TSTP Solution File: KRS115+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS115+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 : n002.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 05:52:57 EDT 2023
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KRS115+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.14 % 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 : n002.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 02:16:19 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.43 Command-line arguments: --no-flatten-goal
% 0.20/0.43
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 Take the following subset of the input axioms:
% 0.20/0.44 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.20/0.44 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.20/0.44 fof(axiom_10, axiom, ![Y, X2]: (rr(X2, Y) => rf1(X2, Y))).
% 0.20/0.44 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y3]: (rf2(X2, Y3) & cp2(Y3)) & (?[Y2]: (rf1(X2, Y2) & cp1(Y2)) & ?[Y4]: (rr(X2, Y4) & cowlThing(Y4)))))).
% 0.20/0.44 fof(axiom_3, axiom, ![X2]: (cp1(X2) => cp2xcomp(X2))).
% 0.20/0.44 fof(axiom_4, axiom, ![X2]: (cp2(X2) <=> ~?[Y4]: ra_Px1(X2, Y4))).
% 0.20/0.44 fof(axiom_5, axiom, ![X2]: (cp2xcomp(X2) <=> ?[Y0]: ra_Px1(X2, Y0))).
% 0.20/0.44 fof(axiom_6, axiom, ![X2]: (cowlThing(X2) => ![Y1, Y0_2]: ((rf1(X2, Y0_2) & rf1(X2, Y1)) => Y0_2=Y1))).
% 0.20/0.44 fof(axiom_7, axiom, ![X2]: (cowlThing(X2) => ![Y0_2, Y1_2]: ((rf2(X2, Y0_2) & rf2(X2, Y1_2)) => Y0_2=Y1_2))).
% 0.20/0.44 fof(axiom_8, axiom, cUnsatisfiable(i2003_11_14_17_21_30578)).
% 0.20/0.44 fof(axiom_9, axiom, ![X2, Y4]: (rr(X2, Y4) => rf2(X2, Y4))).
% 0.20/0.44
% 0.20/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.44 fresh(y, y, x1...xn) = u
% 0.20/0.44 C => fresh(s, t, x1...xn) = v
% 0.20/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.44 variables of u and v.
% 0.20/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.44 input problem has no model of domain size 1).
% 0.20/0.44
% 0.20/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.44
% 0.20/0.44 Axiom 1 (axiom_0): cowlThing(X) = true2.
% 0.20/0.44 Axiom 2 (axiom_8): cUnsatisfiable(i2003_11_14_17_21_30578) = true2.
% 0.20/0.44 Axiom 3 (axiom_2_1): fresh11(X, X, Y) = true2.
% 0.20/0.44 Axiom 4 (axiom_2_2): fresh10(X, X, Y) = true2.
% 0.20/0.44 Axiom 5 (axiom_2_3): fresh9(X, X, Y) = true2.
% 0.20/0.44 Axiom 6 (axiom_2_4): fresh8(X, X, Y) = true2.
% 0.20/0.44 Axiom 7 (axiom_2_5): fresh7(X, X, Y) = true2.
% 0.20/0.44 Axiom 8 (axiom_3): fresh6(X, X, Y) = true2.
% 0.20/0.44 Axiom 9 (axiom_5): fresh5(X, X, Y) = true2.
% 0.20/0.44 Axiom 10 (axiom_6): fresh17(X, X, Y, Z) = Z.
% 0.20/0.44 Axiom 11 (axiom_7): fresh15(X, X, Y, Z) = Z.
% 0.20/0.44 Axiom 12 (axiom_10): fresh12(X, X, Y, Z) = true2.
% 0.20/0.44 Axiom 13 (axiom_2_1): fresh11(cUnsatisfiable(X), true2, X) = cp1(y3(X)).
% 0.20/0.44 Axiom 14 (axiom_2_2): fresh10(cUnsatisfiable(X), true2, X) = cp2(y4(X)).
% 0.20/0.44 Axiom 15 (axiom_2_3): fresh9(cUnsatisfiable(X), true2, X) = rf1(X, y3(X)).
% 0.20/0.44 Axiom 16 (axiom_2_4): fresh8(cUnsatisfiable(X), true2, X) = rf2(X, y4(X)).
% 0.20/0.44 Axiom 17 (axiom_2_5): fresh7(cUnsatisfiable(X), true2, X) = rr(X, y2(X)).
% 0.20/0.44 Axiom 18 (axiom_3): fresh6(cp1(X), true2, X) = cp2xcomp(X).
% 0.20/0.44 Axiom 19 (axiom_5): fresh5(cp2xcomp(X), true2, X) = ra_Px1(X, y0(X)).
% 0.20/0.44 Axiom 20 (axiom_9): fresh3(X, X, Y, Z) = true2.
% 0.20/0.44 Axiom 21 (axiom_7): fresh(X, X, Y, Z, W) = Z.
