TSTP Solution File: KRS077+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS077+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 05:52:49 EDT 2023
% Result : Unsatisfiable 0.18s 0.38s
% 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
% 0.09/0.11 % Problem : KRS077+1 : TPTP v8.1.2. Released v3.1.0.
% 0.09/0.12 % 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 : n011.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 01:48:40 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.38 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.18/0.38
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38
% 0.18/0.38 % 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_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.18/0.38 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (![Y0, Y1]: ((rr(X2, Y0) & rr(X2, Y1)) => Y0=Y1) & (?[Y]: (rr(X2, Y) & ![Z]: (rinvS(Y, Z) => cp(Z))) & (~cp(X2) & ?[Y2]: (rs(X2, Y2) & cp(Y2))))))).
% 0.18/0.38 fof(axiom_3, axiom, ![X2, Y2]: (rinvS(X2, Y2) <=> rs(Y2, X2))).
% 0.18/0.38 fof(axiom_4, axiom, cUnsatisfiable(i2003_11_14_17_19_09372)).
% 0.18/0.38 fof(axiom_5, axiom, ![X2, Y2]: (rs(X2, Y2) => rr(X2, Y2))).
% 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_4): cUnsatisfiable(i2003_11_14_17_19_09372) = true2.
% 0.18/0.38 Axiom 2 (axiom_2_3): fresh9(X, X, Y) = true2.
% 0.18/0.38 Axiom 3 (axiom_2_4): fresh7(X, X, Y) = true2.
% 0.18/0.38 Axiom 4 (axiom_2_6): fresh5(X, X, Y) = true2.
% 0.18/0.38 Axiom 5 (axiom_2_7): fresh11(X, X, Y, Z) = Z.
% 0.18/0.38 Axiom 6 (axiom_2_3): fresh9(cUnsatisfiable(X), true2, X) = rr(X, y2(X)).
% 0.18/0.38 Axiom 7 (axiom_2_4): fresh7(cUnsatisfiable(X), true2, X) = rs(X, y(X)).
% 0.18/0.38 Axiom 8 (axiom_2_6): fresh6(X, X, Y, Z) = cp(Z).
% 0.18/0.38 Axiom 9 (axiom_3_1): fresh3(X, X, Y, Z) = true2.
% 0.18/0.38 Axiom 10 (axiom_5): fresh2(X, X, Y, Z) = true2.
% 0.18/0.38 Axiom 11 (axiom_2_7): fresh(X, X, Y, Z, W) = Z.
% 0.18/0.38 Axiom 12 (axiom_2_7): fresh10(X, X, Y, Z, W) = fresh11(cUnsatisfiable(Y), true2, Z, W).
% 0.18/0.38 Axiom 13 (axiom_3_1): fresh3(rs(X, Y), true2, Y, X) = rinvS(Y, X).
% 0.18/0.38 Axiom 14 (axiom_5): fresh2(rs(X, Y), true2, X, Y) = rr(X, Y).
% 0.18/0.38 Axiom 15 (axiom_2_7): fresh10(rr(X, Y), true2, X, Z, Y) = fresh(rr(X, Z), true2, X, Z, Y).
% 0.18/0.38 Axiom 16 (axiom_2_6): fresh6(rinvS(y2(X), Y), true2, X, Y) = fresh5(cUnsatisfiable(X), true2, Y).
% 0.18/0.38
% 0.18/0.38 Lemma 17: rs(i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372)) = true2.
% 0.18/0.38 Proof:
% 0.18/0.38 rs(i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372))
% 0.18/0.38 = { by axiom 7 (axiom_2_4) R->L }
% 0.18/0.38 fresh7(cUnsatisfiable(i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372)
% 0.18/0.38 = { by axiom 1 (axiom_4) }
% 0.18/0.38 fresh7(true2, true2, i2003_11_14_17_19_09372)
% 0.18/0.38 = { by axiom 3 (axiom_2_4) }
% 0.18/0.38 true2
% 0.18/0.38
% 0.18/0.38 Goal 1 (axiom_2_5): tuple(cUnsatisfiable(X), cp(X)) = tuple(true2, true2).
