TSTP Solution File: KRS076+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS076+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 : n015.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 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KRS076+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 02:06:10 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.43 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.22/0.43
% 0.22/0.43 % SZS status Unsatisfiable
% 0.22/0.43
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 Take the following subset of the input axioms:
% 0.22/0.44 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.22/0.44 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.22/0.44 fof(axiom_10, axiom, ![Y, X2]: (rs(X2, Y) => rf1(X2, Y))).
% 0.22/0.44 fof(axiom_11, axiom, ![X2, Y2]: (rs(X2, Y2) => rf(X2, Y2))).
% 0.22/0.44 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y2]: (rf(X2, Y2) & cp(Y2)) & ?[Y2]: (rf1(X2, Y2) & (~cp(Y2) & ![Z]: (rinvF1(Y2, Z) => ?[W]: (rs(Z, W) & cowlThing(W)))))))).
% 0.22/0.44 fof(axiom_3, axiom, ![X2, Y2, Z2]: ((rf(X2, Y2) & rf(X2, Z2)) => Y2=Z2)).
% 0.22/0.44 fof(axiom_4, axiom, ![X2, Y2, Z2]: ((rf1(X2, Y2) & rf1(X2, Z2)) => Y2=Z2)).
% 0.22/0.44 fof(axiom_6, axiom, ![X2, Y2]: (rinvF1(X2, Y2) <=> rf1(Y2, X2))).
% 0.22/0.44 fof(axiom_9, axiom, cUnsatisfiable(i2003_11_14_17_19_06193)).
% 0.22/0.44
% 0.22/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.44 fresh(y, y, x1...xn) = u
% 0.22/0.44 C => fresh(s, t, x1...xn) = v
% 0.22/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.44 variables of u and v.
% 0.22/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.44 input problem has no model of domain size 1).
% 0.22/0.44
% 0.22/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.44
% 0.22/0.44 Axiom 1 (axiom_9): cUnsatisfiable(i2003_11_14_17_19_06193) = true2.
% 0.22/0.44 Axiom 2 (axiom_2): fresh19(X, X, Y) = true2.
% 0.22/0.44 Axiom 3 (axiom_2_1): fresh18(X, X, Y) = true2.
% 0.22/0.44 Axiom 4 (axiom_2_2): fresh17(X, X, Y) = true2.
% 0.22/0.44 Axiom 5 (axiom_2_5): fresh13(X, X, Y) = true2.
% 0.22/0.44 Axiom 6 (axiom_11): fresh21(X, X, Y, Z) = true2.
% 0.22/0.44 Axiom 7 (axiom_10): fresh20(X, X, Y, Z) = true2.
% 0.22/0.44 Axiom 8 (axiom_2): fresh19(cUnsatisfiable(X), true2, X) = cp(y2(X)).
% 0.22/0.44 Axiom 9 (axiom_2_1): fresh18(cUnsatisfiable(X), true2, X) = rf(X, y2(X)).
% 0.22/0.44 Axiom 10 (axiom_2_2): fresh17(cUnsatisfiable(X), true2, X) = rf1(X, y(X)).
% 0.22/0.44 Axiom 11 (axiom_2_5): fresh14(X, X, Y, Z) = rs(Z, w(Z)).
% 0.22/0.44 Axiom 12 (axiom_6): fresh10(X, X, Y, Z) = true2.
% 0.22/0.44 Axiom 13 (axiom_3): fresh5(X, X, Y, Z) = Z.
% 0.22/0.44 Axiom 14 (axiom_4): fresh3(X, X, Y, Z) = Z.
% 0.22/0.44 Axiom 15 (axiom_11): fresh21(rs(X, Y), true2, X, Y) = rf(X, Y).
% 0.22/0.44 Axiom 16 (axiom_10): fresh20(rs(X, Y), true2, X, Y) = rf1(X, Y).
% 0.22/0.44 Axiom 17 (axiom_6): fresh10(rf1(X, Y), true2, Y, X) = rinvF1(Y, X).
% 0.22/0.44 Axiom 18 (axiom_3): fresh6(X, X, Y, Z, W) = Z.