% 0.20/0.44 Axiom 22 (axiom_6): fresh16(X, X, Y, Z, W) = fresh17(cowlThing(Y), true2, Z, W).
% 0.20/0.44 Axiom 23 (axiom_7): fresh14(X, X, Y, Z, W) = fresh15(cowlThing(Y), true2, Z, W).
% 0.20/0.44 Axiom 24 (axiom_6): fresh2(X, X, Y, Z, W) = Z.
% 0.20/0.44 Axiom 25 (axiom_10): fresh12(rr(X, Y), true2, X, Y) = rf1(X, Y).
% 0.20/0.44 Axiom 26 (axiom_9): fresh3(rr(X, Y), true2, X, Y) = rf2(X, Y).
% 0.20/0.44 Axiom 27 (axiom_7): fresh14(rf2(X, Y), true2, X, Z, Y) = fresh(rf2(X, Z), true2, X, Z, Y).
% 0.20/0.44 Axiom 28 (axiom_6): fresh16(rf1(X, Y), true2, X, Z, Y) = fresh2(rf1(X, Z), true2, X, Z, Y).
% 0.20/0.44
% 0.20/0.44 Lemma 29: rr(i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578)) = true2.
% 0.20/0.44 Proof:
% 0.20/0.44 rr(i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578))
% 0.20/0.44 = { by axiom 17 (axiom_2_5) R->L }
% 0.20/0.44 fresh7(cUnsatisfiable(i2003_11_14_17_21_30578), true2, i2003_11_14_17_21_30578)
% 0.20/0.44 = { by axiom 2 (axiom_8) }
% 0.20/0.44 fresh7(true2, true2, i2003_11_14_17_21_30578)
% 0.20/0.44 = { by axiom 7 (axiom_2_5) }
% 0.20/0.44 true2
% 0.20/0.44
% 0.20/0.44 Lemma 30: y3(i2003_11_14_17_21_30578) = y4(i2003_11_14_17_21_30578).
% 0.20/0.44 Proof:
% 0.20/0.44 y3(i2003_11_14_17_21_30578)
% 0.20/0.44 = { by axiom 10 (axiom_6) R->L }
% 0.20/0.44 fresh17(true2, true2, y2(i2003_11_14_17_21_30578), y3(i2003_11_14_17_21_30578))
% 0.20/0.44 = { by axiom 1 (axiom_0) R->L }
% 0.20/0.44 fresh17(cowlThing(i2003_11_14_17_21_30578), true2, y2(i2003_11_14_17_21_30578), y3(i2003_11_14_17_21_30578))
% 0.20/0.44 = { by axiom 22 (axiom_6) R->L }
% 0.20/0.44 fresh16(true2, true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y3(i2003_11_14_17_21_30578))
% 0.20/0.44 = { by axiom 5 (axiom_2_3) R->L }
% 0.20/0.44 fresh16(fresh9(true2, true2, i2003_11_14_17_21_30578), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y3(i2003_11_14_17_21_30578))
% 0.20/0.44 = { by axiom 2 (axiom_8) R->L }
% 0.20/0.44 fresh16(fresh9(cUnsatisfiable(i2003_11_14_17_21_30578), true2, i2003_11_14_17_21_30578), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y3(i2003_11_14_17_21_30578))
% 0.20/0.44 = { by axiom 15 (axiom_2_3) }
% 0.20/0.44 fresh16(rf1(i2003_11_14_17_21_30578, y3(i2003_11_14_17_21_30578)), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y3(i2003_11_14_17_21_30578))
% 0.20/0.44 = { by axiom 28 (axiom_6) }
% 0.20/0.45 fresh2(rf1(i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578)), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y3(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 25 (axiom_10) R->L }
% 0.20/0.45 fresh2(fresh12(rr(i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578)), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578)), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y3(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by lemma 29 }
% 0.20/0.45 fresh2(fresh12(true2, true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578)), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y3(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 12 (axiom_10) }
% 0.20/0.45 fresh2(true2, true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y3(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 24 (axiom_6) }
% 0.20/0.45 y2(i2003_11_14_17_21_30578)
% 0.20/0.45 = { by axiom 21 (axiom_7) R->L }
% 0.20/0.45 fresh(true2, true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y4(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 20 (axiom_9) R->L }
% 0.20/0.45 fresh(fresh3(true2, true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578)), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y4(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by lemma 29 R->L }
% 0.20/0.45 fresh(fresh3(rr(i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578)), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578)), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y4(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 26 (axiom_9) }
% 0.20/0.45 fresh(rf2(i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578)), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y4(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 27 (axiom_7) R->L }
% 0.20/0.45 fresh14(rf2(i2003_11_14_17_21_30578, y4(i2003_11_14_17_21_30578)), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y4(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 16 (axiom_2_4) R->L }
% 0.20/0.45 fresh14(fresh8(cUnsatisfiable(i2003_11_14_17_21_30578), true2, i2003_11_14_17_21_30578), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y4(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 2 (axiom_8) }
% 0.20/0.45 fresh14(fresh8(true2, true2, i2003_11_14_17_21_30578), true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y4(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 6 (axiom_2_4) }
% 0.20/0.45 fresh14(true2, true2, i2003_11_14_17_21_30578, y2(i2003_11_14_17_21_30578), y4(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 23 (axiom_7) }
% 0.20/0.45 fresh15(cowlThing(i2003_11_14_17_21_30578), true2, y2(i2003_11_14_17_21_30578), y4(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 1 (axiom_0) }
% 0.20/0.45 fresh15(true2, true2, y2(i2003_11_14_17_21_30578), y4(i2003_11_14_17_21_30578))
% 0.20/0.45 = { by axiom 11 (axiom_7) }
% 0.20/0.45 y4(i2003_11_14_17_21_30578)
% 0.20/0.45
% 0.20/0.45 Goal 1 (axiom_4_1): tuple(cp2(X), ra_Px1(X, Y)) = tuple(true2, true2).
