TSTP Solution File: KRS117+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS117+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 : n003.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 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : KRS117+1 : TPTP v8.1.2. Released v3.1.0.
% 0.13/0.14 % 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 : n003.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 01:10:25 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.46 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.21/0.46
% 0.21/0.46 % SZS status Unsatisfiable
% 0.21/0.46
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 Take the following subset of the input axioms:
% 0.21/0.48 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.21/0.48 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.21/0.48 fof(axiom_11, axiom, cUnsatisfiable(i2003_11_14_17_21_37349)).
% 0.21/0.48 fof(axiom_12, axiom, ![Y, X2]: (rf(X2, Y) => rr(X2, Y))).
% 0.21/0.48 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (ccxcomp(X2) & (![Y2]: (rinvR(X2, Y2) => ca_Vx3(Y2)) & ?[Y2]: (rinvF(X2, Y2) & cd(Y2)))))).
% 0.21/0.48 fof(axiom_3, axiom, ![X2]: (cc(X2) <=> ~?[Y2]: ra_Px1(X2, Y2))).
% 0.21/0.48 fof(axiom_4, axiom, ![X2]: (ccxcomp(X2) <=> ?[Y0]: ra_Px1(X2, Y0))).
% 0.21/0.48 fof(axiom_5, axiom, ![X2]: (cd(X2) <=> (?[Y2]: (rf(X2, Y2) & ccxcomp(Y2)) & cc(X2)))).
% 0.21/0.48 fof(axiom_6, axiom, ![X2]: (ca_Vx3(X2) <=> ?[Y2]: (rinvF(X2, Y2) & cd(Y2)))).
% 0.21/0.48 fof(axiom_7, axiom, ![X2]: (cowlThing(X2) => ![Y1, Y0_2]: ((rf(X2, Y0_2) & rf(X2, Y1)) => Y0_2=Y1))).
% 0.21/0.48 fof(axiom_8, axiom, ![X2, Y2]: (rinvF(X2, Y2) <=> rf(Y2, X2))).
% 0.21/0.48 fof(axiom_9, axiom, ![X2, Y2]: (rinvR(X2, Y2) <=> rr(Y2, X2))).
% 0.21/0.48
% 0.21/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.48 fresh(y, y, x1...xn) = u
% 0.21/0.48 C => fresh(s, t, x1...xn) = v
% 0.21/0.48 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.48 variables of u and v.
% 0.21/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.48 input problem has no model of domain size 1).
% 0.21/0.48
% 0.21/0.48 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.48
% 0.21/0.48 Axiom 1 (axiom_11): cUnsatisfiable(i2003_11_14_17_21_37349) = true2.
% 0.21/0.48 Axiom 2 (axiom_0): cowlThing(X) = true2.
% 0.21/0.48 Axiom 3 (axiom_2_1): fresh20(X, X, Y) = true2.
% 0.21/0.48 Axiom 4 (axiom_2_2): fresh19(X, X, Y) = true2.
% 0.21/0.48 Axiom 5 (axiom_2_3): fresh17(X, X, Y) = true2.
% 0.21/0.48 Axiom 6 (axiom_4): fresh15(X, X, Y) = true2.
% 0.21/0.48 Axiom 7 (axiom_5_1): fresh12(X, X, Y) = true2.
% 0.21/0.48 Axiom 8 (axiom_5_2): fresh11(X, X, Y) = true2.
% 0.21/0.48 Axiom 9 (axiom_5_3): fresh10(X, X, Y) = true2.
% 0.21/0.48 Axiom 10 (axiom_6): fresh9(X, X, Y) = true2.
% 0.21/0.48 Axiom 11 (axiom_6_1): fresh8(X, X, Y) = true2.
% 0.21/0.48 Axiom 12 (axiom_7): fresh26(X, X, Y, Z) = Z.
% 0.21/0.48 Axiom 13 (axiom_12): fresh22(X, X, Y, Z) = true2.
% 0.21/0.48 Axiom 14 (axiom_2_1): fresh20(cUnsatisfiable(X), true2, X) = cd(y5(X)).
% 0.21/0.48 Axiom 15 (axiom_2_2): fresh19(cUnsatisfiable(X), true2, X) = rinvF(X, y5(X)).
