TSTP Solution File: KRS085+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS085+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 05:52:51 EDT 2023
% Result : Unsatisfiable 0.13s 0.33s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : KRS085+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Aug 28 01:24:02 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.13/0.33 Command-line arguments: --no-flatten-goal
% 0.13/0.33
% 0.13/0.33 % SZS status Unsatisfiable
% 0.13/0.33
% 0.13/0.34 % SZS output start Proof
% 0.13/0.34 Take the following subset of the input axioms:
% 0.13/0.34 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.13/0.34 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.13/0.34 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y]: (rr(X2, Y) & ?[Z]: (rr(Y, Z) & (cp1(Z) & ![W]: (rinvR(Z, W) => ~cp1(W))))) & cp1(X2)))).
% 0.13/0.34 fof(axiom_5, axiom, ![X2, Y2]: (rinvR(X2, Y2) <=> rr(Y2, X2))).
% 0.13/0.34 fof(axiom_6, axiom, ![X2, Y2, Z2]: ((rr(X2, Y2) & rr(Y2, Z2)) => rr(X2, Z2))).
% 0.13/0.34 fof(axiom_7, axiom, cUnsatisfiable(i2003_11_14_17_19_39537)).
% 0.13/0.34
% 0.13/0.34 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.34 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.34 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.34 fresh(y, y, x1...xn) = u
% 0.13/0.34 C => fresh(s, t, x1...xn) = v
% 0.13/0.34 where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.34 variables of u and v.
% 0.13/0.34 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.34 input problem has no model of domain size 1).
% 0.13/0.34
% 0.13/0.34 The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.34
% 0.13/0.34 Axiom 1 (axiom_7): cUnsatisfiable(i2003_11_14_17_19_39537) = true2.
% 0.13/0.34 Axiom 2 (axiom_2): fresh10(X, X, Y) = true2.
% 0.13/0.34 Axiom 3 (axiom_2_2): fresh9(X, X, Y) = true2.
% 0.13/0.34 Axiom 4 (axiom_2_3): fresh8(X, X, Y) = true2.
% 0.13/0.34 Axiom 5 (axiom_2): fresh10(cUnsatisfiable(X), true2, X) = cp1(X).
% 0.13/0.34 Axiom 6 (axiom_2_2): fresh9(cUnsatisfiable(X), true2, X) = rr(X, y(X)).
% 0.13/0.34 Axiom 7 (axiom_5_1): fresh4(X, X, Y, Z) = true2.
% 0.13/0.34 Axiom 8 (axiom_6): fresh2(X, X, Y, Z) = true2.
% 0.13/0.34 Axiom 9 (axiom_2_3): fresh8(cUnsatisfiable(X), true2, X) = rr(y(X), z(X)).
% 0.13/0.34 Axiom 10 (axiom_6): fresh3(X, X, Y, Z, W) = rr(Y, W).
% 0.13/0.34 Axiom 11 (axiom_5_1): fresh4(rr(X, Y), true2, Y, X) = rinvR(Y, X).
% 0.13/0.34 Axiom 12 (axiom_6): fresh3(rr(X, Y), true2, Z, X, Y) = fresh2(rr(Z, X), true2, Z, Y).
% 0.13/0.34
% 0.13/0.34 Goal 1 (axiom_2_4): tuple(cUnsatisfiable(X), cp1(Y), rinvR(z(X), Y)) = tuple(true2, true2, true2).
