TSTP Solution File: KRS083+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS083+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 : n013.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 05:52:50 EDT 2023
% Result : Unsatisfiable 0.13s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS083+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % 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 : n013.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 01:57:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.41 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.13/0.41
% 0.13/0.41 % SZS status Unsatisfiable
% 0.13/0.41
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 Take the following subset of the input axioms:
% 0.19/0.43 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.19/0.43 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.19/0.43 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (![Y]: (rinvR(X2, Y) => ?[Z]: (rinvF(Y, Z) & cd(Z))) & (~cc(X2) & ?[Y2]: (rinvF(X2, Y2) & cd(Y2)))))).
% 0.19/0.43 fof(axiom_3, axiom, ![X2]: (cd(X2) <=> (?[Y2]: (rf(X2, Y2) & ~cc(Y2)) & cc(X2)))).
% 0.19/0.43 fof(axiom_4, axiom, ![X2]: (cowlThing(X2) => ![Y0, Y1]: ((rf(X2, Y0) & rf(X2, Y1)) => Y0=Y1))).
% 0.19/0.43 fof(axiom_5, axiom, ![X2, Y2]: (rinvF(X2, Y2) <=> rf(Y2, X2))).
% 0.19/0.43 fof(axiom_6, axiom, ![X2, Y2]: (rinvR(X2, Y2) <=> rr(Y2, X2))).
% 0.19/0.43 fof(axiom_8, axiom, cUnsatisfiable(i2003_11_14_17_19_32337)).
% 0.19/0.43 fof(axiom_9, axiom, ![X2, Y2]: (rf(X2, Y2) => rr(X2, Y2))).
% 0.19/0.43
% 0.19/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.43 fresh(y, y, x1...xn) = u
% 0.19/0.43 C => fresh(s, t, x1...xn) = v
% 0.19/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.43 variables of u and v.
% 0.19/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.43 input problem has no model of domain size 1).
% 0.19/0.43
% 0.19/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.43
% 0.19/0.43 Axiom 1 (axiom_8): cUnsatisfiable(i2003_11_14_17_19_32337) = true2.
% 0.19/0.43 Axiom 2 (axiom_0): cowlThing(X) = true2.
% 0.19/0.43 Axiom 3 (axiom_2_1): fresh16(X, X, Y) = true2.
% 0.19/0.43 Axiom 4 (axiom_2): fresh15(X, X, Y) = true2.
% 0.19/0.43 Axiom 5 (axiom_2_3): fresh13(X, X, Y) = true2.
% 0.19/0.43 Axiom 6 (axiom_2_4): fresh11(X, X, Y) = true2.
% 0.19/0.43 Axiom 7 (axiom_3_2): fresh10(X, X, Y) = true2.
% 0.19/0.43 Axiom 8 (axiom_3_3): fresh9(X, X, Y) = true2.
% 0.19/0.43 Axiom 9 (axiom_4): fresh18(X, X, Y, Z) = Z.
% 0.19/0.43 Axiom 10 (axiom_2_1): fresh16(cUnsatisfiable(X), true2, X) = rinvF(X, y3(X)).
% 0.19/0.43 Axiom 11 (axiom_2): fresh15(cUnsatisfiable(X), true2, X) = cd(y3(X)).
% 0.19/0.43 Axiom 12 (axiom_2_3): fresh14(X, X, Y, Z) = cd(z(Z)).
% 0.19/0.43 Axiom 13 (axiom_2_4): fresh12(X, X, Y, Z) = rinvF(Z, z(Z)).
% 0.19/0.43 Axiom 14 (axiom_3_2): fresh10(cd(X), true2, X) = cc(X).
% 0.19/0.43 Axiom 15 (axiom_3_3): fresh9(cd(X), true2, X) = rf(X, y(X)).
% 0.19/0.43 Axiom 16 (axiom_5_1): fresh7(X, X, Y, Z) = true2.
% 0.19/0.43 Axiom 17 (axiom_6_1): fresh5(X, X, Y, Z) = true2.
% 0.19/0.43 Axiom 18 (axiom_9): fresh2(X, X, Y, Z) = true2.
% 0.19/0.43 Axiom 19 (axiom_4): fresh(X, X, Y, Z, W) = Z.
% 0.19/0.43 Axiom 20 (axiom_4): fresh17(X, X, Y, Z, W) = fresh18(cowlThing(Y), true2, Z, W).
