TSTP Solution File: KRS109+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS109+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 : n028.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 05:52:55 EDT 2023
% Result : Unsatisfiable 0.21s 0.44s
% 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
% 0.00/0.12 % Problem : KRS109+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 02:06:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.44 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.44
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 Take the following subset of the input axioms:
% 0.21/0.45 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.21/0.45 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.21/0.45 fof(axiom_11, axiom, ![Y, X2]: (rinvS(X2, Y) <=> rs(Y, X2))).
% 0.21/0.45 fof(axiom_13, axiom, cUnsatisfiable(i2003_11_14_17_21_08508)).
% 0.21/0.45 fof(axiom_14, axiom, ![X2, Y2]: (rs(X2, Y2) => rf(X2, Y2))).
% 0.21/0.45 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (cpxcomp(X2) & ?[Y2]: (rf(X2, Y2) & ca_Ax2(Y2))))).
% 0.21/0.45 fof(axiom_3, axiom, ![X2]: (cp(X2) <=> ~?[Y2]: ra_Px1(X2, Y2))).
% 0.21/0.45 fof(axiom_4, axiom, ![X2]: (cpxcomp(X2) <=> ?[Y0]: ra_Px1(X2, Y0))).
% 0.21/0.45 fof(axiom_5, axiom, ![X2]: (ca_Ax2(X2) <=> (![Y2]: (rinvS(X2, Y2) => cp(Y2)) & ![Y2]: (rinvF(X2, Y2) => ca_Vx3(Y2))))).
% 0.21/0.45 fof(axiom_6, axiom, ![X2]: (ca_Vx3(X2) <=> ?[Y2]: (rs(X2, Y2) & cp(Y2)))).
% 0.21/0.45 fof(axiom_7, axiom, ![Z, X2, Y2]: ((rf(X2, Y2) & rf(X2, Z)) => Y2=Z)).
% 0.21/0.45 fof(axiom_9, axiom, ![X2, Y2]: (rinvF(X2, Y2) <=> rf(Y2, X2))).
% 0.21/0.45
% 0.21/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.45 fresh(y, y, x1...xn) = u
% 0.21/0.45 C => fresh(s, t, x1...xn) = v
% 0.21/0.45 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.45 variables of u and v.
% 0.21/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.46 input problem has no model of domain size 1).
% 0.21/0.46
% 0.21/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.46
% 0.21/0.46 Axiom 1 (axiom_13): cUnsatisfiable(i2003_11_14_17_21_08508) = true2.
% 0.21/0.46 Axiom 2 (axiom_2): fresh24(X, X, Y) = true2.
% 0.21/0.46 Axiom 3 (axiom_2_1): fresh23(X, X, Y) = true2.
% 0.21/0.46 Axiom 4 (axiom_2_2): fresh22(X, X, Y) = true2.
% 0.21/0.46 Axiom 5 (axiom_4): fresh20(X, X, Y) = true2.
% 0.21/0.46 Axiom 6 (axiom_5_1): fresh17(X, X, Y) = true2.
% 0.21/0.46 Axiom 7 (axiom_5_2): fresh15(X, X, Y) = true2.
% 0.21/0.46 Axiom 8 (axiom_6_1): fresh11(X, X, Y) = true2.
% 0.21/0.46 Axiom 9 (axiom_11_1): fresh27(X, X, Y, Z) = true2.
% 0.21/0.46 Axiom 10 (axiom_14): fresh26(X, X, Y, Z) = true2.
% 0.21/0.46 Axiom 11 (axiom_2): fresh24(cUnsatisfiable(X), true2, X) = ca_Ax2(y5(X)).
% 0.21/0.46 Axiom 12 (axiom_2_1): fresh23(cUnsatisfiable(X), true2, X) = cpxcomp(X).
% 0.21/0.46 Axiom 13 (axiom_2_2): fresh22(cUnsatisfiable(X), true2, X) = rf(X, y5(X)).
% 0.21/0.46 Axiom 14 (axiom_4): fresh20(cpxcomp(X), true2, X) = ra_Px1(X, y0(X)).
% 0.21/0.46 Axiom 15 (axiom_5_1): fresh18(X, X, Y, Z) = ca_Vx3(Z).
% 0.21/0.46 Axiom 16 (axiom_5_2): fresh16(X, X, Y, Z) = cp(Z).
% 0.21/0.46 Axiom 17 (axiom_6_1): fresh11(ca_Vx3(X), true2, X) = rs(X, y(X)).
