TSTP Solution File: KRS112+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS112+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 05:52:56 EDT 2023
% Result : Unsatisfiable 0.17s 0.39s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS112+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 01:46:24 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.39 Command-line arguments: --no-flatten-goal
% 0.17/0.39
% 0.17/0.39 % SZS status Unsatisfiable
% 0.17/0.39
% 0.17/0.40 % SZS output start Proof
% 0.17/0.40 Take the following subset of the input axioms:
% 0.17/0.40 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.17/0.40 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.17/0.40 fof(axiom_10, axiom, ![Y, X2]: (rinvF1(X2, Y) <=> rf1(Y, X2))).
% 0.17/0.40 fof(axiom_13, axiom, cUnsatisfiable(i2003_11_14_17_21_19256)).
% 0.17/0.40 fof(axiom_14, axiom, ![X2, Y3]: (rs(X2, Y3) => rf(X2, Y3))).
% 0.17/0.40 fof(axiom_15, axiom, ![X2, Y3]: (rs(X2, Y3) => rf1(X2, Y3))).
% 0.17/0.40 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y3]: (rf1(X2, Y3) & ca_Ax2(Y3)) & ?[Y2]: (rf(X2, Y2) & cp(Y2))))).
% 0.17/0.40 fof(axiom_3, axiom, ![X2]: (cp(X2) <=> ~?[Y3]: ra_Px1(X2, Y3))).
% 0.17/0.40 fof(axiom_4, axiom, ![X2]: (cpxcomp(X2) <=> ?[Y0]: ra_Px1(X2, Y0))).
% 0.17/0.40 fof(axiom_5, axiom, ![X2]: (ca_Ax2(X2) <=> (cpxcomp(X2) & ![Y3]: (rinvF1(X2, Y3) => ca_Vx3(Y3))))).
% 0.17/0.40 fof(axiom_6, axiom, ![X2]: (ca_Vx3(X2) <=> ?[Y3]: (rs(X2, Y3) & cowlThing(Y3)))).
% 0.17/0.40 fof(axiom_7, axiom, ![Z, X2, Y3]: ((rf(X2, Y3) & rf(X2, Z)) => Y3=Z)).
% 0.17/0.40 fof(axiom_8, axiom, ![X2, Y3, Z2]: ((rf1(X2, Y3) & rf1(X2, Z2)) => Y3=Z2)).
% 0.17/0.40
% 0.17/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.17/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.17/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.17/0.40 fresh(y, y, x1...xn) = u
% 0.17/0.40 C => fresh(s, t, x1...xn) = v
% 0.17/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.17/0.40 variables of u and v.
% 0.17/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.17/0.40 input problem has no model of domain size 1).
% 0.17/0.40
% 0.17/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.17/0.40
% 0.17/0.40 Axiom 1 (axiom_13): cUnsatisfiable(i2003_11_14_17_21_19256) = true2.
% 0.17/0.40 Axiom 2 (axiom_2): fresh23(X, X, Y) = true2.
% 0.17/0.40 Axiom 3 (axiom_2_1): fresh22(X, X, Y) = true2.
% 0.17/0.40 Axiom 4 (axiom_2_2): fresh21(X, X, Y) = true2.
% 0.17/0.40 Axiom 5 (axiom_2_3): fresh20(X, X, Y) = true2.
% 0.17/0.40 Axiom 6 (axiom_4): fresh19(X, X, Y) = true2.
% 0.17/0.40 Axiom 7 (axiom_5): fresh17(X, X, Y) = true2.
% 0.17/0.40 Axiom 8 (axiom_5_1): fresh15(X, X, Y) = true2.
% 0.17/0.40 Axiom 9 (axiom_6_1): fresh11(X, X, Y) = true2.
% 0.17/0.40 Axiom 10 (axiom_10): fresh28(X, X, Y, Z) = true2.
% 0.17/0.40 Axiom 11 (axiom_14): fresh25(X, X, Y, Z) = true2.
% 0.17/0.40 Axiom 12 (axiom_15): fresh24(X, X, Y, Z) = true2.
% 0.17/0.40 Axiom 13 (axiom_2): fresh23(cUnsatisfiable(X), true2, X) = ca_Ax2(y5(X)).
% 0.17/0.40 Axiom 14 (axiom_2_1): fresh22(cUnsatisfiable(X), true2, X) = cp(y4(X)).
% 0.17/0.40 Axiom 15 (axiom_2_2): fresh21(cUnsatisfiable(X), true2, X) = rf(X, y4(X)).
% 0.17/0.40 Axiom 16 (axiom_2_3): fresh20(cUnsatisfiable(X), true2, X) = rf1(X, y5(X)).
% 0.17/0.40 Axiom 17 (axiom_4): fresh19(cpxcomp(X), true2, X) = ra_Px1(X, y0(X)).
% 0.17/0.40 Axiom 18 (axiom_5): fresh17(ca_Ax2(X), true2, X) = cpxcomp(X).
% 0.17/0.40 Axiom 19 (axiom_5_1): fresh16(X, X, Y, Z) = ca_Vx3(Z).
