TSTP Solution File: KRS086+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : KRS086+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 : 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 05:52:51 EDT 2023
% Result : Unsatisfiable 0.15s 0.41s
% 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
% 0.07/0.14 % Problem : KRS086+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.16 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37 % Computer : n011.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Aug 28 02:20:55 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.41 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.15/0.41
% 0.15/0.41 % SZS status Unsatisfiable
% 0.15/0.41
% 0.15/0.41 % SZS output start Proof
% 0.15/0.41 Take the following subset of the input axioms:
% 0.15/0.41 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.15/0.41 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.15/0.41 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> ?[Y]: (rf(X2, Y) & (?[Z]: (rinvF(Y, Z) & ?[W]: (rf(Z, W) & ~cp1(W))) & cp1(Y))))).
% 0.15/0.41 fof(axiom_3, axiom, ![X2]: (cowlThing(X2) => ![Y0, Y1]: ((rf(X2, Y0) & rf(X2, Y1)) => Y0=Y1))).
% 0.15/0.41 fof(axiom_4, axiom, ![X2, Y2]: (rinvF(X2, Y2) <=> rf(Y2, X2))).
% 0.15/0.41 fof(axiom_7, axiom, cUnsatisfiable(i2003_11_14_17_19_42328)).
% 0.15/0.41
% 0.15/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.15/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.15/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.15/0.41 fresh(y, y, x1...xn) = u
% 0.15/0.41 C => fresh(s, t, x1...xn) = v
% 0.15/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.15/0.41 variables of u and v.
% 0.15/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.15/0.41 input problem has no model of domain size 1).
% 0.15/0.41
% 0.15/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.15/0.41
% 0.15/0.41 Axiom 1 (axiom_7): cUnsatisfiable(i2003_11_14_17_19_42328) = true2.
% 0.15/0.41 Axiom 2 (axiom_0): cowlThing(X) = true2.
% 0.15/0.41 Axiom 3 (axiom_2): fresh10(X, X, Y) = true2.
% 0.15/0.41 Axiom 4 (axiom_2_2): fresh9(X, X, Y) = true2.
% 0.15/0.41 Axiom 5 (axiom_2_3): fresh8(X, X, Y) = true2.
% 0.15/0.41 Axiom 6 (axiom_3): fresh13(X, X, Y, Z) = Z.
% 0.15/0.41 Axiom 7 (axiom_2): fresh10(cUnsatisfiable(X), true2, X) = cp1(y(X)).
% 0.15/0.41 Axiom 8 (axiom_2_2): fresh9(cUnsatisfiable(X), true2, X) = rf(z(X), w(X)).
% 0.15/0.41 Axiom 9 (axiom_2_3): fresh8(cUnsatisfiable(X), true2, X) = rinvF(y(X), z(X)).
% 0.15/0.41 Axiom 10 (axiom_4_1): fresh6(X, X, Y, Z) = true2.
% 0.15/0.41 Axiom 11 (axiom_3): fresh(X, X, Y, Z, W) = Z.
% 0.15/0.41 Axiom 12 (axiom_3): fresh12(X, X, Y, Z, W) = fresh13(cowlThing(Y), true2, Z, W).
% 0.15/0.41 Axiom 13 (axiom_4_1): fresh6(rinvF(X, Y), true2, X, Y) = rf(Y, X).
% 0.21/0.41 Axiom 14 (axiom_3): fresh12(rf(X, Y), true2, X, Z, Y) = fresh(rf(X, Z), true2, X, Z, Y).
% 0.21/0.41
% 0.21/0.41 Goal 1 (axiom_2_4): tuple(cUnsatisfiable(X), cp1(w(X))) = tuple(true2, true2).