% 0.19/0.43 Axiom 21 (axiom_2_3): fresh14(rinvR(X, Y), true2, X, Y) = fresh13(cUnsatisfiable(X), true2, Y).
% 0.19/0.43 Axiom 22 (axiom_2_4): fresh12(rinvR(X, Y), true2, X, Y) = fresh11(cUnsatisfiable(X), true2, Y).
% 0.19/0.43 Axiom 23 (axiom_5_1): fresh7(rinvF(X, Y), true2, X, Y) = rf(Y, X).
% 0.19/0.43 Axiom 24 (axiom_6_1): fresh5(rr(X, Y), true2, Y, X) = rinvR(Y, X).
% 0.19/0.43 Axiom 25 (axiom_9): fresh2(rf(X, Y), true2, X, Y) = rr(X, Y).
% 0.19/0.43 Axiom 26 (axiom_4): fresh17(rf(X, Y), true2, X, Z, Y) = fresh(rf(X, Z), true2, X, Z, Y).
% 0.19/0.43
% 0.19/0.43 Lemma 27: rinvR(i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337)) = true2.
% 0.19/0.43 Proof:
% 0.19/0.43 rinvR(i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 24 (axiom_6_1) R->L }
% 0.19/0.43 fresh5(rr(y3(i2003_11_14_17_19_32337), i2003_11_14_17_19_32337), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 25 (axiom_9) R->L }
% 0.19/0.43 fresh5(fresh2(rf(y3(i2003_11_14_17_19_32337), i2003_11_14_17_19_32337), true2, y3(i2003_11_14_17_19_32337), i2003_11_14_17_19_32337), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 23 (axiom_5_1) R->L }
% 0.19/0.43 fresh5(fresh2(fresh7(rinvF(i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337)), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337)), true2, y3(i2003_11_14_17_19_32337), i2003_11_14_17_19_32337), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 10 (axiom_2_1) R->L }
% 0.19/0.43 fresh5(fresh2(fresh7(fresh16(cUnsatisfiable(i2003_11_14_17_19_32337), true2, i2003_11_14_17_19_32337), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337)), true2, y3(i2003_11_14_17_19_32337), i2003_11_14_17_19_32337), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 1 (axiom_8) }
% 0.19/0.43 fresh5(fresh2(fresh7(fresh16(true2, true2, i2003_11_14_17_19_32337), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337)), true2, y3(i2003_11_14_17_19_32337), i2003_11_14_17_19_32337), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 3 (axiom_2_1) }
% 0.19/0.43 fresh5(fresh2(fresh7(true2, true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337)), true2, y3(i2003_11_14_17_19_32337), i2003_11_14_17_19_32337), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 16 (axiom_5_1) }
% 0.19/0.43 fresh5(fresh2(true2, true2, y3(i2003_11_14_17_19_32337), i2003_11_14_17_19_32337), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 18 (axiom_9) }
% 0.19/0.43 fresh5(true2, true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 17 (axiom_6_1) }
% 0.19/0.43 true2
% 0.19/0.43
% 0.19/0.43 Lemma 28: cd(z(y3(i2003_11_14_17_19_32337))) = true2.
% 0.19/0.43 Proof:
% 0.19/0.43 cd(z(y3(i2003_11_14_17_19_32337)))
% 0.19/0.43 = { by axiom 12 (axiom_2_3) R->L }
% 0.19/0.43 fresh14(true2, true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by lemma 27 R->L }
% 0.19/0.43 fresh14(rinvR(i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337)), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 21 (axiom_2_3) }
% 0.19/0.43 fresh13(cUnsatisfiable(i2003_11_14_17_19_32337), true2, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 1 (axiom_8) }
% 0.19/0.43 fresh13(true2, true2, y3(i2003_11_14_17_19_32337))
% 0.19/0.43 = { by axiom 5 (axiom_2_3) }
% 0.19/0.43 true2
% 0.19/0.43
% 0.19/0.43 Goal 1 (axiom_3_1): tuple(cc(y(X)), cd(X)) = tuple(true2, true2).
