TSTP Solution File: KRS125+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS125+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 : n011.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 05:52:59 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : KRS125+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
% 0.13/0.35 % Computer : n011.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 02:12:40 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.40 Command-line arguments: --no-flatten-goal
% 0.20/0.40
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Take the following subset of the input axioms:
% 0.20/0.41 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.20/0.41 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.20/0.41 fof(axiom_10, axiom, ![X2]: (ce3(X2) => cc(X2))).
% 0.20/0.41 fof(axiom_11, axiom, ![X2]: (cf(X2) => cd(X2))).
% 0.20/0.41 fof(axiom_12, axiom, cUnsatisfiable(i2003_11_14_17_22_17947)).
% 0.20/0.41 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (ce3(X2) & cf(X2)))).
% 0.20/0.41 fof(axiom_3, axiom, ![X2]: (cc(X2) => cdxcomp(X2))).
% 0.20/0.41 fof(axiom_6, axiom, ![X2]: (cd(X2) <=> ~?[Y]: ra_Px1(X2, Y))).
% 0.20/0.41 fof(axiom_7, axiom, ![X2]: (cdxcomp(X2) <=> ?[Y0]: ra_Px1(X2, Y0))).
% 0.20/0.41 fof(axiom_9, axiom, ![X2]: (cd1xcomp(X2) <=> ~?[Y2]: ra_Px2(X2, Y2))).
% 0.20/0.41
% 0.20/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.41 fresh(y, y, x1...xn) = u
% 0.20/0.41 C => fresh(s, t, x1...xn) = v
% 0.20/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.41 variables of u and v.
% 0.20/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.41 input problem has no model of domain size 1).
% 0.20/0.41
% 0.20/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.41
% 0.20/0.41 Axiom 1 (axiom_12): cUnsatisfiable(i2003_11_14_17_22_17947) = true2.
% 0.20/0.41 Axiom 2 (axiom_11): fresh13(X, X, Y) = true2.
% 0.20/0.41 Axiom 3 (axiom_10): fresh12(X, X, Y) = true2.
% 0.20/0.41 Axiom 4 (axiom_2): fresh11(X, X, Y) = true2.
% 0.20/0.41 Axiom 5 (axiom_2_1): fresh10(X, X, Y) = true2.
% 0.20/0.41 Axiom 6 (axiom_3): fresh7(X, X, Y) = true2.
% 0.20/0.41 Axiom 7 (axiom_7): fresh4(X, X, Y) = true2.
% 0.20/0.41 Axiom 8 (axiom_11): fresh13(cf(X), true2, X) = cd(X).
% 0.20/0.41 Axiom 9 (axiom_10): fresh12(ce3(X), true2, X) = cc(X).
% 0.20/0.41 Axiom 10 (axiom_2): fresh11(cUnsatisfiable(X), true2, X) = ce3(X).
% 0.20/0.41 Axiom 11 (axiom_2_1): fresh10(cUnsatisfiable(X), true2, X) = cf(X).
% 0.20/0.41 Axiom 12 (axiom_3): fresh7(cc(X), true2, X) = cdxcomp(X).
% 0.20/0.41 Axiom 13 (axiom_7): fresh4(cdxcomp(X), true2, X) = ra_Px1(X, y0_2(X)).
% 0.20/0.41
% 0.20/0.41 Goal 1 (axiom_6_1): tuple(cd(X), ra_Px1(X, Y)) = tuple(true2, true2).
% 0.20/0.41 The goal is true when:
% 0.20/0.41 X = i2003_11_14_17_22_17947
% 0.20/0.41 Y = y0_2(i2003_11_14_17_22_17947)
% 0.20/0.41
% 0.20/0.41 Proof:
% 0.20/0.41 tuple(cd(i2003_11_14_17_22_17947), ra_Px1(i2003_11_14_17_22_17947, y0_2(i2003_11_14_17_22_17947)))
% 0.20/0.41 = { by axiom 13 (axiom_7) R->L }
% 0.20/0.41 tuple(cd(i2003_11_14_17_22_17947), fresh4(cdxcomp(i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947))
% 0.20/0.41 = { by axiom 12 (axiom_3) R->L }
% 0.20/0.41 tuple(cd(i2003_11_14_17_22_17947), fresh4(fresh7(cc(i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947))
% 0.20/0.41 = { by axiom 9 (axiom_10) R->L }
% 0.20/0.41 tuple(cd(i2003_11_14_17_22_17947), fresh4(fresh7(fresh12(ce3(i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947))
% 0.20/0.41 = { by axiom 10 (axiom_2) R->L }
% 0.20/0.41 tuple(cd(i2003_11_14_17_22_17947), fresh4(fresh7(fresh12(fresh11(cUnsatisfiable(i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947))
% 0.20/0.41 = { by axiom 1 (axiom_12) }
% 0.20/0.41 tuple(cd(i2003_11_14_17_22_17947), fresh4(fresh7(fresh12(fresh11(true2, true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947))
% 0.20/0.41 = { by axiom 4 (axiom_2) }
% 0.20/0.41 tuple(cd(i2003_11_14_17_22_17947), fresh4(fresh7(fresh12(true2, true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947))
% 0.20/0.41 = { by axiom 3 (axiom_10) }
% 0.20/0.41 tuple(cd(i2003_11_14_17_22_17947), fresh4(fresh7(true2, true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947))
% 0.20/0.41 = { by axiom 6 (axiom_3) }
% 0.20/0.41 tuple(cd(i2003_11_14_17_22_17947), fresh4(true2, true2, i2003_11_14_17_22_17947))
% 0.20/0.41 = { by axiom 7 (axiom_7) }
% 0.20/0.41 tuple(cd(i2003_11_14_17_22_17947), true2)
% 0.20/0.41 = { by axiom 8 (axiom_11) R->L }
% 0.20/0.41 tuple(fresh13(cf(i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2)
% 0.20/0.41 = { by axiom 11 (axiom_2_1) R->L }
% 0.20/0.41 tuple(fresh13(fresh10(cUnsatisfiable(i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2)
% 0.20/0.41 = { by axiom 1 (axiom_12) }
% 0.20/0.41 tuple(fresh13(fresh10(true2, true2, i2003_11_14_17_22_17947), true2, i2003_11_14_17_22_17947), true2)
% 0.20/0.41 = { by axiom 5 (axiom_2_1) }
% 0.20/0.41 tuple(fresh13(true2, true2, i2003_11_14_17_22_17947), true2)
% 0.20/0.41 = { by axiom 2 (axiom_11) }
% 0.20/0.41 tuple(true2, true2)
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------