TSTP Solution File: KRS111+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS111+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 : n024.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 05:52:56 EDT 2023
% Result : Unsatisfiable 0.18s 0.42s
% 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
% 0.06/0.12 % Problem : KRS111+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.13 % 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 : n024.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 01:49:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.42 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.18/0.42
% 0.18/0.42 % SZS status Unsatisfiable
% 0.18/0.42
% 0.18/0.43 % SZS output start Proof
% 0.18/0.43 Take the following subset of the input axioms:
% 0.18/0.43 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.18/0.43 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.18/0.43 fof(axiom_11, axiom, cUnsatisfiable(i2003_11_14_17_21_15425)).
% 0.18/0.43 fof(axiom_12, axiom, ![Y, X2]: (rs(X2, Y) => rf(X2, Y))).
% 0.18/0.43 fof(axiom_13, axiom, ![X2, Y4]: (rs(X2, Y4) => rf1(X2, Y4))).
% 0.18/0.43 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y3]: (rf1(X2, Y3) & cpxcomp(Y3)) & (?[Y4]: (rs(X2, Y4) & cowlThing(Y4)) & ?[Y2]: (rf(X2, Y2) & cp(Y2)))))).
% 0.18/0.43 fof(axiom_3, axiom, ![X2]: (cp(X2) <=> ~?[Y4]: ra_Px1(X2, Y4))).
% 0.18/0.43 fof(axiom_4, axiom, ![X2]: (cpxcomp(X2) <=> ?[Y0]: ra_Px1(X2, Y0))).
% 0.18/0.43 fof(axiom_5, axiom, ![Z, X2, Y4]: ((rf(X2, Y4) & rf(X2, Z)) => Y4=Z)).
% 0.18/0.43 fof(axiom_6, axiom, ![X2, Y4, Z2]: ((rf1(X2, Y4) & rf1(X2, Z2)) => Y4=Z2)).
% 0.18/0.43
% 0.18/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.43 fresh(y, y, x1...xn) = u
% 0.18/0.43 C => fresh(s, t, x1...xn) = v
% 0.18/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.43 variables of u and v.
% 0.18/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.43 input problem has no model of domain size 1).
% 0.18/0.43
% 0.18/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.43
% 0.18/0.43 Axiom 1 (axiom_11): cUnsatisfiable(i2003_11_14_17_21_15425) = true2.
% 0.18/0.43 Axiom 2 (axiom_2_1): fresh19(X, X, Y) = true2.
% 0.18/0.43 Axiom 3 (axiom_2_2): fresh18(X, X, Y) = true2.
% 0.18/0.43 Axiom 4 (axiom_2_3): fresh17(X, X, Y) = true2.
% 0.18/0.43 Axiom 5 (axiom_2_4): fresh16(X, X, Y) = true2.
% 0.18/0.43 Axiom 6 (axiom_2_5): fresh15(X, X, Y) = true2.
% 0.18/0.43 Axiom 7 (axiom_4): fresh14(X, X, Y) = true2.
% 0.18/0.43 Axiom 8 (axiom_13): fresh22(X, X, Y, Z) = true2.
% 0.18/0.43 Axiom 9 (axiom_12): fresh21(X, X, Y, Z) = true2.
% 0.18/0.43 Axiom 10 (axiom_2_1): fresh19(cUnsatisfiable(X), true2, X) = cp(y2(X)).
% 0.18/0.43 Axiom 11 (axiom_2_2): fresh18(cUnsatisfiable(X), true2, X) = cpxcomp(y4(X)).
% 0.18/0.43 Axiom 12 (axiom_2_3): fresh17(cUnsatisfiable(X), true2, X) = rf(X, y2(X)).
% 0.18/0.43 Axiom 13 (axiom_2_4): fresh16(cUnsatisfiable(X), true2, X) = rf1(X, y4(X)).
% 0.18/0.43 Axiom 14 (axiom_2_5): fresh15(cUnsatisfiable(X), true2, X) = rs(X, y3(X)).