% 0.13/0.34 The goal is true when:
% 0.13/0.34 X = i2003_11_14_17_19_39537
% 0.13/0.34 Y = i2003_11_14_17_19_39537
% 0.13/0.34
% 0.13/0.34 Proof:
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), rinvR(z(i2003_11_14_17_19_39537), i2003_11_14_17_19_39537))
% 0.13/0.34 = { by axiom 11 (axiom_5_1) R->L }
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), fresh4(rr(i2003_11_14_17_19_39537, z(i2003_11_14_17_19_39537)), true2, z(i2003_11_14_17_19_39537), i2003_11_14_17_19_39537))
% 0.13/0.34 = { by axiom 10 (axiom_6) R->L }
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), fresh4(fresh3(true2, true2, i2003_11_14_17_19_39537, y(i2003_11_14_17_19_39537), z(i2003_11_14_17_19_39537)), true2, z(i2003_11_14_17_19_39537), i2003_11_14_17_19_39537))
% 0.13/0.34 = { by axiom 4 (axiom_2_3) R->L }
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), fresh4(fresh3(fresh8(true2, true2, i2003_11_14_17_19_39537), true2, i2003_11_14_17_19_39537, y(i2003_11_14_17_19_39537), z(i2003_11_14_17_19_39537)), true2, z(i2003_11_14_17_19_39537), i2003_11_14_17_19_39537))
% 0.13/0.34 = { by axiom 1 (axiom_7) R->L }
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), fresh4(fresh3(fresh8(cUnsatisfiable(i2003_11_14_17_19_39537), true2, i2003_11_14_17_19_39537), true2, i2003_11_14_17_19_39537, y(i2003_11_14_17_19_39537), z(i2003_11_14_17_19_39537)), true2, z(i2003_11_14_17_19_39537), i2003_11_14_17_19_39537))
% 0.13/0.34 = { by axiom 9 (axiom_2_3) }
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), fresh4(fresh3(rr(y(i2003_11_14_17_19_39537), z(i2003_11_14_17_19_39537)), true2, i2003_11_14_17_19_39537, y(i2003_11_14_17_19_39537), z(i2003_11_14_17_19_39537)), true2, z(i2003_11_14_17_19_39537), i2003_11_14_17_19_39537))
% 0.13/0.34 = { by axiom 12 (axiom_6) }
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), fresh4(fresh2(rr(i2003_11_14_17_19_39537, y(i2003_11_14_17_19_39537)), true2, i2003_11_14_17_19_39537, z(i2003_11_14_17_19_39537)), true2, z(i2003_11_14_17_19_39537), i2003_11_14_17_19_39537))
% 0.13/0.34 = { by axiom 6 (axiom_2_2) R->L }
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), fresh4(fresh2(fresh9(cUnsatisfiable(i2003_11_14_17_19_39537), true2, i2003_11_14_17_19_39537), true2, i2003_11_14_17_19_39537, z(i2003_11_14_17_19_39537)), true2, z(i2003_11_14_17_19_39537), i2003_11_14_17_19_39537))
% 0.13/0.34 = { by axiom 1 (axiom_7) }
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), fresh4(fresh2(fresh9(true2, true2, i2003_11_14_17_19_39537), true2, i2003_11_14_17_19_39537, z(i2003_11_14_17_19_39537)), true2, z(i2003_11_14_17_19_39537), i2003_11_14_17_19_39537))
% 0.13/0.34 = { by axiom 3 (axiom_2_2) }
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), fresh4(fresh2(true2, true2, i2003_11_14_17_19_39537, z(i2003_11_14_17_19_39537)), true2, z(i2003_11_14_17_19_39537), i2003_11_14_17_19_39537))
% 0.13/0.34 = { by axiom 8 (axiom_6) }
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), fresh4(true2, true2, z(i2003_11_14_17_19_39537), i2003_11_14_17_19_39537))
% 0.13/0.34 = { by axiom 7 (axiom_5_1) }
% 0.13/0.34 tuple(cUnsatisfiable(i2003_11_14_17_19_39537), cp1(i2003_11_14_17_19_39537), true2)
% 0.13/0.34 = { by axiom 1 (axiom_7) }
% 0.13/0.34 tuple(true2, cp1(i2003_11_14_17_19_39537), true2)
% 0.13/0.34 = { by axiom 5 (axiom_2) R->L }
% 0.13/0.34 tuple(true2, fresh10(cUnsatisfiable(i2003_11_14_17_19_39537), true2, i2003_11_14_17_19_39537), true2)
% 0.13/0.34 = { by axiom 1 (axiom_7) }
% 0.13/0.34 tuple(true2, fresh10(true2, true2, i2003_11_14_17_19_39537), true2)
% 0.13/0.34 = { by axiom 2 (axiom_2) }
% 0.13/0.34 tuple(true2, true2, true2)
% 0.13/0.34 % SZS output end Proof
% 0.13/0.34
% 0.13/0.34 RESULT: Unsatisfiable (the axioms are contradictory).
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