% 0.21/0.46 Axiom 18 (axiom_9): fresh8(X, X, Y, Z) = true2.
% 0.21/0.46 Axiom 19 (axiom_7): fresh5(X, X, Y, Z) = Z.
% 0.21/0.46 Axiom 20 (axiom_7): fresh6(X, X, Y, Z, W) = Z.
% 0.21/0.46 Axiom 21 (axiom_11_1): fresh27(rs(X, Y), true2, Y, X) = rinvS(Y, X).
% 0.21/0.46 Axiom 22 (axiom_14): fresh26(rs(X, Y), true2, X, Y) = rf(X, Y).
% 0.21/0.46 Axiom 23 (axiom_5_1): fresh18(rinvF(X, Y), true2, X, Y) = fresh17(ca_Ax2(X), true2, Y).
% 0.21/0.46 Axiom 24 (axiom_5_2): fresh16(rinvS(X, Y), true2, X, Y) = fresh15(ca_Ax2(X), true2, Y).
% 0.21/0.46 Axiom 25 (axiom_9): fresh8(rf(X, Y), true2, Y, X) = rinvF(Y, X).
% 0.21/0.46 Axiom 26 (axiom_7): fresh6(rf(X, Y), true2, X, Z, Y) = fresh5(rf(X, Z), true2, Z, Y).
% 0.21/0.46
% 0.21/0.46 Lemma 27: ca_Ax2(y5(i2003_11_14_17_21_08508)) = true2.
% 0.21/0.46 Proof:
% 0.21/0.46 ca_Ax2(y5(i2003_11_14_17_21_08508))
% 0.21/0.46 = { by axiom 11 (axiom_2) R->L }
% 0.21/0.46 fresh24(cUnsatisfiable(i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by axiom 1 (axiom_13) }
% 0.21/0.46 fresh24(true2, true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by axiom 2 (axiom_2) }
% 0.21/0.46 true2
% 0.21/0.46
% 0.21/0.46 Lemma 28: rf(i2003_11_14_17_21_08508, y5(i2003_11_14_17_21_08508)) = true2.
% 0.21/0.46 Proof:
% 0.21/0.46 rf(i2003_11_14_17_21_08508, y5(i2003_11_14_17_21_08508))
% 0.21/0.46 = { by axiom 13 (axiom_2_2) R->L }
% 0.21/0.46 fresh22(cUnsatisfiable(i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by axiom 1 (axiom_13) }
% 0.21/0.46 fresh22(true2, true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by axiom 4 (axiom_2_2) }
% 0.21/0.46 true2
% 0.21/0.46
% 0.21/0.46 Lemma 29: rs(i2003_11_14_17_21_08508, y(i2003_11_14_17_21_08508)) = true2.
% 0.21/0.46 Proof:
% 0.21/0.46 rs(i2003_11_14_17_21_08508, y(i2003_11_14_17_21_08508))
% 0.21/0.46 = { by axiom 17 (axiom_6_1) R->L }
% 0.21/0.46 fresh11(ca_Vx3(i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by axiom 15 (axiom_5_1) R->L }
% 0.21/0.46 fresh11(fresh18(true2, true2, y5(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by axiom 18 (axiom_9) R->L }
% 0.21/0.46 fresh11(fresh18(fresh8(true2, true2, y5(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2, y5(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by lemma 28 R->L }
% 0.21/0.46 fresh11(fresh18(fresh8(rf(i2003_11_14_17_21_08508, y5(i2003_11_14_17_21_08508)), true2, y5(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2, y5(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by axiom 25 (axiom_9) }
% 0.21/0.46 fresh11(fresh18(rinvF(y5(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2, y5(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by axiom 23 (axiom_5_1) }
% 0.21/0.46 fresh11(fresh17(ca_Ax2(y5(i2003_11_14_17_21_08508)), true2, i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by lemma 27 }
% 0.21/0.46 fresh11(fresh17(true2, true2, i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by axiom 6 (axiom_5_1) }
% 0.21/0.46 fresh11(true2, true2, i2003_11_14_17_21_08508)
% 0.21/0.46 = { by axiom 8 (axiom_6_1) }
% 0.21/0.46 true2
% 0.21/0.46
% 0.21/0.46 Goal 1 (axiom_3_1): tuple(cp(X), ra_Px1(X, Y)) = tuple(true2, true2).
