TSTP Solution File: KRS128+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS128+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 : n017.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 05:53:00 EDT 2023
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KRS128+1 : TPTP v8.1.2. Released v3.1.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 01:17:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.42 Command-line arguments: --flatten
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 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, ![X2]: (ca_Cx4xcomp(X2) <=> (cd(X2) & cexcomp(X2)))).
% 0.20/0.44 fof(axiom_11, axiom, cUnsatisfiable(i2003_11_14_17_22_31584)).
% 0.20/0.44 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y]: (rr(X2, Y) & cexcomp(Y)) & (![Y2]: (rr(X2, Y2) => cd(Y2)) & ![Y2]: (rr(X2, Y2) => ca_Cx4(Y2)))))).
% 0.20/0.44 fof(axiom_5, axiom, ![X2]: (cdxcomp(X2) <=> ~?[Y2]: ra_Px2(X2, Y2))).
% 0.20/0.44 fof(axiom_6, axiom, ![X2]: (ce(X2) <=> ~?[Y2]: ra_Px1(X2, Y2))).
% 0.20/0.44 fof(axiom_8, axiom, ![X2]: (ca_Cx4(X2) <=> ?[Y0]: ra_Px4(X2, Y0))).
% 0.20/0.44 fof(axiom_9, axiom, ![X2]: (ca_Cx4xcomp(X2) <=> ~?[Y2]: ra_Px4(X2, Y2))).
% 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_11): cUnsatisfiable(i2003_11_14_17_22_31584) = true2.
% 0.20/0.44 Axiom 2 (axiom_10): fresh17(X, X, Y) = true2.
% 0.20/0.44 Axiom 3 (axiom_10): fresh16(X, X, Y) = ca_Cx4xcomp(Y).
% 0.20/0.44 Axiom 4 (axiom_2): fresh13(X, X, Y) = true2.
% 0.20/0.44 Axiom 5 (axiom_2_1): fresh12(X, X, Y) = true2.
% 0.20/0.44 Axiom 6 (axiom_2_2): fresh10(X, X, Y) = true2.
% 0.20/0.44 Axiom 7 (axiom_2_3): fresh8(X, X, Y) = true2.
% 0.20/0.44 Axiom 8 (axiom_8): fresh2(X, X, Y) = true2.
% 0.20/0.44 Axiom 9 (axiom_10): fresh16(cd(X), true2, X) = fresh17(cexcomp(X), true2, X).
% 0.20/0.44 Axiom 10 (axiom_2): fresh13(cUnsatisfiable(X), true2, X) = rr(X, y6(X)).
% 0.20/0.44 Axiom 11 (axiom_2_1): fresh12(cUnsatisfiable(X), true2, X) = cexcomp(y6(X)).
% 0.20/0.44 Axiom 12 (axiom_2_2): fresh11(X, X, Y, Z) = cd(Z).
% 0.20/0.44 Axiom 13 (axiom_2_3): fresh9(X, X, Y, Z) = ca_Cx4(Z).
% 0.20/0.44 Axiom 14 (axiom_8): fresh2(ca_Cx4(X), true2, X) = ra_Px4(X, y0(X)).
% 0.20/0.44 Axiom 15 (axiom_2_2): fresh11(rr(X, Y), true2, X, Y) = fresh10(cUnsatisfiable(X), true2, Y).
% 0.20/0.44 Axiom 16 (axiom_2_3): fresh9(rr(X, Y), true2, X, Y) = fresh8(cUnsatisfiable(X), true2, Y).
% 0.20/0.44
% 0.20/0.44 Lemma 17: rr(i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584)) = cUnsatisfiable(i2003_11_14_17_22_31584).