% 0.21/0.48 Axiom 16 (axiom_2_3): fresh18(X, X, Y, Z) = ca_Vx3(Z).
% 0.21/0.48 Axiom 17 (axiom_4): fresh15(ccxcomp(X), true2, X) = ra_Px1(X, y0(X)).
% 0.21/0.48 Axiom 18 (axiom_5_1): fresh12(cd(X), true2, X) = cc(X).
% 0.21/0.48 Axiom 19 (axiom_5_2): fresh11(cd(X), true2, X) = ccxcomp(y2(X)).
% 0.21/0.48 Axiom 20 (axiom_5_3): fresh10(cd(X), true2, X) = rf(X, y2(X)).
% 0.21/0.48 Axiom 21 (axiom_6): fresh9(ca_Vx3(X), true2, X) = cd(y(X)).
% 0.21/0.48 Axiom 22 (axiom_6_1): fresh8(ca_Vx3(X), true2, X) = rinvF(X, y(X)).
% 0.21/0.48 Axiom 23 (axiom_8_1): fresh4(X, X, Y, Z) = true2.
% 0.21/0.48 Axiom 24 (axiom_9_1): fresh2(X, X, Y, Z) = true2.
% 0.21/0.48 Axiom 25 (axiom_7): fresh(X, X, Y, Z, W) = Z.
% 0.21/0.48 Axiom 26 (axiom_7): fresh25(X, X, Y, Z, W) = fresh26(cowlThing(Y), true2, Z, W).
% 0.21/0.48 Axiom 27 (axiom_12): fresh22(rf(X, Y), true2, X, Y) = rr(X, Y).
% 0.21/0.48 Axiom 28 (axiom_2_3): fresh18(rinvR(X, Y), true2, X, Y) = fresh17(cUnsatisfiable(X), true2, Y).
% 0.21/0.48 Axiom 29 (axiom_8_1): fresh4(rinvF(X, Y), true2, X, Y) = rf(Y, X).
% 0.21/0.48 Axiom 30 (axiom_9_1): fresh2(rr(X, Y), true2, Y, X) = rinvR(Y, X).
% 0.21/0.48 Axiom 31 (axiom_7): fresh25(rf(X, Y), true2, X, Z, Y) = fresh(rf(X, Z), true2, X, Z, Y).
% 0.21/0.48
% 0.21/0.48 Lemma 32: ca_Vx3(y5(i2003_11_14_17_21_37349)) = true2.
% 0.21/0.48 Proof:
% 0.21/0.48 ca_Vx3(y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 16 (axiom_2_3) R->L }
% 0.21/0.48 fresh18(true2, true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 24 (axiom_9_1) R->L }
% 0.21/0.48 fresh18(fresh2(true2, true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 13 (axiom_12) R->L }
% 0.21/0.48 fresh18(fresh2(fresh22(true2, true2, y5(i2003_11_14_17_21_37349), i2003_11_14_17_21_37349), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 23 (axiom_8_1) R->L }
% 0.21/0.48 fresh18(fresh2(fresh22(fresh4(true2, true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, y5(i2003_11_14_17_21_37349), i2003_11_14_17_21_37349), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 4 (axiom_2_2) R->L }
% 0.21/0.48 fresh18(fresh2(fresh22(fresh4(fresh19(true2, true2, i2003_11_14_17_21_37349), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, y5(i2003_11_14_17_21_37349), i2003_11_14_17_21_37349), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 1 (axiom_11) R->L }
% 0.21/0.48 fresh18(fresh2(fresh22(fresh4(fresh19(cUnsatisfiable(i2003_11_14_17_21_37349), true2, i2003_11_14_17_21_37349), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, y5(i2003_11_14_17_21_37349), i2003_11_14_17_21_37349), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 15 (axiom_2_2) }
% 0.21/0.48 fresh18(fresh2(fresh22(fresh4(rinvF(i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, y5(i2003_11_14_17_21_37349), i2003_11_14_17_21_37349), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 29 (axiom_8_1) }
% 0.21/0.48 fresh18(fresh2(fresh22(rf(y5(i2003_11_14_17_21_37349), i2003_11_14_17_21_37349), true2, y5(i2003_11_14_17_21_37349), i2003_11_14_17_21_37349), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 27 (axiom_12) }
% 0.21/0.48 fresh18(fresh2(rr(y5(i2003_11_14_17_21_37349), i2003_11_14_17_21_37349), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 30 (axiom_9_1) }
% 0.21/0.48 fresh18(rinvR(i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349)), true2, i2003_11_14_17_21_37349, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 28 (axiom_2_3) }
% 0.21/0.48 fresh17(cUnsatisfiable(i2003_11_14_17_21_37349), true2, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 1 (axiom_11) }
% 0.21/0.48 fresh17(true2, true2, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 5 (axiom_2_3) }
% 0.21/0.48 true2
% 0.21/0.48
% 0.21/0.48 Lemma 33: cd(y(y5(i2003_11_14_17_21_37349))) = true2.