% 0.19/0.43 The goal is true when:
% 0.19/0.43 X = z(y3(i2003_11_14_17_19_32337))
% 0.19/0.43
% 0.19/0.43 Proof:
% 0.19/0.43 tuple(cc(y(z(y3(i2003_11_14_17_19_32337)))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.43 = { by axiom 19 (axiom_4) R->L }
% 0.19/0.43 tuple(cc(fresh(true2, true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.43 = { by axiom 8 (axiom_3_3) R->L }
% 0.19/0.43 tuple(cc(fresh(fresh9(true2, true2, z(y3(i2003_11_14_17_19_32337))), true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.43 = { by lemma 28 R->L }
% 0.19/0.43 tuple(cc(fresh(fresh9(cd(z(y3(i2003_11_14_17_19_32337))), true2, z(y3(i2003_11_14_17_19_32337))), true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.43 = { by axiom 15 (axiom_3_3) }
% 0.19/0.44 tuple(cc(fresh(rf(z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337)))), true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 26 (axiom_4) R->L }
% 0.19/0.44 tuple(cc(fresh17(rf(z(y3(i2003_11_14_17_19_32337)), y3(i2003_11_14_17_19_32337)), true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 23 (axiom_5_1) R->L }
% 0.19/0.44 tuple(cc(fresh17(fresh7(rinvF(y3(i2003_11_14_17_19_32337), z(y3(i2003_11_14_17_19_32337))), true2, y3(i2003_11_14_17_19_32337), z(y3(i2003_11_14_17_19_32337))), true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 13 (axiom_2_4) R->L }
% 0.19/0.44 tuple(cc(fresh17(fresh7(fresh12(true2, true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337)), true2, y3(i2003_11_14_17_19_32337), z(y3(i2003_11_14_17_19_32337))), true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by lemma 27 R->L }
% 0.19/0.44 tuple(cc(fresh17(fresh7(fresh12(rinvR(i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337)), true2, i2003_11_14_17_19_32337, y3(i2003_11_14_17_19_32337)), true2, y3(i2003_11_14_17_19_32337), z(y3(i2003_11_14_17_19_32337))), true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 22 (axiom_2_4) }
% 0.19/0.44 tuple(cc(fresh17(fresh7(fresh11(cUnsatisfiable(i2003_11_14_17_19_32337), true2, y3(i2003_11_14_17_19_32337)), true2, y3(i2003_11_14_17_19_32337), z(y3(i2003_11_14_17_19_32337))), true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 1 (axiom_8) }
% 0.19/0.44 tuple(cc(fresh17(fresh7(fresh11(true2, true2, y3(i2003_11_14_17_19_32337)), true2, y3(i2003_11_14_17_19_32337), z(y3(i2003_11_14_17_19_32337))), true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 6 (axiom_2_4) }
% 0.19/0.44 tuple(cc(fresh17(fresh7(true2, true2, y3(i2003_11_14_17_19_32337), z(y3(i2003_11_14_17_19_32337))), true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 16 (axiom_5_1) }
% 0.19/0.44 tuple(cc(fresh17(true2, true2, z(y3(i2003_11_14_17_19_32337)), y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 20 (axiom_4) }
% 0.19/0.44 tuple(cc(fresh18(cowlThing(z(y3(i2003_11_14_17_19_32337))), true2, y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 2 (axiom_0) }
% 0.19/0.44 tuple(cc(fresh18(true2, true2, y(z(y3(i2003_11_14_17_19_32337))), y3(i2003_11_14_17_19_32337))), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 9 (axiom_4) }
% 0.19/0.44 tuple(cc(y3(i2003_11_14_17_19_32337)), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 14 (axiom_3_2) R->L }
% 0.19/0.44 tuple(fresh10(cd(y3(i2003_11_14_17_19_32337)), true2, y3(i2003_11_14_17_19_32337)), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 11 (axiom_2) R->L }
% 0.19/0.44 tuple(fresh10(fresh15(cUnsatisfiable(i2003_11_14_17_19_32337), true2, i2003_11_14_17_19_32337), true2, y3(i2003_11_14_17_19_32337)), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 1 (axiom_8) }
% 0.19/0.44 tuple(fresh10(fresh15(true2, true2, i2003_11_14_17_19_32337), true2, y3(i2003_11_14_17_19_32337)), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 4 (axiom_2) }
% 0.19/0.44 tuple(fresh10(true2, true2, y3(i2003_11_14_17_19_32337)), cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by axiom 7 (axiom_3_2) }
% 0.19/0.44 tuple(true2, cd(z(y3(i2003_11_14_17_19_32337))))
% 0.19/0.44 = { by lemma 28 }
% 0.19/0.44 tuple(true2, true2)
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44
% 0.19/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------