TSTP Solution File: KRS120+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS120+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 : n025.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 05:52:58 EDT 2023
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS120+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 02:21:39 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.42 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 Take the following subset of the input axioms:
% 0.20/0.43 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.20/0.43 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.20/0.43 fof(axiom_11, axiom, cUnsatisfiable(i2003_11_14_17_21_48796)).
% 0.20/0.43 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> ?[Y]: (rf(X2, Y) & ca_Ax2(Y)))).
% 0.20/0.43 fof(axiom_3, axiom, ![X2]: (cp1(X2) <=> ~?[Y2]: ra_Px1(X2, Y2))).
% 0.20/0.43 fof(axiom_4, axiom, ![X2]: (cp1xcomp(X2) <=> ?[Y0]: ra_Px1(X2, Y0))).
% 0.20/0.43 fof(axiom_5, axiom, ![X2]: (ca_Ax2(X2) <=> (?[Y2]: (rinvF(X2, Y2) & ca_Vx3(Y2)) & cp1(X2)))).
% 0.20/0.43 fof(axiom_6, axiom, ![X2]: (ca_Vx3(X2) <=> ?[Y2]: (rf(X2, Y2) & cp1xcomp(Y2)))).
% 0.20/0.43 fof(axiom_7, axiom, ![X2]: (cowlThing(X2) => ![Y1, Y0_2]: ((rf(X2, Y0_2) & rf(X2, Y1)) => Y0_2=Y1))).
% 0.20/0.43 fof(axiom_8, axiom, ![X2, Y2]: (rinvF(X2, Y2) <=> rf(Y2, X2))).
% 0.20/0.43
% 0.20/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.43 fresh(y, y, x1...xn) = u
% 0.20/0.43 C => fresh(s, t, x1...xn) = v
% 0.20/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.43 variables of u and v.
% 0.20/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.43 input problem has no model of domain size 1).
% 0.20/0.43
% 0.20/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.43
% 0.20/0.43 Axiom 1 (axiom_11): cUnsatisfiable(i2003_11_14_17_21_48796) = true2.
% 0.20/0.43 Axiom 2 (axiom_0): cowlThing(X) = true2.
% 0.20/0.43 Axiom 3 (axiom_2): fresh19(X, X, Y) = true2.
% 0.20/0.43 Axiom 4 (axiom_4): fresh15(X, X, Y) = true2.
% 0.20/0.43 Axiom 5 (axiom_5): fresh13(X, X, Y) = true2.
% 0.20/0.43 Axiom 6 (axiom_5_1): fresh12(X, X, Y) = true2.
% 0.20/0.43 Axiom 7 (axiom_5_2): fresh11(X, X, Y) = true2.
% 0.20/0.43 Axiom 8 (axiom_6): fresh9(X, X, Y) = true2.
% 0.20/0.43 Axiom 9 (axiom_6_1): fresh8(X, X, Y) = true2.
% 0.20/0.43 Axiom 10 (axiom_7): fresh23(X, X, Y, Z) = Z.
% 0.20/0.43 Axiom 11 (axiom_2): fresh19(cUnsatisfiable(X), true2, X) = ca_Ax2(y4(X)).
% 0.20/0.43 Axiom 12 (axiom_4): fresh15(cp1xcomp(X), true2, X) = ra_Px1(X, y0(X)).
% 0.20/0.43 Axiom 13 (axiom_5): fresh13(ca_Ax2(X), true2, X) = ca_Vx3(y2(X)).
% 0.20/0.43 Axiom 14 (axiom_5_1): fresh12(ca_Ax2(X), true2, X) = cp1(X).
% 0.20/0.43 Axiom 15 (axiom_5_2): fresh11(ca_Ax2(X), true2, X) = rinvF(X, y2(X)).
% 0.20/0.43 Axiom 16 (axiom_6): fresh9(ca_Vx3(X), true2, X) = cp1xcomp(y(X)).
% 0.20/0.43 Axiom 17 (axiom_6_1): fresh8(ca_Vx3(X), true2, X) = rf(X, y(X)).
% 0.20/0.43 Axiom 18 (axiom_8_1): fresh4(X, X, Y, Z) = true2.
% 0.20/0.43 Axiom 19 (axiom_7): fresh(X, X, Y, Z, W) = Z.
