TSTP Solution File: KRS074+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS074+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 : n009.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 05:52:48 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% 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 : KRS074+1 : TPTP v8.1.2. Released v3.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 02:12:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.40 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
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% 0.20/0.40 % SZS status Unsatisfiable
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% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Take the following subset of the input axioms:
% 0.20/0.40 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.20/0.40 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.20/0.40 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y]: (rs(X2, Y) & (cp(Y) & ?[Z]: (rinvS(Y, Z) & cp(Z)))) & ![Y2]: (rs(X2, Y2) => ~cp(Y2))))).
% 0.20/0.40 fof(axiom_9, axiom, cUnsatisfiable(i2003_11_14_17_18_59896)).
% 0.20/0.40
% 0.20/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40 fresh(y, y, x1...xn) = u
% 0.20/0.40 C => fresh(s, t, x1...xn) = v
% 0.20/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40 variables of u and v.
% 0.20/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40 input problem has no model of domain size 1).
% 0.20/0.40
% 0.20/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.40
% 0.20/0.40 Axiom 1 (axiom_9): cUnsatisfiable(i2003_11_14_17_18_59896) = true2.
% 0.20/0.40 Axiom 2 (axiom_2): fresh16(X, X, Y) = true2.
% 0.20/0.40 Axiom 3 (axiom_2_3): fresh13(X, X, Y) = true2.
% 0.20/0.40 Axiom 4 (axiom_2): fresh16(cUnsatisfiable(X), true2, X) = cp(y2(X)).
% 0.20/0.40 Axiom 5 (axiom_2_3): fresh13(cUnsatisfiable(X), true2, X) = rs(X, y2(X)).
% 0.20/0.40
% 0.20/0.40 Goal 1 (axiom_2_4): tuple(cUnsatisfiable(X), cp(Y), rs(X, Y)) = tuple(true2, true2, true2).
% 0.20/0.40 The goal is true when:
% 0.20/0.40 X = i2003_11_14_17_18_59896
% 0.20/0.40 Y = y2(i2003_11_14_17_18_59896)
% 0.20/0.40
% 0.20/0.40 Proof:
% 0.20/0.40 tuple(cUnsatisfiable(i2003_11_14_17_18_59896), cp(y2(i2003_11_14_17_18_59896)), rs(i2003_11_14_17_18_59896, y2(i2003_11_14_17_18_59896)))
% 0.20/0.40 = { by axiom 5 (axiom_2_3) R->L }
% 0.20/0.40 tuple(cUnsatisfiable(i2003_11_14_17_18_59896), cp(y2(i2003_11_14_17_18_59896)), fresh13(cUnsatisfiable(i2003_11_14_17_18_59896), true2, i2003_11_14_17_18_59896))
% 0.20/0.40 = { by axiom 1 (axiom_9) }
% 0.20/0.40 tuple(cUnsatisfiable(i2003_11_14_17_18_59896), cp(y2(i2003_11_14_17_18_59896)), fresh13(true2, true2, i2003_11_14_17_18_59896))
% 0.20/0.40 = { by axiom 3 (axiom_2_3) }
% 0.20/0.40 tuple(cUnsatisfiable(i2003_11_14_17_18_59896), cp(y2(i2003_11_14_17_18_59896)), true2)
% 0.20/0.40 = { by axiom 1 (axiom_9) }
% 0.20/0.40 tuple(true2, cp(y2(i2003_11_14_17_18_59896)), true2)
% 0.20/0.40 = { by axiom 4 (axiom_2) R->L }
% 0.20/0.40 tuple(true2, fresh16(cUnsatisfiable(i2003_11_14_17_18_59896), true2, i2003_11_14_17_18_59896), true2)
% 0.20/0.40 = { by axiom 1 (axiom_9) }
% 0.20/0.40 tuple(true2, fresh16(true2, true2, i2003_11_14_17_18_59896), true2)
% 0.20/0.40 = { by axiom 2 (axiom_2) }
% 0.20/0.40 tuple(true2, true2, true2)
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40
% 0.20/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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