TSTP Solution File: KRS097+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : KRS097+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 : n021.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 05:52:53 EDT 2023
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS097+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
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 02:31:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.42 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Take the following subset of the input axioms:
% 0.20/0.43 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.20/0.43 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.20/0.43 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y0]: rr(X2, Y0) & (?[Y2]: (rr(X2, Y2) & cd(Y2)) & (~?[Y1, Y0_2]: (rr(X2, Y0_2) & (rr(X2, Y1) & Y0_2!=Y1)) & ?[Y]: (rr(X2, Y) & cc(Y))))))).
% 0.20/0.43 fof(axiom_4, axiom, cUnsatisfiable(i2003_11_14_17_20_21603)).
% 0.20/0.43 fof(axiom_5, axiom, ![X2]: ~(cd(X2) & ce(X2))).
% 0.20/0.43 fof(axiom_6, axiom, ![X2]: ~(cd(X2) & cc(X2))).
% 0.20/0.43 fof(axiom_7, axiom, ![X2]: ~(ce(X2) & cc(X2))).
% 0.20/0.43
% 0.20/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.43 fresh(y, y, x1...xn) = u
% 0.20/0.43 C => fresh(s, t, x1...xn) = v
% 0.20/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.43 variables of u and v.
% 0.20/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.43 input problem has no model of domain size 1).
% 0.20/0.43
% 0.20/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.43
% 0.20/0.43 Axiom 1 (axiom_4): cUnsatisfiable(i2003_11_14_17_20_21603) = true2.
% 0.20/0.43 Axiom 2 (axiom_2_1): fresh10(X, X, Y) = true2.
% 0.20/0.43 Axiom 3 (axiom_2_2): fresh9(X, X, Y) = true2.
% 0.20/0.43 Axiom 4 (axiom_2_3): fresh8(X, X, Y) = true2.
% 0.20/0.43 Axiom 5 (axiom_2_4): fresh7(X, X, Y) = true2.
% 0.20/0.43 Axiom 6 (axiom_2_5): fresh6(X, X, Y) = true2.
% 0.20/0.43 Axiom 7 (axiom_2_6): fresh22(X, X, Y, Z) = Z.
% 0.20/0.43 Axiom 8 (axiom_2_1): fresh10(cUnsatisfiable(X), true2, X) = cc(y(X)).
% 0.20/0.43 Axiom 9 (axiom_2_2): fresh9(cUnsatisfiable(X), true2, X) = cd(y2(X)).
% 0.20/0.43 Axiom 10 (axiom_2_3): fresh8(cUnsatisfiable(X), true2, X) = rr(X, y0_2(X)).
% 0.20/0.43 Axiom 11 (axiom_2_4): fresh7(cUnsatisfiable(X), true2, X) = rr(X, y2(X)).
% 0.20/0.43 Axiom 12 (axiom_2_5): fresh6(cUnsatisfiable(X), true2, X) = rr(X, y(X)).
% 0.20/0.43 Axiom 13 (axiom_2_6): fresh(X, X, Y, Z, W) = Z.
% 0.20/0.43 Axiom 14 (axiom_2_6): fresh21(X, X, Y, Z, W) = fresh22(cUnsatisfiable(Y), true2, Z, W).
% 0.20/0.43 Axiom 15 (axiom_2_6): fresh21(rr(X, Y), true2, X, Z, Y) = fresh(rr(X, Z), true2, X, Z, Y).
% 0.20/0.43
% 0.20/0.43 Lemma 16: fresh(rr(i2003_11_14_17_20_21603, X), true2, i2003_11_14_17_20_21603, X, y0_2(i2003_11_14_17_20_21603)) = y0_2(i2003_11_14_17_20_21603).
% 0.20/0.43 Proof:
% 0.20/0.43 fresh(rr(i2003_11_14_17_20_21603, X), true2, i2003_11_14_17_20_21603, X, y0_2(i2003_11_14_17_20_21603))
% 0.20/0.43 = { by axiom 15 (axiom_2_6) R->L }
% 0.20/0.43 fresh21(rr(i2003_11_14_17_20_21603, y0_2(i2003_11_14_17_20_21603)), true2, i2003_11_14_17_20_21603, X, y0_2(i2003_11_14_17_20_21603))
% 0.20/0.43 = { by axiom 10 (axiom_2_3) R->L }
% 0.20/0.43 fresh21(fresh8(cUnsatisfiable(i2003_11_14_17_20_21603), true2, i2003_11_14_17_20_21603), true2, i2003_11_14_17_20_21603, X, y0_2(i2003_11_14_17_20_21603))
% 0.20/0.43 = { by axiom 1 (axiom_4) }
% 0.20/0.43 fresh21(fresh8(true2, true2, i2003_11_14_17_20_21603), true2, i2003_11_14_17_20_21603, X, y0_2(i2003_11_14_17_20_21603))
% 0.20/0.43 = { by axiom 4 (axiom_2_3) }
% 0.20/0.43 fresh21(true2, true2, i2003_11_14_17_20_21603, X, y0_2(i2003_11_14_17_20_21603))
% 0.20/0.43 = { by axiom 14 (axiom_2_6) }
% 0.20/0.43 fresh22(cUnsatisfiable(i2003_11_14_17_20_21603), true2, X, y0_2(i2003_11_14_17_20_21603))
% 0.20/0.43 = { by axiom 1 (axiom_4) }
% 0.20/0.43 fresh22(true2, true2, X, y0_2(i2003_11_14_17_20_21603))
% 0.20/0.43 = { by axiom 7 (axiom_2_6) }
% 0.20/0.43 y0_2(i2003_11_14_17_20_21603)
% 0.20/0.43
% 0.20/0.43 Goal 1 (axiom_6): tuple(cc(X), cd(X)) = tuple(true2, true2).