% 0.20/0.43 Axiom 20 (axiom_7): fresh22(X, X, Y, Z, W) = fresh23(cowlThing(Y), true2, Z, W).
% 0.20/0.43 Axiom 21 (axiom_8_1): fresh4(rinvF(X, Y), true2, X, Y) = rf(Y, X).
% 0.20/0.43 Axiom 22 (axiom_7): fresh22(rf(X, Y), true2, X, Z, Y) = fresh(rf(X, Z), true2, X, Z, Y).
% 0.20/0.43
% 0.20/0.43 Lemma 23: ca_Ax2(y4(i2003_11_14_17_21_48796)) = true2.
% 0.20/0.43 Proof:
% 0.20/0.43 ca_Ax2(y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 11 (axiom_2) R->L }
% 0.20/0.43 fresh19(cUnsatisfiable(i2003_11_14_17_21_48796), true2, i2003_11_14_17_21_48796)
% 0.20/0.43 = { by axiom 1 (axiom_11) }
% 0.20/0.43 fresh19(true2, true2, i2003_11_14_17_21_48796)
% 0.20/0.43 = { by axiom 3 (axiom_2) }
% 0.20/0.43 true2
% 0.20/0.43
% 0.20/0.43 Lemma 24: ca_Vx3(y2(y4(i2003_11_14_17_21_48796))) = true2.
% 0.20/0.43 Proof:
% 0.20/0.43 ca_Vx3(y2(y4(i2003_11_14_17_21_48796)))
% 0.20/0.43 = { by axiom 13 (axiom_5) R->L }
% 0.20/0.43 fresh13(ca_Ax2(y4(i2003_11_14_17_21_48796)), true2, y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by lemma 23 }
% 0.20/0.43 fresh13(true2, true2, y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 5 (axiom_5) }
% 0.20/0.43 true2
% 0.20/0.43
% 0.20/0.43 Lemma 25: y(y2(y4(i2003_11_14_17_21_48796))) = y4(i2003_11_14_17_21_48796).
% 0.20/0.43 Proof:
% 0.20/0.43 y(y2(y4(i2003_11_14_17_21_48796)))
% 0.20/0.43 = { by axiom 19 (axiom_7) R->L }
% 0.20/0.43 fresh(true2, true2, y2(y4(i2003_11_14_17_21_48796)), y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 9 (axiom_6_1) R->L }
% 0.20/0.43 fresh(fresh8(true2, true2, y2(y4(i2003_11_14_17_21_48796))), true2, y2(y4(i2003_11_14_17_21_48796)), y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by lemma 24 R->L }
% 0.20/0.43 fresh(fresh8(ca_Vx3(y2(y4(i2003_11_14_17_21_48796))), true2, y2(y4(i2003_11_14_17_21_48796))), true2, y2(y4(i2003_11_14_17_21_48796)), y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 17 (axiom_6_1) }
% 0.20/0.43 fresh(rf(y2(y4(i2003_11_14_17_21_48796)), y(y2(y4(i2003_11_14_17_21_48796)))), true2, y2(y4(i2003_11_14_17_21_48796)), y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 22 (axiom_7) R->L }
% 0.20/0.43 fresh22(rf(y2(y4(i2003_11_14_17_21_48796)), y4(i2003_11_14_17_21_48796)), true2, y2(y4(i2003_11_14_17_21_48796)), y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 21 (axiom_8_1) R->L }
% 0.20/0.43 fresh22(fresh4(rinvF(y4(i2003_11_14_17_21_48796), y2(y4(i2003_11_14_17_21_48796))), true2, y4(i2003_11_14_17_21_48796), y2(y4(i2003_11_14_17_21_48796))), true2, y2(y4(i2003_11_14_17_21_48796)), y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 15 (axiom_5_2) R->L }
% 0.20/0.43 fresh22(fresh4(fresh11(ca_Ax2(y4(i2003_11_14_17_21_48796)), true2, y4(i2003_11_14_17_21_48796)), true2, y4(i2003_11_14_17_21_48796), y2(y4(i2003_11_14_17_21_48796))), true2, y2(y4(i2003_11_14_17_21_48796)), y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by lemma 23 }
% 0.20/0.43 fresh22(fresh4(fresh11(true2, true2, y4(i2003_11_14_17_21_48796)), true2, y4(i2003_11_14_17_21_48796), y2(y4(i2003_11_14_17_21_48796))), true2, y2(y4(i2003_11_14_17_21_48796)), y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 7 (axiom_5_2) }
% 0.20/0.43 fresh22(fresh4(true2, true2, y4(i2003_11_14_17_21_48796), y2(y4(i2003_11_14_17_21_48796))), true2, y2(y4(i2003_11_14_17_21_48796)), y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 18 (axiom_8_1) }
% 0.20/0.43 fresh22(true2, true2, y2(y4(i2003_11_14_17_21_48796)), y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 20 (axiom_7) }
% 0.20/0.43 fresh23(cowlThing(y2(y4(i2003_11_14_17_21_48796))), true2, y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 2 (axiom_0) }
% 0.20/0.43 fresh23(true2, true2, y(y2(y4(i2003_11_14_17_21_48796))), y4(i2003_11_14_17_21_48796))
% 0.20/0.43 = { by axiom 10 (axiom_7) }
% 0.20/0.43 y4(i2003_11_14_17_21_48796)
% 0.20/0.43
% 0.20/0.43 Goal 1 (axiom_3_1): tuple(cp1(X), ra_Px1(X, Y)) = tuple(true2, true2).