% 0.21/0.46 The goal is true when:
% 0.21/0.46 X = i2003_11_14_17_21_08508
% 0.21/0.46 Y = y0(i2003_11_14_17_21_08508)
% 0.21/0.46
% 0.21/0.46 Proof:
% 0.21/0.46 tuple(cp(i2003_11_14_17_21_08508), ra_Px1(i2003_11_14_17_21_08508, y0(i2003_11_14_17_21_08508)))
% 0.21/0.46 = { by axiom 14 (axiom_4) R->L }
% 0.21/0.46 tuple(cp(i2003_11_14_17_21_08508), fresh20(cpxcomp(i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508))
% 0.21/0.46 = { by axiom 12 (axiom_2_1) R->L }
% 0.21/0.46 tuple(cp(i2003_11_14_17_21_08508), fresh20(fresh23(cUnsatisfiable(i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508))
% 0.21/0.46 = { by axiom 1 (axiom_13) }
% 0.21/0.46 tuple(cp(i2003_11_14_17_21_08508), fresh20(fresh23(true2, true2, i2003_11_14_17_21_08508), true2, i2003_11_14_17_21_08508))
% 0.21/0.46 = { by axiom 3 (axiom_2_1) }
% 0.21/0.46 tuple(cp(i2003_11_14_17_21_08508), fresh20(true2, true2, i2003_11_14_17_21_08508))
% 0.21/0.46 = { by axiom 5 (axiom_4) }
% 0.21/0.46 tuple(cp(i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by axiom 16 (axiom_5_2) R->L }
% 0.21/0.46 tuple(fresh16(true2, true2, y(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by axiom 9 (axiom_11_1) R->L }
% 0.21/0.46 tuple(fresh16(fresh27(true2, true2, y(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2, y(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by lemma 29 R->L }
% 0.21/0.46 tuple(fresh16(fresh27(rs(i2003_11_14_17_21_08508, y(i2003_11_14_17_21_08508)), true2, y(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2, y(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by axiom 21 (axiom_11_1) }
% 0.21/0.46 tuple(fresh16(rinvS(y(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2, y(i2003_11_14_17_21_08508), i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by axiom 24 (axiom_5_2) }
% 0.21/0.46 tuple(fresh15(ca_Ax2(y(i2003_11_14_17_21_08508)), true2, i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by axiom 20 (axiom_7) R->L }
% 0.21/0.46 tuple(fresh15(ca_Ax2(fresh6(true2, true2, i2003_11_14_17_21_08508, y(i2003_11_14_17_21_08508), y5(i2003_11_14_17_21_08508))), true2, i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by lemma 28 R->L }
% 0.21/0.46 tuple(fresh15(ca_Ax2(fresh6(rf(i2003_11_14_17_21_08508, y5(i2003_11_14_17_21_08508)), true2, i2003_11_14_17_21_08508, y(i2003_11_14_17_21_08508), y5(i2003_11_14_17_21_08508))), true2, i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by axiom 26 (axiom_7) }
% 0.21/0.46 tuple(fresh15(ca_Ax2(fresh5(rf(i2003_11_14_17_21_08508, y(i2003_11_14_17_21_08508)), true2, y(i2003_11_14_17_21_08508), y5(i2003_11_14_17_21_08508))), true2, i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by axiom 22 (axiom_14) R->L }
% 0.21/0.46 tuple(fresh15(ca_Ax2(fresh5(fresh26(rs(i2003_11_14_17_21_08508, y(i2003_11_14_17_21_08508)), true2, i2003_11_14_17_21_08508, y(i2003_11_14_17_21_08508)), true2, y(i2003_11_14_17_21_08508), y5(i2003_11_14_17_21_08508))), true2, i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by lemma 29 }
% 0.21/0.46 tuple(fresh15(ca_Ax2(fresh5(fresh26(true2, true2, i2003_11_14_17_21_08508, y(i2003_11_14_17_21_08508)), true2, y(i2003_11_14_17_21_08508), y5(i2003_11_14_17_21_08508))), true2, i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by axiom 10 (axiom_14) }
% 0.21/0.46 tuple(fresh15(ca_Ax2(fresh5(true2, true2, y(i2003_11_14_17_21_08508), y5(i2003_11_14_17_21_08508))), true2, i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by axiom 19 (axiom_7) }
% 0.21/0.46 tuple(fresh15(ca_Ax2(y5(i2003_11_14_17_21_08508)), true2, i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by lemma 27 }
% 0.21/0.46 tuple(fresh15(true2, true2, i2003_11_14_17_21_08508), true2)
% 0.21/0.46 = { by axiom 7 (axiom_5_2) }
% 0.21/0.46 tuple(true2, true2)
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46
% 0.21/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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