TSTP Solution File: KRS106+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS106+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 05:52:55 EDT 2023
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS106+1 : TPTP v8.1.2. Released v3.1.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 01:51:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.40 Command-line arguments: --no-flatten-goal
% 0.13/0.40
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 Take the following subset of the input axioms:
% 0.13/0.41 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.13/0.41 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.13/0.42 fof(axiom_10, axiom, ![Y, X2]: (rf3(X2, Y) => rf2(X2, Y))).
% 0.13/0.42 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y3]: (rf3(X2, Y3) & cp2(Y3)) & (?[Y4]: (rf1(X2, Y4) & cp1(Y4)) & ?[Y2]: (rf2(X2, Y2) & cp1xcomp(Y2)))))).
% 0.13/0.42 fof(axiom_3, axiom, ![X2]: (cp1(X2) <=> ~?[Y4]: ra_Px1(X2, Y4))).
% 0.13/0.42 fof(axiom_4, axiom, ![X2]: (cp1xcomp(X2) <=> ?[Y0]: ra_Px1(X2, Y0))).
% 0.13/0.42 fof(axiom_5, axiom, ![Z, X2, Y4]: ((rf1(X2, Y4) & rf1(X2, Z)) => Y4=Z)).
% 0.13/0.42 fof(axiom_6, axiom, ![X2, Y4, Z2]: ((rf2(X2, Y4) & rf2(X2, Z2)) => Y4=Z2)).
% 0.13/0.42 fof(axiom_8, axiom, cUnsatisfiable(i2003_11_14_17_20_57644)).
% 0.13/0.42 fof(axiom_9, axiom, ![X2, Y4]: (rf3(X2, Y4) => rf1(X2, Y4))).
% 0.13/0.42
% 0.13/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.42 fresh(y, y, x1...xn) = u
% 0.13/0.42 C => fresh(s, t, x1...xn) = v
% 0.13/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.42 variables of u and v.
% 0.13/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.42 input problem has no model of domain size 1).
% 0.13/0.42
% 0.13/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.42
% 0.13/0.42 Axiom 1 (axiom_8): cUnsatisfiable(i2003_11_14_17_20_57644) = true2.
% 0.19/0.42 Axiom 2 (axiom_2): fresh16(X, X, Y) = true2.
% 0.19/0.42 Axiom 3 (axiom_2_1): fresh14(X, X, Y) = true2.
% 0.19/0.42 Axiom 4 (axiom_2_3): fresh12(X, X, Y) = true2.
% 0.19/0.42 Axiom 5 (axiom_2_4): fresh11(X, X, Y) = true2.
% 0.19/0.42 Axiom 6 (axiom_2_5): fresh10(X, X, Y) = true2.
% 0.19/0.42 Axiom 7 (axiom_4): fresh9(X, X, Y) = true2.
% 0.19/0.42 Axiom 8 (axiom_2): fresh16(cUnsatisfiable(X), true2, X) = cp1(y3(X)).
% 0.19/0.42 Axiom 9 (axiom_10): fresh15(X, X, Y, Z) = true2.
% 0.19/0.42 Axiom 10 (axiom_2_1): fresh14(cUnsatisfiable(X), true2, X) = cp1xcomp(y2(X)).
% 0.19/0.42 Axiom 11 (axiom_2_3): fresh12(cUnsatisfiable(X), true2, X) = rf1(X, y3(X)).
% 0.19/0.42 Axiom 12 (axiom_2_4): fresh11(cUnsatisfiable(X), true2, X) = rf2(X, y2(X)).
% 0.19/0.42 Axiom 13 (axiom_2_5): fresh10(cUnsatisfiable(X), true2, X) = rf3(X, y4(X)).
% 0.19/0.42 Axiom 14 (axiom_4): fresh9(cp1xcomp(X), true2, X) = ra_Px1(X, y0(X)).
% 0.19/0.42 Axiom 15 (axiom_9): fresh7(X, X, Y, Z) = true2.
% 0.19/0.42 Axiom 16 (axiom_5): fresh5(X, X, Y, Z) = Z.
% 0.19/0.42 Axiom 17 (axiom_6): fresh3(X, X, Y, Z) = Z.
% 0.19/0.42 Axiom 18 (axiom_5): fresh6(X, X, Y, Z, W) = Z.
% 0.19/0.42 Axiom 19 (axiom_6): fresh4(X, X, Y, Z, W) = Z.
% 0.19/0.42 Axiom 20 (axiom_10): fresh15(rf3(X, Y), true2, X, Y) = rf2(X, Y).