% 0.17/0.40 Axiom 20 (axiom_6_1): fresh11(ca_Vx3(X), true2, X) = rs(X, y(X)).
% 0.17/0.40 Axiom 21 (axiom_7): fresh5(X, X, Y, Z) = Z.
% 0.17/0.41 Axiom 22 (axiom_8): fresh3(X, X, Y, Z) = Z.
% 0.17/0.41 Axiom 23 (axiom_7): fresh6(X, X, Y, Z, W) = Z.
% 0.17/0.41 Axiom 24 (axiom_8): fresh4(X, X, Y, Z, W) = Z.
% 0.17/0.41 Axiom 25 (axiom_10): fresh28(rf1(X, Y), true2, Y, X) = rinvF1(Y, X).
% 0.17/0.41 Axiom 26 (axiom_14): fresh25(rs(X, Y), true2, X, Y) = rf(X, Y).
% 0.17/0.41 Axiom 27 (axiom_15): fresh24(rs(X, Y), true2, X, Y) = rf1(X, Y).
% 0.17/0.41 Axiom 28 (axiom_5_1): fresh16(rinvF1(X, Y), true2, X, Y) = fresh15(ca_Ax2(X), true2, Y).
% 0.17/0.41 Axiom 29 (axiom_7): fresh6(rf(X, Y), true2, X, Z, Y) = fresh5(rf(X, Z), true2, Z, Y).
% 0.17/0.41 Axiom 30 (axiom_8): fresh4(rf1(X, Y), true2, X, Z, Y) = fresh3(rf1(X, Z), true2, Z, Y).
% 0.17/0.41
% 0.17/0.41 Lemma 31: ca_Ax2(y5(i2003_11_14_17_21_19256)) = true2.
% 0.17/0.41 Proof:
% 0.17/0.41 ca_Ax2(y5(i2003_11_14_17_21_19256))
% 0.17/0.41 = { by axiom 13 (axiom_2) R->L }
% 0.17/0.41 fresh23(cUnsatisfiable(i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by axiom 1 (axiom_13) }
% 0.17/0.41 fresh23(true2, true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by axiom 2 (axiom_2) }
% 0.17/0.41 true2
% 0.17/0.41
% 0.17/0.41 Lemma 32: rf1(i2003_11_14_17_21_19256, y5(i2003_11_14_17_21_19256)) = true2.
% 0.17/0.41 Proof:
% 0.17/0.41 rf1(i2003_11_14_17_21_19256, y5(i2003_11_14_17_21_19256))
% 0.17/0.41 = { by axiom 16 (axiom_2_3) R->L }
% 0.17/0.41 fresh20(cUnsatisfiable(i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by axiom 1 (axiom_13) }
% 0.17/0.41 fresh20(true2, true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by axiom 5 (axiom_2_3) }
% 0.17/0.41 true2
% 0.17/0.41
% 0.17/0.41 Lemma 33: rs(i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256)) = true2.
% 0.17/0.41 Proof:
% 0.17/0.41 rs(i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256))
% 0.17/0.41 = { by axiom 20 (axiom_6_1) R->L }
% 0.17/0.41 fresh11(ca_Vx3(i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by axiom 19 (axiom_5_1) R->L }
% 0.17/0.41 fresh11(fresh16(true2, true2, y5(i2003_11_14_17_21_19256), i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by axiom 10 (axiom_10) R->L }
% 0.17/0.41 fresh11(fresh16(fresh28(true2, true2, y5(i2003_11_14_17_21_19256), i2003_11_14_17_21_19256), true2, y5(i2003_11_14_17_21_19256), i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by lemma 32 R->L }
% 0.17/0.41 fresh11(fresh16(fresh28(rf1(i2003_11_14_17_21_19256, y5(i2003_11_14_17_21_19256)), true2, y5(i2003_11_14_17_21_19256), i2003_11_14_17_21_19256), true2, y5(i2003_11_14_17_21_19256), i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by axiom 25 (axiom_10) }
% 0.17/0.41 fresh11(fresh16(rinvF1(y5(i2003_11_14_17_21_19256), i2003_11_14_17_21_19256), true2, y5(i2003_11_14_17_21_19256), i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by axiom 28 (axiom_5_1) }
% 0.17/0.41 fresh11(fresh15(ca_Ax2(y5(i2003_11_14_17_21_19256)), true2, i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by lemma 31 }
% 0.17/0.41 fresh11(fresh15(true2, true2, i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by axiom 8 (axiom_5_1) }
% 0.17/0.41 fresh11(true2, true2, i2003_11_14_17_21_19256)
% 0.17/0.41 = { by axiom 9 (axiom_6_1) }
% 0.17/0.41 true2
% 0.17/0.41
% 0.17/0.41 Goal 1 (axiom_3_1): tuple(cp(X), ra_Px1(X, Y)) = tuple(true2, true2).
