fresh2(rhasEuroMP(X, Y), true2, Y, X) = risEuroMPFrom(Y, X).
% 0.18/0.38
% 0.18/0.38 Goal 1 (axiom_10): cEuroMP(iKinnock) = true2.
% 0.18/0.38 Proof:
% 0.18/0.38 cEuroMP(iKinnock)
% 0.18/0.38 = { by axiom 4 (axiom_3_2) R->L }
% 0.18/0.38 fresh5(true2, true2, iKinnock, iUK)
% 0.18/0.38 = { by axiom 5 (axiom_5) R->L }
% 0.18/0.38 fresh5(fresh2(true2, true2, iKinnock, iUK), true2, iKinnock, iUK)
% 0.18/0.38 = { by axiom 2 (axiom_14) R->L }
% 0.18/0.38 fresh5(fresh2(rhasEuroMP(iUK, iKinnock), true2, iKinnock, iUK), true2, iKinnock, iUK)
% 0.18/0.38 = { by axiom 7 (axiom_5) }
% 0.18/0.38 fresh5(risEuroMPFrom(iKinnock, iUK), true2, iKinnock, iUK)
% 0.18/0.38 = { by axiom 6 (axiom_3_2) }
% 0.18/0.38 fresh4(cowlThing(iUK), true2, iKinnock)
% 0.18/0.38 = { by axiom 1 (axiom_0) }
% 0.18/0.38 fresh4(true2, true2, iKinnock)
% 0.18/0.38 = { by axiom 3 (axiom_3_2) }
% 0.18/0.38 true2
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38
% 0.18/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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