% 0.20/0.43 The goal is true when:
% 0.20/0.43 X = y4(i2003_11_14_17_21_48796)
% 0.20/0.43 Y = y0(y4(i2003_11_14_17_21_48796))
% 0.20/0.43
% 0.20/0.43 Proof:
% 0.20/0.43 tuple(cp1(y4(i2003_11_14_17_21_48796)), ra_Px1(y4(i2003_11_14_17_21_48796), y0(y4(i2003_11_14_17_21_48796))))
% 0.20/0.43 = { by lemma 25 R->L }
% 0.20/0.43 tuple(cp1(y4(i2003_11_14_17_21_48796)), ra_Px1(y4(i2003_11_14_17_21_48796), y0(y(y2(y4(i2003_11_14_17_21_48796))))))
% 0.20/0.43 = { by lemma 25 R->L }
% 0.20/0.43 tuple(cp1(y4(i2003_11_14_17_21_48796)), ra_Px1(y(y2(y4(i2003_11_14_17_21_48796))), y0(y(y2(y4(i2003_11_14_17_21_48796))))))
% 0.20/0.43 = { by axiom 12 (axiom_4) R->L }
% 0.20/0.43 tuple(cp1(y4(i2003_11_14_17_21_48796)), fresh15(cp1xcomp(y(y2(y4(i2003_11_14_17_21_48796)))), true2, y(y2(y4(i2003_11_14_17_21_48796)))))
% 0.20/0.43 = { by axiom 16 (axiom_6) R->L }
% 0.20/0.43 tuple(cp1(y4(i2003_11_14_17_21_48796)), fresh15(fresh9(ca_Vx3(y2(y4(i2003_11_14_17_21_48796))), true2, y2(y4(i2003_11_14_17_21_48796))), true2, y(y2(y4(i2003_11_14_17_21_48796)))))
% 0.20/0.43 = { by lemma 24 }
% 0.20/0.43 tuple(cp1(y4(i2003_11_14_17_21_48796)), fresh15(fresh9(true2, true2, y2(y4(i2003_11_14_17_21_48796))), true2, y(y2(y4(i2003_11_14_17_21_48796)))))
% 0.20/0.43 = { by axiom 8 (axiom_6) }
% 0.20/0.43 tuple(cp1(y4(i2003_11_14_17_21_48796)), fresh15(true2, true2, y(y2(y4(i2003_11_14_17_21_48796)))))
% 0.20/0.43 = { by axiom 4 (axiom_4) }
% 0.20/0.43 tuple(cp1(y4(i2003_11_14_17_21_48796)), true2)
% 0.20/0.43 = { by axiom 14 (axiom_5_1) R->L }
% 0.20/0.43 tuple(fresh12(ca_Ax2(y4(i2003_11_14_17_21_48796)), true2, y4(i2003_11_14_17_21_48796)), true2)
% 0.20/0.43 = { by lemma 23 }
% 0.20/0.43 tuple(fresh12(true2, true2, y4(i2003_11_14_17_21_48796)), true2)
% 0.20/0.43 = { by axiom 6 (axiom_5_1) }
% 0.20/0.43 tuple(true2, true2)
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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