TSTP Solution File: KRS072+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : KRS072+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 : n004.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 05:52:48 EDT 2023
% Result : Unsatisfiable 0.19s 0.41s
% 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
% 0.00/0.12 % Problem : KRS072+1 : TPTP v8.1.2. Released v3.1.0.
% 0.13/0.13 % 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 : n004.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 02:22:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.41 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.41
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Take the following subset of the input axioms:
% 0.19/0.42 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.19/0.42 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.19/0.42 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y]: (rinvR(X2, Y) & (![Z0, Z1]: ((rr(Y, Z0) & rr(Y, Z1)) => Z0=Z1) & ?[Z]: (rr(Y, Z) & cp1(Z)))) & cp2(X2)))).
% 0.19/0.42 fof(axiom_3, axiom, ![X2]: (cp1(X2) => ~(cp3(X2) | (cp2(X2) | (cp4(X2) | cp5(X2)))))).
% 0.19/0.42 fof(axiom_4, axiom, ![X2]: (cp2(X2) => ~(cp3(X2) | (cp4(X2) | cp5(X2))))).
% 0.19/0.42 fof(axiom_5, axiom, ![X2]: (cp3(X2) => ~(cp4(X2) | cp5(X2)))).
% 0.19/0.42 fof(axiom_6, axiom, ![X2]: (cp4(X2) => ~cp5(X2))).
% 0.19/0.42 fof(axiom_7, axiom, ![X2, Y2]: (rinvR(X2, Y2) <=> rr(Y2, X2))).
% 0.19/0.42 fof(axiom_8, axiom, cUnsatisfiable(i2003_11_14_17_18_50190)).
% 0.19/0.42
% 0.19/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.42 fresh(y, y, x1...xn) = u
% 0.19/0.42 C => fresh(s, t, x1...xn) = v
% 0.19/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.42 variables of u and v.
% 0.19/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.42 input problem has no model of domain size 1).
% 0.19/0.42
% 0.19/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.42
% 0.19/0.42 Axiom 1 (axiom_8): cUnsatisfiable(i2003_11_14_17_18_50190) = true2.
% 0.19/0.42 Axiom 2 (axiom_2_1): fresh7(X, X, Y) = true2.
% 0.19/0.42 Axiom 3 (axiom_2_2): fresh6(X, X, Y) = true2.
% 0.19/0.42 Axiom 4 (axiom_2_3): fresh5(X, X, Y) = true2.
% 0.19/0.42 Axiom 5 (axiom_2_4): fresh4(X, X, Y) = true2.
% 0.19/0.42 Axiom 6 (axiom_2_5): fresh14(X, X, Y, Z) = Z.
% 0.19/0.42 Axiom 7 (axiom_2_1): fresh7(cUnsatisfiable(X), true2, X) = cp1(z(X)).
% 0.19/0.42 Axiom 8 (axiom_2_2): fresh6(cUnsatisfiable(X), true2, X) = cp2(X).
% 0.19/0.42 Axiom 9 (axiom_2_3): fresh5(cUnsatisfiable(X), true2, X) = rinvR(X, y(X)).
% 0.19/0.42 Axiom 10 (axiom_2_4): fresh4(cUnsatisfiable(X), true2, X) = rr(y(X), z(X)).
% 0.19/0.42 Axiom 11 (axiom_7): fresh3(X, X, Y, Z) = true2.
% 0.19/0.42 Axiom 12 (axiom_2_5): fresh(X, X, Y, Z, W) = Z.
% 0.19/0.42 Axiom 13 (axiom_2_5): fresh13(X, X, Y, Z, W) = fresh14(cUnsatisfiable(Y), true2, Z, W).
% 0.19/0.42 Axiom 14 (axiom_7): fresh3(rinvR(X, Y), true2, X, Y) = rr(Y, X).
% 0.19/0.42 Axiom 15 (axiom_2_5): fresh13(rr(y(X), Y), true2, X, Z, Y) = fresh(rr(y(X), Z), true2, X, Z, Y).
% 0.19/0.42
% 0.19/0.42 Goal 1 (axiom_3): tuple(cp1(X), cp2(X)) = tuple(true2, true2).