% 0.17/0.41 The goal is true when:
% 0.17/0.41 X = y4(i2003_11_14_17_21_19256)
% 0.17/0.41 Y = y0(y5(i2003_11_14_17_21_19256))
% 0.17/0.41
% 0.17/0.41 Proof:
% 0.17/0.41 tuple(cp(y4(i2003_11_14_17_21_19256)), ra_Px1(y4(i2003_11_14_17_21_19256), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 14 (axiom_2_1) R->L }
% 0.17/0.41 tuple(fresh22(cUnsatisfiable(i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256), ra_Px1(y4(i2003_11_14_17_21_19256), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 1 (axiom_13) }
% 0.17/0.41 tuple(fresh22(true2, true2, i2003_11_14_17_21_19256), ra_Px1(y4(i2003_11_14_17_21_19256), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 3 (axiom_2_1) }
% 0.17/0.41 tuple(true2, ra_Px1(y4(i2003_11_14_17_21_19256), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 21 (axiom_7) R->L }
% 0.17/0.41 tuple(true2, ra_Px1(fresh5(true2, true2, y(i2003_11_14_17_21_19256), y4(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 11 (axiom_14) R->L }
% 0.17/0.41 tuple(true2, ra_Px1(fresh5(fresh25(true2, true2, i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256)), true2, y(i2003_11_14_17_21_19256), y4(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by lemma 33 R->L }
% 0.17/0.41 tuple(true2, ra_Px1(fresh5(fresh25(rs(i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256)), true2, i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256)), true2, y(i2003_11_14_17_21_19256), y4(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 26 (axiom_14) }
% 0.17/0.41 tuple(true2, ra_Px1(fresh5(rf(i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256)), true2, y(i2003_11_14_17_21_19256), y4(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 29 (axiom_7) R->L }
% 0.17/0.41 tuple(true2, ra_Px1(fresh6(rf(i2003_11_14_17_21_19256, y4(i2003_11_14_17_21_19256)), true2, i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256), y4(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 15 (axiom_2_2) R->L }
% 0.17/0.41 tuple(true2, ra_Px1(fresh6(fresh21(cUnsatisfiable(i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256), y4(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 1 (axiom_13) }
% 0.17/0.41 tuple(true2, ra_Px1(fresh6(fresh21(true2, true2, i2003_11_14_17_21_19256), true2, i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256), y4(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 4 (axiom_2_2) }
% 0.17/0.41 tuple(true2, ra_Px1(fresh6(true2, true2, i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256), y4(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 23 (axiom_7) }
% 0.17/0.41 tuple(true2, ra_Px1(y(i2003_11_14_17_21_19256), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 24 (axiom_8) R->L }
% 0.17/0.41 tuple(true2, ra_Px1(fresh4(true2, true2, i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256), y5(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by lemma 32 R->L }
% 0.17/0.41 tuple(true2, ra_Px1(fresh4(rf1(i2003_11_14_17_21_19256, y5(i2003_11_14_17_21_19256)), true2, i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256), y5(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 30 (axiom_8) }
% 0.17/0.41 tuple(true2, ra_Px1(fresh3(rf1(i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256)), true2, y(i2003_11_14_17_21_19256), y5(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 27 (axiom_15) R->L }
% 0.17/0.41 tuple(true2, ra_Px1(fresh3(fresh24(rs(i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256)), true2, i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256)), true2, y(i2003_11_14_17_21_19256), y5(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by lemma 33 }
% 0.17/0.41 tuple(true2, ra_Px1(fresh3(fresh24(true2, true2, i2003_11_14_17_21_19256, y(i2003_11_14_17_21_19256)), true2, y(i2003_11_14_17_21_19256), y5(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 12 (axiom_15) }
% 0.17/0.41 tuple(true2, ra_Px1(fresh3(true2, true2, y(i2003_11_14_17_21_19256), y5(i2003_11_14_17_21_19256)), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 22 (axiom_8) }
% 0.17/0.41 tuple(true2, ra_Px1(y5(i2003_11_14_17_21_19256), y0(y5(i2003_11_14_17_21_19256))))
% 0.17/0.41 = { by axiom 17 (axiom_4) R->L }
% 0.17/0.41 tuple(true2, fresh19(cpxcomp(y5(i2003_11_14_17_21_19256)), true2, y5(i2003_11_14_17_21_19256)))
% 0.17/0.41 = { by axiom 18 (axiom_5) R->L }
% 0.17/0.41 tuple(true2, fresh19(fresh17(ca_Ax2(y5(i2003_11_14_17_21_19256)), true2, y5(i2003_11_14_17_21_19256)), true2, y5(i2003_11_14_17_21_19256)))
% 0.17/0.41 = { by lemma 31 }
% 0.17/0.41 tuple(true2, fresh19(fresh17(true2, true2, y5(i2003_11_14_17_21_19256)), true2, y5(i2003_11_14_17_21_19256)))
% 0.17/0.41 = { by axiom 7 (axiom_5) }
% 0.17/0.41 tuple(true2, fresh19(true2, true2, y5(i2003_11_14_17_21_19256)))
% 0.17/0.41 = { by axiom 6 (axiom_4) }
% 0.17/0.41 tuple(true2, true2)
% 0.17/0.41 % SZS output end Proof
% 0.17/0.41
% 0.17/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------