% 0.18/0.43 Axiom 15 (axiom_4): fresh14(cpxcomp(X), true2, X) = ra_Px1(X, y0(X)).
% 0.18/0.43 Axiom 16 (axiom_5): fresh5(X, X, Y, Z) = Z.
% 0.18/0.43 Axiom 17 (axiom_6): fresh3(X, X, Y, Z) = Z.
% 0.18/0.43 Axiom 18 (axiom_5): fresh6(X, X, Y, Z, W) = Z.
% 0.18/0.43 Axiom 19 (axiom_6): fresh4(X, X, Y, Z, W) = Z.
% 0.18/0.43 Axiom 20 (axiom_13): fresh22(rs(X, Y), true2, X, Y) = rf1(X, Y).
% 0.18/0.43 Axiom 21 (axiom_12): fresh21(rs(X, Y), true2, X, Y) = rf(X, Y).
% 0.18/0.43 Axiom 22 (axiom_5): fresh6(rf(X, Y), true2, X, Z, Y) = fresh5(rf(X, Z), true2, Z, Y).
% 0.18/0.43 Axiom 23 (axiom_6): fresh4(rf1(X, Y), true2, X, Z, Y) = fresh3(rf1(X, Z), true2, Z, Y).
% 0.18/0.43
% 0.18/0.43 Lemma 24: rs(i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425)) = true2.
% 0.18/0.43 Proof:
% 0.18/0.43 rs(i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425))
% 0.18/0.43 = { by axiom 14 (axiom_2_5) R->L }
% 0.18/0.43 fresh15(cUnsatisfiable(i2003_11_14_17_21_15425), true2, i2003_11_14_17_21_15425)
% 0.18/0.43 = { by axiom 1 (axiom_11) }
% 0.18/0.43 fresh15(true2, true2, i2003_11_14_17_21_15425)
% 0.18/0.43 = { by axiom 6 (axiom_2_5) }
% 0.18/0.44 true2
% 0.18/0.44
% 0.18/0.44 Goal 1 (axiom_3_1): tuple(cp(X), ra_Px1(X, Y)) = tuple(true2, true2).
% 0.18/0.44 The goal is true when:
% 0.18/0.44 X = y4(i2003_11_14_17_21_15425)
% 0.18/0.44 Y = y0(y4(i2003_11_14_17_21_15425))
% 0.18/0.44
% 0.18/0.44 Proof:
% 0.18/0.44 tuple(cp(y4(i2003_11_14_17_21_15425)), ra_Px1(y4(i2003_11_14_17_21_15425), y0(y4(i2003_11_14_17_21_15425))))
% 0.18/0.44 = { by axiom 15 (axiom_4) R->L }
% 0.18/0.44 tuple(cp(y4(i2003_11_14_17_21_15425)), fresh14(cpxcomp(y4(i2003_11_14_17_21_15425)), true2, y4(i2003_11_14_17_21_15425)))
% 0.18/0.44 = { by axiom 11 (axiom_2_2) R->L }
% 0.18/0.44 tuple(cp(y4(i2003_11_14_17_21_15425)), fresh14(fresh18(cUnsatisfiable(i2003_11_14_17_21_15425), true2, i2003_11_14_17_21_15425), true2, y4(i2003_11_14_17_21_15425)))
% 0.18/0.44 = { by axiom 1 (axiom_11) }
% 0.18/0.44 tuple(cp(y4(i2003_11_14_17_21_15425)), fresh14(fresh18(true2, true2, i2003_11_14_17_21_15425), true2, y4(i2003_11_14_17_21_15425)))
% 0.18/0.44 = { by axiom 3 (axiom_2_2) }
% 0.18/0.44 tuple(cp(y4(i2003_11_14_17_21_15425)), fresh14(true2, true2, y4(i2003_11_14_17_21_15425)))
% 0.18/0.44 = { by axiom 7 (axiom_4) }
% 0.18/0.44 tuple(cp(y4(i2003_11_14_17_21_15425)), true2)
% 0.18/0.44 = { by axiom 17 (axiom_6) R->L }
% 0.18/0.44 tuple(cp(fresh3(true2, true2, y3(i2003_11_14_17_21_15425), y4(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 8 (axiom_13) R->L }
% 0.18/0.44 tuple(cp(fresh3(fresh22(true2, true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425)), true2, y3(i2003_11_14_17_21_15425), y4(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by lemma 24 R->L }
% 0.18/0.44 tuple(cp(fresh3(fresh22(rs(i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425)), true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425)), true2, y3(i2003_11_14_17_21_15425), y4(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 20 (axiom_13) }
% 0.18/0.44 tuple(cp(fresh3(rf1(i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425)), true2, y3(i2003_11_14_17_21_15425), y4(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 23 (axiom_6) R->L }