% 0.19/0.42 The goal is true when:
% 0.19/0.42 X = i2003_11_14_17_18_50190
% 0.19/0.42
% 0.19/0.42 Proof:
% 0.19/0.42 tuple(cp1(i2003_11_14_17_18_50190), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 6 (axiom_2_5) R->L }
% 0.19/0.42 tuple(cp1(fresh14(true2, true2, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 1 (axiom_8) R->L }
% 0.19/0.42 tuple(cp1(fresh14(cUnsatisfiable(i2003_11_14_17_18_50190), true2, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 13 (axiom_2_5) R->L }
% 0.19/0.42 tuple(cp1(fresh13(true2, true2, i2003_11_14_17_18_50190, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 11 (axiom_7) R->L }
% 0.19/0.42 tuple(cp1(fresh13(fresh3(true2, true2, i2003_11_14_17_18_50190, y(i2003_11_14_17_18_50190)), true2, i2003_11_14_17_18_50190, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 4 (axiom_2_3) R->L }
% 0.19/0.42 tuple(cp1(fresh13(fresh3(fresh5(true2, true2, i2003_11_14_17_18_50190), true2, i2003_11_14_17_18_50190, y(i2003_11_14_17_18_50190)), true2, i2003_11_14_17_18_50190, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 1 (axiom_8) R->L }
% 0.19/0.42 tuple(cp1(fresh13(fresh3(fresh5(cUnsatisfiable(i2003_11_14_17_18_50190), true2, i2003_11_14_17_18_50190), true2, i2003_11_14_17_18_50190, y(i2003_11_14_17_18_50190)), true2, i2003_11_14_17_18_50190, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 9 (axiom_2_3) }
% 0.19/0.42 tuple(cp1(fresh13(fresh3(rinvR(i2003_11_14_17_18_50190, y(i2003_11_14_17_18_50190)), true2, i2003_11_14_17_18_50190, y(i2003_11_14_17_18_50190)), true2, i2003_11_14_17_18_50190, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 14 (axiom_7) }
% 0.19/0.42 tuple(cp1(fresh13(rr(y(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190), true2, i2003_11_14_17_18_50190, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 15 (axiom_2_5) }
% 0.19/0.42 tuple(cp1(fresh(rr(y(i2003_11_14_17_18_50190), z(i2003_11_14_17_18_50190)), true2, i2003_11_14_17_18_50190, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 10 (axiom_2_4) R->L }
% 0.19/0.42 tuple(cp1(fresh(fresh4(cUnsatisfiable(i2003_11_14_17_18_50190), true2, i2003_11_14_17_18_50190), true2, i2003_11_14_17_18_50190, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 1 (axiom_8) }
% 0.19/0.42 tuple(cp1(fresh(fresh4(true2, true2, i2003_11_14_17_18_50190), true2, i2003_11_14_17_18_50190, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 5 (axiom_2_4) }
% 0.19/0.42 tuple(cp1(fresh(true2, true2, i2003_11_14_17_18_50190, z(i2003_11_14_17_18_50190), i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 12 (axiom_2_5) }
% 0.19/0.42 tuple(cp1(z(i2003_11_14_17_18_50190)), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 7 (axiom_2_1) R->L }
% 0.19/0.42 tuple(fresh7(cUnsatisfiable(i2003_11_14_17_18_50190), true2, i2003_11_14_17_18_50190), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 1 (axiom_8) }
% 0.19/0.42 tuple(fresh7(true2, true2, i2003_11_14_17_18_50190), cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 2 (axiom_2_1) }
% 0.19/0.42 tuple(true2, cp2(i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 8 (axiom_2_2) R->L }
% 0.19/0.42 tuple(true2, fresh6(cUnsatisfiable(i2003_11_14_17_18_50190), true2, i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 1 (axiom_8) }
% 0.19/0.42 tuple(true2, fresh6(true2, true2, i2003_11_14_17_18_50190))
% 0.19/0.42 = { by axiom 3 (axiom_2_2) }
% 0.19/0.42 tuple(true2, true2)
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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