% 0.21/0.48 Proof:
% 0.21/0.48 cd(y(y5(i2003_11_14_17_21_37349)))
% 0.21/0.48 = { by axiom 21 (axiom_6) R->L }
% 0.21/0.48 fresh9(ca_Vx3(y5(i2003_11_14_17_21_37349)), true2, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by lemma 32 }
% 0.21/0.48 fresh9(true2, true2, y5(i2003_11_14_17_21_37349))
% 0.21/0.48 = { by axiom 10 (axiom_6) }
% 0.21/0.49 true2
% 0.21/0.49
% 0.21/0.49 Goal 1 (axiom_3_1): tuple(cc(X), ra_Px1(X, Y)) = tuple(true2, true2).
% 0.21/0.49 The goal is true when:
% 0.21/0.49 X = y2(y(y5(i2003_11_14_17_21_37349)))
% 0.21/0.49 Y = y0(y2(y(y5(i2003_11_14_17_21_37349))))
% 0.21/0.49
% 0.21/0.49 Proof:
% 0.21/0.49 tuple(cc(y2(y(y5(i2003_11_14_17_21_37349)))), ra_Px1(y2(y(y5(i2003_11_14_17_21_37349))), y0(y2(y(y5(i2003_11_14_17_21_37349))))))
% 0.21/0.49 = { by axiom 17 (axiom_4) R->L }
% 0.21/0.49 tuple(cc(y2(y(y5(i2003_11_14_17_21_37349)))), fresh15(ccxcomp(y2(y(y5(i2003_11_14_17_21_37349)))), true2, y2(y(y5(i2003_11_14_17_21_37349)))))
% 0.21/0.49 = { by axiom 19 (axiom_5_2) R->L }
% 0.21/0.49 tuple(cc(y2(y(y5(i2003_11_14_17_21_37349)))), fresh15(fresh11(cd(y(y5(i2003_11_14_17_21_37349))), true2, y(y5(i2003_11_14_17_21_37349))), true2, y2(y(y5(i2003_11_14_17_21_37349)))))
% 0.21/0.49 = { by lemma 33 }
% 0.21/0.49 tuple(cc(y2(y(y5(i2003_11_14_17_21_37349)))), fresh15(fresh11(true2, true2, y(y5(i2003_11_14_17_21_37349))), true2, y2(y(y5(i2003_11_14_17_21_37349)))))
% 0.21/0.49 = { by axiom 8 (axiom_5_2) }
% 0.21/0.49 tuple(cc(y2(y(y5(i2003_11_14_17_21_37349)))), fresh15(true2, true2, y2(y(y5(i2003_11_14_17_21_37349)))))
% 0.21/0.49 = { by axiom 6 (axiom_4) }
% 0.21/0.49 tuple(cc(y2(y(y5(i2003_11_14_17_21_37349)))), true2)
% 0.21/0.49 = { by axiom 25 (axiom_7) R->L }
% 0.21/0.49 tuple(cc(fresh(true2, true2, y(y5(i2003_11_14_17_21_37349)), y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by axiom 9 (axiom_5_3) R->L }
% 0.21/0.49 tuple(cc(fresh(fresh10(true2, true2, y(y5(i2003_11_14_17_21_37349))), true2, y(y5(i2003_11_14_17_21_37349)), y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by lemma 33 R->L }
% 0.21/0.49 tuple(cc(fresh(fresh10(cd(y(y5(i2003_11_14_17_21_37349))), true2, y(y5(i2003_11_14_17_21_37349))), true2, y(y5(i2003_11_14_17_21_37349)), y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by axiom 20 (axiom_5_3) }
% 0.21/0.49 tuple(cc(fresh(rf(y(y5(i2003_11_14_17_21_37349)), y2(y(y5(i2003_11_14_17_21_37349)))), true2, y(y5(i2003_11_14_17_21_37349)), y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by axiom 31 (axiom_7) R->L }
