TSTP Solution File: KRS078+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS078+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 : n032.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 05:52:49 EDT 2023
% Result : Unsatisfiable 0.08s 0.31s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : KRS078+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Mon Aug 28 01:53:00 EDT 2023
% 0.08/0.27 % CPUTime :
% 0.08/0.31 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.08/0.31
% 0.08/0.31 % SZS status Unsatisfiable
% 0.08/0.31
% 0.11/0.32 % SZS output start Proof
% 0.11/0.32 Take the following subset of the input axioms:
% 0.11/0.32 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.11/0.32 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.11/0.32 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y]: (rr(X2, Y) & (?[Z]: (rinvR(Y, Z) & ![W]: (rs(Z, W) => cp(W))) & ![Z0, Z1]: ((rinvR(Y, Z0) & rinvR(Y, Z1)) => Z0=Z1))) & ?[Y2]: (rs(X2, Y2) & (~cq(Y2) & ~cp(Y2)))))).
% 0.11/0.32 fof(axiom_3, axiom, ![X2, Y2]: (rinvR(X2, Y2) <=> rr(Y2, X2))).
% 0.11/0.32 fof(axiom_4, axiom, cUnsatisfiable(i2003_11_14_17_19_13721)).
% 0.11/0.32
% 0.11/0.32 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.11/0.32 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.11/0.32 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.11/0.32 fresh(y, y, x1...xn) = u
% 0.11/0.32 C => fresh(s, t, x1...xn) = v
% 0.11/0.32 where fresh is a fresh function symbol and x1..xn are the free
% 0.11/0.32 variables of u and v.
% 0.11/0.32 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.11/0.32 input problem has no model of domain size 1).
% 0.11/0.32
% 0.11/0.32 The encoding turns the above axioms into the following unit equations and goals:
% 0.11/0.32
% 0.11/0.32 Axiom 1 (axiom_4): cUnsatisfiable(i2003_11_14_17_19_13721) = true2.
% 0.11/0.32 Axiom 2 (axiom_2_3): fresh8(X, X, Y) = true2.
% 0.11/0.32 Axiom 3 (axiom_2_2): fresh7(X, X, Y) = true2.
% 0.11/0.32 Axiom 4 (axiom_2_4): fresh6(X, X, Y) = true2.
% 0.11/0.32 Axiom 5 (axiom_2_8): fresh4(X, X, Y) = true2.
% 0.11/0.32 Axiom 6 (axiom_2_7): fresh10(X, X, Y, Z) = Z.
% 0.11/0.32 Axiom 7 (axiom_2_3): fresh8(cUnsatisfiable(X), true2, X) = rr(X, y2(X)).
% 0.11/0.32 Axiom 8 (axiom_2_4): fresh6(cUnsatisfiable(X), true2, X) = rs(X, y(X)).
% 0.11/0.32 Axiom 9 (axiom_2_8): fresh5(X, X, Y, Z) = cp(Z).
% 0.11/0.32 Axiom 10 (axiom_3_1): fresh2(X, X, Y, Z) = true2.
% 0.11/0.32 Axiom 11 (axiom_2_2): fresh7(cUnsatisfiable(X), true2, X) = rinvR(y2(X), z(X)).
% 0.11/0.32 Axiom 12 (axiom_2_7): fresh(X, X, Y, Z, W) = Z.
% 0.11/0.32 Axiom 13 (axiom_2_7): fresh9(X, X, Y, Z, W) = fresh10(cUnsatisfiable(Y), true2, Z, W).
% 0.11/0.32 Axiom 14 (axiom_3_1): fresh2(rr(X, Y), true2, Y, X) = rinvR(Y, X).
% 0.11/0.32 Axiom 15 (axiom_2_8): fresh5(rs(z(X), Y), true2, X, Y) = fresh4(cUnsatisfiable(X), true2, Y).
% 0.11/0.32 Axiom 16 (axiom_2_7): fresh9(rinvR(y2(X), Y), true2, X, Z, Y) = fresh(rinvR(y2(X), Z), true2, X, Z, Y).
% 0.11/0.32
% 0.11/0.32 Goal 1 (axiom_2_5): tuple(cUnsatisfiable(X), cp(y(X))) = tuple(true2, true2).
% 0.11/0.32 The goal is true when:
% 0.11/0.32 X = i2003_11_14_17_19_13721
% 0.11/0.32
% 0.11/0.32 Proof:
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), cp(y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 9 (axiom_2_8) R->L }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(true2, true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 4 (axiom_2_4) R->L }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(fresh6(true2, true2, i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 1 (axiom_4) R->L }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(fresh6(cUnsatisfiable(i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 8 (axiom_2_4) }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 6 (axiom_2_7) R->L }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh10(true2, true2, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 1 (axiom_4) R->L }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh10(cUnsatisfiable(i2003_11_14_17_19_13721), true2, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 13 (axiom_2_7) R->L }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh9(true2, true2, i2003_11_14_17_19_13721, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 10 (axiom_3_1) R->L }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh9(fresh2(true2, true2, y2(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 2 (axiom_2_3) R->L }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh9(fresh2(fresh8(true2, true2, i2003_11_14_17_19_13721), true2, y2(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 1 (axiom_4) R->L }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh9(fresh2(fresh8(cUnsatisfiable(i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721), true2, y2(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 7 (axiom_2_3) }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh9(fresh2(rr(i2003_11_14_17_19_13721, y2(i2003_11_14_17_19_13721)), true2, y2(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 14 (axiom_3_1) }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh9(rinvR(y2(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 16 (axiom_2_7) }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh(rinvR(y2(i2003_11_14_17_19_13721), z(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 11 (axiom_2_2) R->L }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh(fresh7(cUnsatisfiable(i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 1 (axiom_4) }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh(fresh7(true2, true2, i2003_11_14_17_19_13721), true2, i2003_11_14_17_19_13721, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 3 (axiom_2_2) }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(fresh(true2, true2, i2003_11_14_17_19_13721, z(i2003_11_14_17_19_13721), i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 12 (axiom_2_7) }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh5(rs(z(i2003_11_14_17_19_13721), y(i2003_11_14_17_19_13721)), true2, i2003_11_14_17_19_13721, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 15 (axiom_2_8) }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh4(cUnsatisfiable(i2003_11_14_17_19_13721), true2, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 1 (axiom_4) }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), fresh4(true2, true2, y(i2003_11_14_17_19_13721)))
% 0.11/0.32 = { by axiom 5 (axiom_2_8) }
% 0.11/0.32 tuple(cUnsatisfiable(i2003_11_14_17_19_13721), true2)
% 0.11/0.32 = { by axiom 1 (axiom_4) }
% 0.11/0.32 tuple(true2, true2)
% 0.11/0.32 % SZS output end Proof
% 0.11/0.32
% 0.11/0.32 RESULT: Unsatisfiable (the axioms are contradictory).
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