% 0.20/0.43 The goal is true when:
% 0.20/0.43 X = y(i2003_11_14_17_20_21603)
% 0.20/0.43
% 0.20/0.43 Proof:
% 0.20/0.43 tuple(cc(y(i2003_11_14_17_20_21603)), cd(y(i2003_11_14_17_20_21603)))
% 0.20/0.43 = { by axiom 8 (axiom_2_1) R->L }
% 0.20/0.43 tuple(fresh10(cUnsatisfiable(i2003_11_14_17_20_21603), true2, i2003_11_14_17_20_21603), cd(y(i2003_11_14_17_20_21603)))
% 0.20/0.43 = { by axiom 1 (axiom_4) }
% 0.20/0.43 tuple(fresh10(true2, true2, i2003_11_14_17_20_21603), cd(y(i2003_11_14_17_20_21603)))
% 0.20/0.43 = { by axiom 2 (axiom_2_1) }
% 0.20/0.43 tuple(true2, cd(y(i2003_11_14_17_20_21603)))
% 0.20/0.43 = { by axiom 13 (axiom_2_6) R->L }
% 0.20/0.43 tuple(true2, cd(fresh(true2, true2, i2003_11_14_17_20_21603, y(i2003_11_14_17_20_21603), y0_2(i2003_11_14_17_20_21603))))
% 0.20/0.43 = { by axiom 6 (axiom_2_5) R->L }
% 0.20/0.43 tuple(true2, cd(fresh(fresh6(true2, true2, i2003_11_14_17_20_21603), true2, i2003_11_14_17_20_21603, y(i2003_11_14_17_20_21603), y0_2(i2003_11_14_17_20_21603))))
% 0.20/0.43 = { by axiom 1 (axiom_4) R->L }
% 0.20/0.43 tuple(true2, cd(fresh(fresh6(cUnsatisfiable(i2003_11_14_17_20_21603), true2, i2003_11_14_17_20_21603), true2, i2003_11_14_17_20_21603, y(i2003_11_14_17_20_21603), y0_2(i2003_11_14_17_20_21603))))
% 0.20/0.43 = { by axiom 12 (axiom_2_5) }
% 0.20/0.43 tuple(true2, cd(fresh(rr(i2003_11_14_17_20_21603, y(i2003_11_14_17_20_21603)), true2, i2003_11_14_17_20_21603, y(i2003_11_14_17_20_21603), y0_2(i2003_11_14_17_20_21603))))
% 0.20/0.43 = { by lemma 16 }
% 0.20/0.43 tuple(true2, cd(y0_2(i2003_11_14_17_20_21603)))
% 0.20/0.43 = { by lemma 16 R->L }
% 0.20/0.43 tuple(true2, cd(fresh(rr(i2003_11_14_17_20_21603, y2(i2003_11_14_17_20_21603)), true2, i2003_11_14_17_20_21603, y2(i2003_11_14_17_20_21603), y0_2(i2003_11_14_17_20_21603))))
% 0.20/0.43 = { by axiom 11 (axiom_2_4) R->L }
% 0.20/0.43 tuple(true2, cd(fresh(fresh7(cUnsatisfiable(i2003_11_14_17_20_21603), true2, i2003_11_14_17_20_21603), true2, i2003_11_14_17_20_21603, y2(i2003_11_14_17_20_21603), y0_2(i2003_11_14_17_20_21603))))
% 0.20/0.43 = { by axiom 1 (axiom_4) }
% 0.20/0.43 tuple(true2, cd(fresh(fresh7(true2, true2, i2003_11_14_17_20_21603), true2, i2003_11_14_17_20_21603, y2(i2003_11_14_17_20_21603), y0_2(i2003_11_14_17_20_21603))))
% 0.20/0.43 = { by axiom 5 (axiom_2_4) }
% 0.20/0.43 tuple(true2, cd(fresh(true2, true2, i2003_11_14_17_20_21603, y2(i2003_11_14_17_20_21603), y0_2(i2003_11_14_17_20_21603))))
% 0.20/0.43 = { by axiom 13 (axiom_2_6) }
% 0.20/0.43 tuple(true2, cd(y2(i2003_11_14_17_20_21603)))
% 0.20/0.43 = { by axiom 9 (axiom_2_2) R->L }
% 0.20/0.43 tuple(true2, fresh9(cUnsatisfiable(i2003_11_14_17_20_21603), true2, i2003_11_14_17_20_21603))
% 0.20/0.43 = { by axiom 1 (axiom_4) }
% 0.20/0.43 tuple(true2, fresh9(true2, true2, i2003_11_14_17_20_21603))
% 0.20/0.43 = { by axiom 3 (axiom_2_2) }
% 0.20/0.43 tuple(true2, true2)
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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