% 0.22/0.44 Axiom 19 (axiom_4): fresh4(X, X, Y, Z, W) = Z.
% 0.22/0.44 Axiom 20 (axiom_2_5): fresh14(rinvF1(y(X), Y), true2, X, Y) = fresh13(cUnsatisfiable(X), true2, Y).
% 0.22/0.44 Axiom 21 (axiom_3): fresh6(rf(X, Y), true2, X, Z, Y) = fresh5(rf(X, Z), true2, Z, Y).
% 0.22/0.44 Axiom 22 (axiom_4): fresh4(rf1(X, Y), true2, X, Z, Y) = fresh3(rf1(X, Z), true2, Z, Y).
% 0.22/0.44
% 0.22/0.44 Lemma 23: rf1(i2003_11_14_17_19_06193, y(i2003_11_14_17_19_06193)) = true2.
% 0.22/0.44 Proof:
% 0.22/0.44 rf1(i2003_11_14_17_19_06193, y(i2003_11_14_17_19_06193))
% 0.22/0.44 = { by axiom 10 (axiom_2_2) R->L }
% 0.22/0.44 fresh17(cUnsatisfiable(i2003_11_14_17_19_06193), true2, i2003_11_14_17_19_06193)
% 0.22/0.44 = { by axiom 1 (axiom_9) }
% 0.22/0.44 fresh17(true2, true2, i2003_11_14_17_19_06193)
% 0.22/0.44 = { by axiom 4 (axiom_2_2) }
% 0.22/0.44 true2
% 0.22/0.44
% 0.22/0.44 Lemma 24: rs(i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193)) = true2.
% 0.22/0.44 Proof:
% 0.22/0.44 rs(i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193))
% 0.22/0.44 = { by axiom 11 (axiom_2_5) R->L }
% 0.22/0.44 fresh14(true2, true2, i2003_11_14_17_19_06193, i2003_11_14_17_19_06193)
% 0.22/0.44 = { by axiom 12 (axiom_6) R->L }
% 0.22/0.44 fresh14(fresh10(true2, true2, y(i2003_11_14_17_19_06193), i2003_11_14_17_19_06193), true2, i2003_11_14_17_19_06193, i2003_11_14_17_19_06193)
% 0.22/0.44 = { by lemma 23 R->L }
% 0.22/0.44 fresh14(fresh10(rf1(i2003_11_14_17_19_06193, y(i2003_11_14_17_19_06193)), true2, y(i2003_11_14_17_19_06193), i2003_11_14_17_19_06193), true2, i2003_11_14_17_19_06193, i2003_11_14_17_19_06193)
% 0.22/0.44 = { by axiom 17 (axiom_6) }
% 0.22/0.44 fresh14(rinvF1(y(i2003_11_14_17_19_06193), i2003_11_14_17_19_06193), true2, i2003_11_14_17_19_06193, i2003_11_14_17_19_06193)
% 0.22/0.44 = { by axiom 20 (axiom_2_5) }
% 0.22/0.44 fresh13(cUnsatisfiable(i2003_11_14_17_19_06193), true2, i2003_11_14_17_19_06193)
% 0.22/0.44 = { by axiom 1 (axiom_9) }
% 0.22/0.44 fresh13(true2, true2, i2003_11_14_17_19_06193)
% 0.22/0.44 = { by axiom 5 (axiom_2_5) }
% 0.22/0.44 true2
% 0.22/0.44
% 0.22/0.44 Goal 1 (axiom_2_3): tuple(cUnsatisfiable(X), cp(y(X))) = tuple(true2, true2).