% 0.21/0.49 tuple(cc(fresh25(rf(y(y5(i2003_11_14_17_21_37349)), y5(i2003_11_14_17_21_37349)), true2, y(y5(i2003_11_14_17_21_37349)), y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by axiom 29 (axiom_8_1) R->L }
% 0.21/0.49 tuple(cc(fresh25(fresh4(rinvF(y5(i2003_11_14_17_21_37349), y(y5(i2003_11_14_17_21_37349))), true2, y5(i2003_11_14_17_21_37349), y(y5(i2003_11_14_17_21_37349))), true2, y(y5(i2003_11_14_17_21_37349)), y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by axiom 22 (axiom_6_1) R->L }
% 0.21/0.49 tuple(cc(fresh25(fresh4(fresh8(ca_Vx3(y5(i2003_11_14_17_21_37349)), true2, y5(i2003_11_14_17_21_37349)), true2, y5(i2003_11_14_17_21_37349), y(y5(i2003_11_14_17_21_37349))), true2, y(y5(i2003_11_14_17_21_37349)), y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by lemma 32 }
% 0.21/0.49 tuple(cc(fresh25(fresh4(fresh8(true2, true2, y5(i2003_11_14_17_21_37349)), true2, y5(i2003_11_14_17_21_37349), y(y5(i2003_11_14_17_21_37349))), true2, y(y5(i2003_11_14_17_21_37349)), y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by axiom 11 (axiom_6_1) }
% 0.21/0.49 tuple(cc(fresh25(fresh4(true2, true2, y5(i2003_11_14_17_21_37349), y(y5(i2003_11_14_17_21_37349))), true2, y(y5(i2003_11_14_17_21_37349)), y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by axiom 23 (axiom_8_1) }
% 0.21/0.49 tuple(cc(fresh25(true2, true2, y(y5(i2003_11_14_17_21_37349)), y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by axiom 26 (axiom_7) }
% 0.21/0.49 tuple(cc(fresh26(cowlThing(y(y5(i2003_11_14_17_21_37349))), true2, y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by axiom 2 (axiom_0) }
% 0.21/0.49 tuple(cc(fresh26(true2, true2, y2(y(y5(i2003_11_14_17_21_37349))), y5(i2003_11_14_17_21_37349))), true2)
% 0.21/0.49 = { by axiom 12 (axiom_7) }
% 0.21/0.49 tuple(cc(y5(i2003_11_14_17_21_37349)), true2)
% 0.21/0.49 = { by axiom 18 (axiom_5_1) R->L }
% 0.21/0.49 tuple(fresh12(cd(y5(i2003_11_14_17_21_37349)), true2, y5(i2003_11_14_17_21_37349)), true2)
% 0.21/0.49 = { by axiom 14 (axiom_2_1) R->L }
% 0.21/0.49 tuple(fresh12(fresh20(cUnsatisfiable(i2003_11_14_17_21_37349), true2, i2003_11_14_17_21_37349), true2, y5(i2003_11_14_17_21_37349)), true2)
% 0.21/0.49 = { by axiom 1 (axiom_11) }
% 0.21/0.49 tuple(fresh12(fresh20(true2, true2, i2003_11_14_17_21_37349), true2, y5(i2003_11_14_17_21_37349)), true2)
% 0.21/0.49 = { by axiom 3 (axiom_2_1) }
% 0.21/0.49 tuple(fresh12(true2, true2, y5(i2003_11_14_17_21_37349)), true2)
% 0.21/0.49 = { by axiom 7 (axiom_5_1) }
% 0.21/0.49 tuple(true2, true2)
% 0.21/0.49 % SZS output end Proof
% 0.21/0.49
% 0.21/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------