% 0.20/0.44 Proof:
% 0.20/0.44 rr(i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584))
% 0.20/0.44 = { by axiom 10 (axiom_2) R->L }
% 0.20/0.44 fresh13(cUnsatisfiable(i2003_11_14_17_22_31584), true2, i2003_11_14_17_22_31584)
% 0.20/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.20/0.44 fresh13(cUnsatisfiable(i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584), i2003_11_14_17_22_31584)
% 0.20/0.44 = { by axiom 4 (axiom_2) }
% 0.20/0.44 true2
% 0.20/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.20/0.44 cUnsatisfiable(i2003_11_14_17_22_31584)
% 0.20/0.44
% 0.20/0.44 Goal 1 (axiom_9_1): tuple(ra_Px4(X, Y), ca_Cx4xcomp(X)) = tuple(true2, true2).
% 0.20/0.44 The goal is true when:
% 0.20/0.44 X = y6(i2003_11_14_17_22_31584)
% 0.20/0.44 Y = y0(y6(i2003_11_14_17_22_31584))
% 0.20/0.44
% 0.20/0.44 Proof:
% 0.20/0.44 tuple(ra_Px4(y6(i2003_11_14_17_22_31584), y0(y6(i2003_11_14_17_22_31584))), ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 14 (axiom_8) R->L }
% 0.20/0.44 tuple(fresh2(ca_Cx4(y6(i2003_11_14_17_22_31584)), true2, y6(i2003_11_14_17_22_31584)), ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.20/0.44 tuple(fresh2(ca_Cx4(y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)), ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 13 (axiom_2_3) R->L }
% 0.20/0.44 tuple(fresh2(fresh9(cUnsatisfiable(i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584), i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)), ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by lemma 17 R->L }
% 0.20/0.44 tuple(fresh2(fresh9(rr(i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)), ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) }
% 0.20/0.44 tuple(fresh2(fresh9(rr(i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584)), true2, i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)), ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 16 (axiom_2_3) }
% 0.20/0.44 tuple(fresh2(fresh8(cUnsatisfiable(i2003_11_14_17_22_31584), true2, y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)), ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.20/0.44 tuple(fresh2(fresh8(cUnsatisfiable(i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)), ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 7 (axiom_2_3) }
% 0.20/0.44 tuple(fresh2(true2, cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)), ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.20/0.44 tuple(fresh2(cUnsatisfiable(i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)), ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 8 (axiom_8) }
% 0.20/0.44 tuple(true2, ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), ca_Cx4xcomp(y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 3 (axiom_10) R->L }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh16(cUnsatisfiable(i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh16(true2, cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 6 (axiom_2_2) R->L }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh16(fresh10(cUnsatisfiable(i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh16(fresh10(cUnsatisfiable(i2003_11_14_17_22_31584), true2, y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 15 (axiom_2_2) R->L }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh16(fresh11(rr(i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584)), true2, i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh16(fresh11(rr(i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by lemma 17 }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh16(fresh11(cUnsatisfiable(i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584), i2003_11_14_17_22_31584, y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 12 (axiom_2_2) }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh16(cd(y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh16(cd(y6(i2003_11_14_17_22_31584)), true2, y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 9 (axiom_10) }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh17(cexcomp(y6(i2003_11_14_17_22_31584)), true2, y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh17(cexcomp(y6(i2003_11_14_17_22_31584)), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 11 (axiom_2_1) R->L }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh17(fresh12(cUnsatisfiable(i2003_11_14_17_22_31584), true2, i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh17(fresh12(cUnsatisfiable(i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584), i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 5 (axiom_2_1) }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh17(true2, cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), fresh17(cUnsatisfiable(i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584), y6(i2003_11_14_17_22_31584)))
% 0.20/0.44 = { by axiom 2 (axiom_10) }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), true2)
% 0.20/0.44 = { by axiom 1 (axiom_11) R->L }
% 0.20/0.44 tuple(cUnsatisfiable(i2003_11_14_17_22_31584), cUnsatisfiable(i2003_11_14_17_22_31584))
% 0.20/0.44 = { by axiom 1 (axiom_11) }
% 0.20/0.44 tuple(true2, cUnsatisfiable(i2003_11_14_17_22_31584))
% 0.20/0.44 = { by axiom 1 (axiom_11) }
% 0.20/0.44 tuple(true2, true2)
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------