% 0.18/0.44 tuple(cp(fresh4(rf1(i2003_11_14_17_21_15425, y4(i2003_11_14_17_21_15425)), true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425), y4(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 13 (axiom_2_4) R->L }
% 0.18/0.44 tuple(cp(fresh4(fresh16(cUnsatisfiable(i2003_11_14_17_21_15425), true2, i2003_11_14_17_21_15425), true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425), y4(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 1 (axiom_11) }
% 0.18/0.44 tuple(cp(fresh4(fresh16(true2, true2, i2003_11_14_17_21_15425), true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425), y4(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 5 (axiom_2_4) }
% 0.18/0.44 tuple(cp(fresh4(true2, true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425), y4(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 19 (axiom_6) }
% 0.18/0.44 tuple(cp(y3(i2003_11_14_17_21_15425)), true2)
% 0.18/0.44 = { by axiom 18 (axiom_5) R->L }
% 0.18/0.44 tuple(cp(fresh6(true2, true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425), y2(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 4 (axiom_2_3) R->L }
% 0.18/0.44 tuple(cp(fresh6(fresh17(true2, true2, i2003_11_14_17_21_15425), true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425), y2(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.18/0.44 tuple(cp(fresh6(fresh17(cUnsatisfiable(i2003_11_14_17_21_15425), true2, i2003_11_14_17_21_15425), true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425), y2(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 12 (axiom_2_3) }
% 0.18/0.44 tuple(cp(fresh6(rf(i2003_11_14_17_21_15425, y2(i2003_11_14_17_21_15425)), true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425), y2(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 22 (axiom_5) }
% 0.18/0.44 tuple(cp(fresh5(rf(i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425)), true2, y3(i2003_11_14_17_21_15425), y2(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 21 (axiom_12) R->L }
% 0.18/0.44 tuple(cp(fresh5(fresh21(rs(i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425)), true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425)), true2, y3(i2003_11_14_17_21_15425), y2(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by lemma 24 }
% 0.18/0.44 tuple(cp(fresh5(fresh21(true2, true2, i2003_11_14_17_21_15425, y3(i2003_11_14_17_21_15425)), true2, y3(i2003_11_14_17_21_15425), y2(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 9 (axiom_12) }
% 0.18/0.44 tuple(cp(fresh5(true2, true2, y3(i2003_11_14_17_21_15425), y2(i2003_11_14_17_21_15425))), true2)
% 0.18/0.44 = { by axiom 16 (axiom_5) }
% 0.18/0.44 tuple(cp(y2(i2003_11_14_17_21_15425)), true2)
% 0.18/0.44 = { by axiom 10 (axiom_2_1) R->L }
% 0.18/0.44 tuple(fresh19(cUnsatisfiable(i2003_11_14_17_21_15425), true2, i2003_11_14_17_21_15425), true2)
% 0.18/0.44 = { by axiom 1 (axiom_11) }
% 0.18/0.44 tuple(fresh19(true2, true2, i2003_11_14_17_21_15425), true2)
% 0.18/0.44 = { by axiom 2 (axiom_2_1) }
% 0.18/0.44 tuple(true2, true2)
% 0.18/0.44 % SZS output end Proof
% 0.18/0.44
% 0.18/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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