% 0.19/0.42 Axiom 21 (axiom_9): fresh7(rf3(X, Y), true2, X, Y) = rf1(X, Y).
% 0.19/0.42 Axiom 22 (axiom_5): fresh6(rf1(X, Y), true2, X, Z, Y) = fresh5(rf1(X, Z), true2, Z, Y).
% 0.19/0.42 Axiom 23 (axiom_6): fresh4(rf2(X, Y), true2, X, Z, Y) = fresh3(rf2(X, Z), true2, Z, Y).
% 0.19/0.42
% 0.19/0.42 Lemma 24: rf3(i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644)) = true2.
% 0.19/0.42 Proof:
% 0.19/0.42 rf3(i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644))
% 0.19/0.42 = { by axiom 13 (axiom_2_5) R->L }
% 0.19/0.42 fresh10(cUnsatisfiable(i2003_11_14_17_20_57644), true2, i2003_11_14_17_20_57644)
% 0.19/0.42 = { by axiom 1 (axiom_8) }
% 0.19/0.42 fresh10(true2, true2, i2003_11_14_17_20_57644)
% 0.19/0.42 = { by axiom 6 (axiom_2_5) }
% 0.19/0.42 true2
% 0.19/0.42
% 0.19/0.42 Lemma 25: y2(i2003_11_14_17_20_57644) = y4(i2003_11_14_17_20_57644).
% 0.19/0.42 Proof:
% 0.19/0.42 y2(i2003_11_14_17_20_57644)
% 0.19/0.42 = { by axiom 17 (axiom_6) R->L }
% 0.19/0.42 fresh3(true2, true2, y4(i2003_11_14_17_20_57644), y2(i2003_11_14_17_20_57644))
% 0.19/0.42 = { by axiom 9 (axiom_10) R->L }
% 0.19/0.42 fresh3(fresh15(true2, true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644)), true2, y4(i2003_11_14_17_20_57644), y2(i2003_11_14_17_20_57644))
% 0.19/0.42 = { by lemma 24 R->L }
% 0.19/0.42 fresh3(fresh15(rf3(i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644)), true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644)), true2, y4(i2003_11_14_17_20_57644), y2(i2003_11_14_17_20_57644))
% 0.19/0.42 = { by axiom 20 (axiom_10) }
% 0.19/0.42 fresh3(rf2(i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644)), true2, y4(i2003_11_14_17_20_57644), y2(i2003_11_14_17_20_57644))
% 0.19/0.42 = { by axiom 23 (axiom_6) R->L }
% 0.19/0.42 fresh4(rf2(i2003_11_14_17_20_57644, y2(i2003_11_14_17_20_57644)), true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644), y2(i2003_11_14_17_20_57644))
% 0.19/0.42 = { by axiom 12 (axiom_2_4) R->L }
% 0.19/0.42 fresh4(fresh11(cUnsatisfiable(i2003_11_14_17_20_57644), true2, i2003_11_14_17_20_57644), true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644), y2(i2003_11_14_17_20_57644))
% 0.19/0.42 = { by axiom 1 (axiom_8) }
% 0.19/0.42 fresh4(fresh11(true2, true2, i2003_11_14_17_20_57644), true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644), y2(i2003_11_14_17_20_57644))
% 0.19/0.42 = { by axiom 5 (axiom_2_4) }
% 0.19/0.42 fresh4(true2, true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644), y2(i2003_11_14_17_20_57644))
% 0.19/0.42 = { by axiom 19 (axiom_6) }
% 0.19/0.42 y4(i2003_11_14_17_20_57644)
% 0.19/0.42
% 0.19/0.42 Goal 1 (axiom_3_1): tuple(cp1(X), ra_Px1(X, Y)) = tuple(true2, true2).