% 0.20/0.45 The goal is true when:
% 0.20/0.45 X = y4(i2003_11_14_17_21_30578)
% 0.20/0.45 Y = y0(y4(i2003_11_14_17_21_30578))
% 0.20/0.45
% 0.20/0.45 Proof:
% 0.20/0.45 tuple(cp2(y4(i2003_11_14_17_21_30578)), ra_Px1(y4(i2003_11_14_17_21_30578), y0(y4(i2003_11_14_17_21_30578))))
% 0.20/0.45 = { by lemma 30 R->L }
% 0.20/0.45 tuple(cp2(y4(i2003_11_14_17_21_30578)), ra_Px1(y4(i2003_11_14_17_21_30578), y0(y3(i2003_11_14_17_21_30578))))
% 0.20/0.45 = { by lemma 30 R->L }
% 0.20/0.45 tuple(cp2(y4(i2003_11_14_17_21_30578)), ra_Px1(y3(i2003_11_14_17_21_30578), y0(y3(i2003_11_14_17_21_30578))))
% 0.20/0.45 = { by axiom 19 (axiom_5) R->L }
% 0.20/0.45 tuple(cp2(y4(i2003_11_14_17_21_30578)), fresh5(cp2xcomp(y3(i2003_11_14_17_21_30578)), true2, y3(i2003_11_14_17_21_30578)))
% 0.20/0.45 = { by axiom 18 (axiom_3) R->L }
% 0.20/0.45 tuple(cp2(y4(i2003_11_14_17_21_30578)), fresh5(fresh6(cp1(y3(i2003_11_14_17_21_30578)), true2, y3(i2003_11_14_17_21_30578)), true2, y3(i2003_11_14_17_21_30578)))
% 0.20/0.45 = { by axiom 13 (axiom_2_1) R->L }
% 0.20/0.45 tuple(cp2(y4(i2003_11_14_17_21_30578)), fresh5(fresh6(fresh11(cUnsatisfiable(i2003_11_14_17_21_30578), true2, i2003_11_14_17_21_30578), true2, y3(i2003_11_14_17_21_30578)), true2, y3(i2003_11_14_17_21_30578)))
% 0.20/0.45 = { by axiom 2 (axiom_8) }
% 0.20/0.45 tuple(cp2(y4(i2003_11_14_17_21_30578)), fresh5(fresh6(fresh11(true2, true2, i2003_11_14_17_21_30578), true2, y3(i2003_11_14_17_21_30578)), true2, y3(i2003_11_14_17_21_30578)))
% 0.20/0.45 = { by axiom 3 (axiom_2_1) }
% 0.20/0.45 tuple(cp2(y4(i2003_11_14_17_21_30578)), fresh5(fresh6(true2, true2, y3(i2003_11_14_17_21_30578)), true2, y3(i2003_11_14_17_21_30578)))
% 0.20/0.45 = { by axiom 8 (axiom_3) }
% 0.20/0.45 tuple(cp2(y4(i2003_11_14_17_21_30578)), fresh5(true2, true2, y3(i2003_11_14_17_21_30578)))
% 0.20/0.45 = { by axiom 9 (axiom_5) }
% 0.20/0.45 tuple(cp2(y4(i2003_11_14_17_21_30578)), true2)
% 0.20/0.45 = { by axiom 14 (axiom_2_2) R->L }
% 0.20/0.45 tuple(fresh10(cUnsatisfiable(i2003_11_14_17_21_30578), true2, i2003_11_14_17_21_30578), true2)
% 0.20/0.45 = { by axiom 2 (axiom_8) }
% 0.20/0.45 tuple(fresh10(true2, true2, i2003_11_14_17_21_30578), true2)
% 0.20/0.45 = { by axiom 4 (axiom_2_2) }
% 0.20/0.45 tuple(true2, true2)
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45
% 0.20/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------