% 0.18/0.38 The goal is true when:
% 0.18/0.38 X = i2003_11_14_17_19_09372
% 0.18/0.38
% 0.18/0.38 Proof:
% 0.18/0.38 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), cp(i2003_11_14_17_19_09372))
% 0.18/0.38 = { by axiom 8 (axiom_2_6) R->L }
% 0.18/0.38 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(true2, true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.38 = { by axiom 9 (axiom_3_1) R->L }
% 0.18/0.38 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(fresh3(true2, true2, y(i2003_11_14_17_19_09372), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.38 = { by lemma 17 R->L }
% 0.18/0.38 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(fresh3(rs(i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372)), true2, y(i2003_11_14_17_19_09372), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.38 = { by axiom 13 (axiom_3_1) }
% 0.18/0.38 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(y(i2003_11_14_17_19_09372), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.38 = { by axiom 11 (axiom_2_7) R->L }
% 0.18/0.38 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(fresh(true2, true2, i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372), y2(i2003_11_14_17_19_09372)), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.38 = { by axiom 10 (axiom_5) R->L }
% 0.18/0.38 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(fresh(fresh2(true2, true2, i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372)), true2, i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372), y2(i2003_11_14_17_19_09372)), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.38 = { by lemma 17 R->L }
% 0.18/0.38 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(fresh(fresh2(rs(i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372)), true2, i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372)), true2, i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372), y2(i2003_11_14_17_19_09372)), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.38 = { by axiom 14 (axiom_5) }
% 0.18/0.38 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(fresh(rr(i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372)), true2, i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372), y2(i2003_11_14_17_19_09372)), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.38 = { by axiom 15 (axiom_2_7) R->L }
% 0.18/0.39 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(fresh10(rr(i2003_11_14_17_19_09372, y2(i2003_11_14_17_19_09372)), true2, i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372), y2(i2003_11_14_17_19_09372)), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.39 = { by axiom 6 (axiom_2_3) R->L }
% 0.18/0.39 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(fresh10(fresh9(cUnsatisfiable(i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372), y2(i2003_11_14_17_19_09372)), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.39 = { by axiom 1 (axiom_4) }
% 0.18/0.39 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(fresh10(fresh9(true2, true2, i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372), y2(i2003_11_14_17_19_09372)), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.39 = { by axiom 2 (axiom_2_3) }
% 0.18/0.39 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(fresh10(true2, true2, i2003_11_14_17_19_09372, y(i2003_11_14_17_19_09372), y2(i2003_11_14_17_19_09372)), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.39 = { by axiom 12 (axiom_2_7) }
% 0.18/0.39 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(fresh11(cUnsatisfiable(i2003_11_14_17_19_09372), true2, y(i2003_11_14_17_19_09372), y2(i2003_11_14_17_19_09372)), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.39 = { by axiom 1 (axiom_4) }
% 0.18/0.39 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(fresh11(true2, true2, y(i2003_11_14_17_19_09372), y2(i2003_11_14_17_19_09372)), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.39 = { by axiom 5 (axiom_2_7) }
% 0.18/0.39 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh6(rinvS(y2(i2003_11_14_17_19_09372), i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372, i2003_11_14_17_19_09372))
% 0.18/0.39 = { by axiom 16 (axiom_2_6) }
% 0.18/0.39 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh5(cUnsatisfiable(i2003_11_14_17_19_09372), true2, i2003_11_14_17_19_09372))
% 0.18/0.39 = { by axiom 1 (axiom_4) }
% 0.18/0.39 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), fresh5(true2, true2, i2003_11_14_17_19_09372))
% 0.18/0.39 = { by axiom 4 (axiom_2_6) }
% 0.18/0.39 tuple(cUnsatisfiable(i2003_11_14_17_19_09372), true2)
% 0.18/0.39 = { by axiom 1 (axiom_4) }
% 0.18/0.39 tuple(true2, true2)
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39
% 0.18/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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