% 0.22/0.44 The goal is true when:
% 0.22/0.44 X = i2003_11_14_17_19_06193
% 0.22/0.44
% 0.22/0.44 Proof:
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(y(i2003_11_14_17_19_06193)))
% 0.22/0.44 = { by axiom 14 (axiom_4) R->L }
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh3(true2, true2, w(i2003_11_14_17_19_06193), y(i2003_11_14_17_19_06193))))
% 0.22/0.44 = { by axiom 7 (axiom_10) R->L }
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh3(fresh20(true2, true2, i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193)), true2, w(i2003_11_14_17_19_06193), y(i2003_11_14_17_19_06193))))
% 0.22/0.44 = { by lemma 24 R->L }
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh3(fresh20(rs(i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193)), true2, i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193)), true2, w(i2003_11_14_17_19_06193), y(i2003_11_14_17_19_06193))))
% 0.22/0.44 = { by axiom 16 (axiom_10) }
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh3(rf1(i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193)), true2, w(i2003_11_14_17_19_06193), y(i2003_11_14_17_19_06193))))
% 0.22/0.44 = { by axiom 22 (axiom_4) R->L }
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh4(rf1(i2003_11_14_17_19_06193, y(i2003_11_14_17_19_06193)), true2, i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193), y(i2003_11_14_17_19_06193))))
% 0.22/0.44 = { by lemma 23 }
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh4(true2, true2, i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193), y(i2003_11_14_17_19_06193))))
% 0.22/0.44 = { by axiom 19 (axiom_4) }
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(w(i2003_11_14_17_19_06193)))
% 0.22/0.44 = { by axiom 18 (axiom_3) R->L }
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh6(true2, true2, i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193), y2(i2003_11_14_17_19_06193))))
% 0.22/0.44 = { by axiom 3 (axiom_2_1) R->L }
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh6(fresh18(true2, true2, i2003_11_14_17_19_06193), true2, i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193), y2(i2003_11_14_17_19_06193))))
% 0.22/0.44 = { by axiom 1 (axiom_9) R->L }
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh6(fresh18(cUnsatisfiable(i2003_11_14_17_19_06193), true2, i2003_11_14_17_19_06193), true2, i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193), y2(i2003_11_14_17_19_06193))))
% 0.22/0.44 = { by axiom 9 (axiom_2_1) }
% 0.22/0.44 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh6(rf(i2003_11_14_17_19_06193, y2(i2003_11_14_17_19_06193)), true2, i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193), y2(i2003_11_14_17_19_06193))))
% 0.22/0.44 = { by axiom 21 (axiom_3) }
% 0.22/0.45 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh5(rf(i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193)), true2, w(i2003_11_14_17_19_06193), y2(i2003_11_14_17_19_06193))))
% 0.22/0.45 = { by axiom 15 (axiom_11) R->L }
% 0.22/0.45 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh5(fresh21(rs(i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193)), true2, i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193)), true2, w(i2003_11_14_17_19_06193), y2(i2003_11_14_17_19_06193))))
% 0.22/0.45 = { by lemma 24 }
% 0.22/0.45 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh5(fresh21(true2, true2, i2003_11_14_17_19_06193, w(i2003_11_14_17_19_06193)), true2, w(i2003_11_14_17_19_06193), y2(i2003_11_14_17_19_06193))))
% 0.22/0.45 = { by axiom 6 (axiom_11) }
% 0.22/0.45 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(fresh5(true2, true2, w(i2003_11_14_17_19_06193), y2(i2003_11_14_17_19_06193))))
% 0.22/0.45 = { by axiom 13 (axiom_3) }
% 0.22/0.45 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), cp(y2(i2003_11_14_17_19_06193)))
% 0.22/0.45 = { by axiom 8 (axiom_2) R->L }
% 0.22/0.45 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), fresh19(cUnsatisfiable(i2003_11_14_17_19_06193), true2, i2003_11_14_17_19_06193))
% 0.22/0.45 = { by axiom 1 (axiom_9) }
% 0.22/0.45 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), fresh19(true2, true2, i2003_11_14_17_19_06193))
% 0.22/0.45 = { by axiom 2 (axiom_2) }
% 0.22/0.45 tuple(cUnsatisfiable(i2003_11_14_17_19_06193), true2)
% 0.22/0.45 = { by axiom 1 (axiom_9) }
% 0.22/0.45 tuple(true2, true2)
% 0.22/0.45 % SZS output end Proof
% 0.22/0.45
% 0.22/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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