% 0.21/0.41 The goal is true when:
% 0.21/0.41 X = i2003_11_14_17_19_42328
% 0.21/0.41
% 0.21/0.41 Proof:
% 0.21/0.41 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(w(i2003_11_14_17_19_42328)))
% 0.21/0.41 = { by axiom 6 (axiom_3) R->L }
% 0.21/0.41 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh13(true2, true2, y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.41 = { by axiom 2 (axiom_0) R->L }
% 0.21/0.41 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh13(cowlThing(z(i2003_11_14_17_19_42328)), true2, y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.41 = { by axiom 12 (axiom_3) R->L }
% 0.21/0.41 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh12(true2, true2, z(i2003_11_14_17_19_42328), y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.41 = { by axiom 4 (axiom_2_2) R->L }
% 0.21/0.41 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh12(fresh9(true2, true2, i2003_11_14_17_19_42328), true2, z(i2003_11_14_17_19_42328), y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.41 = { by axiom 1 (axiom_7) R->L }
% 0.21/0.41 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh12(fresh9(cUnsatisfiable(i2003_11_14_17_19_42328), true2, i2003_11_14_17_19_42328), true2, z(i2003_11_14_17_19_42328), y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.41 = { by axiom 8 (axiom_2_2) }
% 0.21/0.41 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh12(rf(z(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328)), true2, z(i2003_11_14_17_19_42328), y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.41 = { by axiom 14 (axiom_3) }
% 0.21/0.41 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh(rf(z(i2003_11_14_17_19_42328), y(i2003_11_14_17_19_42328)), true2, z(i2003_11_14_17_19_42328), y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.41 = { by axiom 13 (axiom_4_1) R->L }
% 0.21/0.41 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh(fresh6(rinvF(y(i2003_11_14_17_19_42328), z(i2003_11_14_17_19_42328)), true2, y(i2003_11_14_17_19_42328), z(i2003_11_14_17_19_42328)), true2, z(i2003_11_14_17_19_42328), y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.41 = { by axiom 9 (axiom_2_3) R->L }
% 0.21/0.42 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh(fresh6(fresh8(cUnsatisfiable(i2003_11_14_17_19_42328), true2, i2003_11_14_17_19_42328), true2, y(i2003_11_14_17_19_42328), z(i2003_11_14_17_19_42328)), true2, z(i2003_11_14_17_19_42328), y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.42 = { by axiom 1 (axiom_7) }
% 0.21/0.42 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh(fresh6(fresh8(true2, true2, i2003_11_14_17_19_42328), true2, y(i2003_11_14_17_19_42328), z(i2003_11_14_17_19_42328)), true2, z(i2003_11_14_17_19_42328), y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.42 = { by axiom 5 (axiom_2_3) }
% 0.21/0.42 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh(fresh6(true2, true2, y(i2003_11_14_17_19_42328), z(i2003_11_14_17_19_42328)), true2, z(i2003_11_14_17_19_42328), y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.42 = { by axiom 10 (axiom_4_1) }
% 0.21/0.42 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(fresh(true2, true2, z(i2003_11_14_17_19_42328), y(i2003_11_14_17_19_42328), w(i2003_11_14_17_19_42328))))
% 0.21/0.42 = { by axiom 11 (axiom_3) }
% 0.21/0.42 tuple(cUnsatisfiable(i2003_11_14_17_19_42328), cp1(y(i2003_11_14_17_19_42328)))
% 0.21/0.42 = { by axiom 1 (axiom_7) }
% 0.21/0.42 tuple(true2, cp1(y(i2003_11_14_17_19_42328)))
% 0.21/0.42 = { by axiom 7 (axiom_2) R->L }
% 0.21/0.42 tuple(true2, fresh10(cUnsatisfiable(i2003_11_14_17_19_42328), true2, i2003_11_14_17_19_42328))
% 0.21/0.42 = { by axiom 1 (axiom_7) }
% 0.21/0.42 tuple(true2, fresh10(true2, true2, i2003_11_14_17_19_42328))
% 0.21/0.42 = { by axiom 3 (axiom_2) }
% 0.21/0.42 tuple(true2, true2)
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42
% 0.21/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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