% 0.19/0.42 The goal is true when:
% 0.19/0.42 X = y4(i2003_11_14_17_20_57644)
% 0.19/0.42 Y = y0(y4(i2003_11_14_17_20_57644))
% 0.19/0.42
% 0.19/0.42 Proof:
% 0.19/0.42 tuple(cp1(y4(i2003_11_14_17_20_57644)), ra_Px1(y4(i2003_11_14_17_20_57644), y0(y4(i2003_11_14_17_20_57644))))
% 0.19/0.42 = { by lemma 25 R->L }
% 0.19/0.42 tuple(cp1(y4(i2003_11_14_17_20_57644)), ra_Px1(y4(i2003_11_14_17_20_57644), y0(y2(i2003_11_14_17_20_57644))))
% 0.19/0.42 = { by lemma 25 R->L }
% 0.19/0.42 tuple(cp1(y4(i2003_11_14_17_20_57644)), ra_Px1(y2(i2003_11_14_17_20_57644), y0(y2(i2003_11_14_17_20_57644))))
% 0.19/0.42 = { by axiom 14 (axiom_4) R->L }
% 0.19/0.42 tuple(cp1(y4(i2003_11_14_17_20_57644)), fresh9(cp1xcomp(y2(i2003_11_14_17_20_57644)), true2, y2(i2003_11_14_17_20_57644)))
% 0.19/0.42 = { by axiom 10 (axiom_2_1) R->L }
% 0.19/0.42 tuple(cp1(y4(i2003_11_14_17_20_57644)), fresh9(fresh14(cUnsatisfiable(i2003_11_14_17_20_57644), true2, i2003_11_14_17_20_57644), true2, y2(i2003_11_14_17_20_57644)))
% 0.19/0.42 = { by axiom 1 (axiom_8) }
% 0.19/0.42 tuple(cp1(y4(i2003_11_14_17_20_57644)), fresh9(fresh14(true2, true2, i2003_11_14_17_20_57644), true2, y2(i2003_11_14_17_20_57644)))
% 0.19/0.42 = { by axiom 3 (axiom_2_1) }
% 0.19/0.42 tuple(cp1(y4(i2003_11_14_17_20_57644)), fresh9(true2, true2, y2(i2003_11_14_17_20_57644)))
% 0.19/0.42 = { by axiom 7 (axiom_4) }
% 0.19/0.42 tuple(cp1(y4(i2003_11_14_17_20_57644)), true2)
% 0.19/0.42 = { by axiom 18 (axiom_5) R->L }
% 0.19/0.42 tuple(cp1(fresh6(true2, true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644), y3(i2003_11_14_17_20_57644))), true2)
% 0.19/0.42 = { by axiom 4 (axiom_2_3) R->L }
% 0.19/0.42 tuple(cp1(fresh6(fresh12(true2, true2, i2003_11_14_17_20_57644), true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644), y3(i2003_11_14_17_20_57644))), true2)
% 0.19/0.42 = { by axiom 1 (axiom_8) R->L }
% 0.19/0.42 tuple(cp1(fresh6(fresh12(cUnsatisfiable(i2003_11_14_17_20_57644), true2, i2003_11_14_17_20_57644), true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644), y3(i2003_11_14_17_20_57644))), true2)
% 0.19/0.42 = { by axiom 11 (axiom_2_3) }
% 0.19/0.42 tuple(cp1(fresh6(rf1(i2003_11_14_17_20_57644, y3(i2003_11_14_17_20_57644)), true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644), y3(i2003_11_14_17_20_57644))), true2)
% 0.19/0.42 = { by axiom 22 (axiom_5) }
% 0.19/0.42 tuple(cp1(fresh5(rf1(i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644)), true2, y4(i2003_11_14_17_20_57644), y3(i2003_11_14_17_20_57644))), true2)
% 0.19/0.42 = { by axiom 21 (axiom_9) R->L }
% 0.19/0.42 tuple(cp1(fresh5(fresh7(rf3(i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644)), true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644)), true2, y4(i2003_11_14_17_20_57644), y3(i2003_11_14_17_20_57644))), true2)
% 0.19/0.42 = { by lemma 24 }
% 0.19/0.42 tuple(cp1(fresh5(fresh7(true2, true2, i2003_11_14_17_20_57644, y4(i2003_11_14_17_20_57644)), true2, y4(i2003_11_14_17_20_57644), y3(i2003_11_14_17_20_57644))), true2)
% 0.19/0.42 = { by axiom 15 (axiom_9) }
% 0.19/0.42 tuple(cp1(fresh5(true2, true2, y4(i2003_11_14_17_20_57644), y3(i2003_11_14_17_20_57644))), true2)
% 0.19/0.42 = { by axiom 16 (axiom_5) }
% 0.19/0.42 tuple(cp1(y3(i2003_11_14_17_20_57644)), true2)
% 0.19/0.42 = { by axiom 8 (axiom_2) R->L }
% 0.19/0.42 tuple(fresh16(cUnsatisfiable(i2003_11_14_17_20_57644), true2, i2003_11_14_17_20_57644), true2)
% 0.19/0.42 = { by axiom 1 (axiom_8) }
% 0.19/0.42 tuple(fresh16(true2, true2, i2003_11_14_17_20_57644), true2)
% 0.19/0.42 = { by axiom 2 (axiom_2) }
% 0.19/0.42 tuple(true2, true2)
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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