TSTP Solution File: KRS092+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS092+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 : n026.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 05:52:52 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KRS092+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
% 0.13/0.35 % Computer : n026.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 01:59:19 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.40 Command-line arguments: --no-flatten-goal
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 Take the following subset of the input axioms:
% 0.21/0.41 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.21/0.41 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.21/0.41 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y]: (rr(X2, Y) & cowlThing(Y)) & ![Y2]: (rr(X2, Y2) => (cd(Y2) & cc(Y2)))))).
% 0.21/0.41 fof(axiom_3, axiom, ![X2]: (cc(X2) => ~cd(X2))).
% 0.21/0.41 fof(axiom_5, axiom, ![X2]: (cc1(X2) => ~cd1(X2))).
% 0.21/0.41 fof(axiom_8, axiom, cUnsatisfiable(i2003_11_14_17_20_04172)).
% 0.21/0.41
% 0.21/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.41 fresh(y, y, x1...xn) = u
% 0.21/0.41 C => fresh(s, t, x1...xn) = v
% 0.21/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.41 variables of u and v.
% 0.21/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.41 input problem has no model of domain size 1).
% 0.21/0.41
% 0.21/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.41
% 0.21/0.41 Axiom 1 (axiom_8): cUnsatisfiable(i2003_11_14_17_20_04172) = true2.
% 0.21/0.41 Axiom 2 (axiom_2_3): fresh8(X, X, Y) = true2.
% 0.21/0.41 Axiom 3 (axiom_2_4): fresh6(X, X, Y) = true2.
% 0.21/0.41 Axiom 4 (axiom_2_5): fresh4(X, X, Y) = true2.
% 0.21/0.41 Axiom 5 (axiom_2_3): fresh8(cUnsatisfiable(X), true2, X) = rr(X, y2(X)).
% 0.21/0.41 Axiom 6 (axiom_2_4): fresh7(X, X, Y, Z) = cd(Z).
% 0.21/0.41 Axiom 7 (axiom_2_5): fresh5(X, X, Y, Z) = cc(Z).
% 0.21/0.41 Axiom 8 (axiom_2_4): fresh7(rr(X, Y), true2, X, Y) = fresh6(cUnsatisfiable(X), true2, Y).
% 0.21/0.41 Axiom 9 (axiom_2_5): fresh5(rr(X, Y), true2, X, Y) = fresh4(cUnsatisfiable(X), true2, Y).
% 0.21/0.41
% 0.21/0.41 Lemma 10: rr(i2003_11_14_17_20_04172, y2(i2003_11_14_17_20_04172)) = true2.
% 0.21/0.41 Proof:
% 0.21/0.41 rr(i2003_11_14_17_20_04172, y2(i2003_11_14_17_20_04172))
% 0.21/0.41 = { by axiom 5 (axiom_2_3) R->L }
% 0.21/0.41 fresh8(cUnsatisfiable(i2003_11_14_17_20_04172), true2, i2003_11_14_17_20_04172)
% 0.21/0.41 = { by axiom 1 (axiom_8) }
% 0.21/0.41 fresh8(true2, true2, i2003_11_14_17_20_04172)
% 0.21/0.41 = { by axiom 2 (axiom_2_3) }
% 0.21/0.41 true2
% 0.21/0.41
% 0.21/0.41 Goal 1 (axiom_3): tuple(cd(X), cc(X)) = tuple(true2, true2).
% 0.21/0.41 The goal is true when:
% 0.21/0.41 X = y2(i2003_11_14_17_20_04172)
% 0.21/0.41
% 0.21/0.41 Proof:
% 0.21/0.41 tuple(cd(y2(i2003_11_14_17_20_04172)), cc(y2(i2003_11_14_17_20_04172)))
% 0.21/0.41 = { by axiom 7 (axiom_2_5) R->L }
% 0.21/0.41 tuple(cd(y2(i2003_11_14_17_20_04172)), fresh5(true2, true2, i2003_11_14_17_20_04172, y2(i2003_11_14_17_20_04172)))
% 0.21/0.41 = { by lemma 10 R->L }
% 0.21/0.41 tuple(cd(y2(i2003_11_14_17_20_04172)), fresh5(rr(i2003_11_14_17_20_04172, y2(i2003_11_14_17_20_04172)), true2, i2003_11_14_17_20_04172, y2(i2003_11_14_17_20_04172)))
% 0.21/0.41 = { by axiom 9 (axiom_2_5) }
% 0.21/0.41 tuple(cd(y2(i2003_11_14_17_20_04172)), fresh4(cUnsatisfiable(i2003_11_14_17_20_04172), true2, y2(i2003_11_14_17_20_04172)))
% 0.21/0.41 = { by axiom 1 (axiom_8) }
% 0.21/0.41 tuple(cd(y2(i2003_11_14_17_20_04172)), fresh4(true2, true2, y2(i2003_11_14_17_20_04172)))
% 0.21/0.41 = { by axiom 4 (axiom_2_5) }
% 0.21/0.41 tuple(cd(y2(i2003_11_14_17_20_04172)), true2)
% 0.21/0.41 = { by axiom 6 (axiom_2_4) R->L }
% 0.21/0.41 tuple(fresh7(true2, true2, i2003_11_14_17_20_04172, y2(i2003_11_14_17_20_04172)), true2)
% 0.21/0.41 = { by lemma 10 R->L }
% 0.21/0.41 tuple(fresh7(rr(i2003_11_14_17_20_04172, y2(i2003_11_14_17_20_04172)), true2, i2003_11_14_17_20_04172, y2(i2003_11_14_17_20_04172)), true2)
% 0.21/0.41 = { by axiom 8 (axiom_2_4) }
% 0.21/0.41 tuple(fresh6(cUnsatisfiable(i2003_11_14_17_20_04172), true2, y2(i2003_11_14_17_20_04172)), true2)
% 0.21/0.41 = { by axiom 1 (axiom_8) }
% 0.21/0.41 tuple(fresh6(true2, true2, y2(i2003_11_14_17_20_04172)), true2)
% 0.21/0.41 = { by axiom 3 (axiom_2_4) }
% 0.21/0.41 tuple(true2, true2)
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41
% 0.21/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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