TSTP Solution File: KRS094+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS094+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 : n024.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 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS094+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.13 % 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 : n024.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 02:25:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.38 Command-line arguments: --no-flatten-goal
% 0.18/0.38
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 Take the following subset of the input axioms:
% 0.18/0.38 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.18/0.38 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.18/0.38 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> cc1(X2))).
% 0.18/0.38 fof(axiom_3, axiom, ![X2]: (cc(X2) => ~cd(X2))).
% 0.18/0.38 fof(axiom_4, axiom, ![X2]: (cc1(X2) => ~cd1(X2))).
% 0.18/0.38 fof(axiom_5, axiom, ![X2]: (cc1(X2) => cd1(X2))).
% 0.18/0.38 fof(axiom_8, axiom, cUnsatisfiable(i2003_11_14_17_20_11330)).
% 0.18/0.38
% 0.18/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.38 fresh(y, y, x1...xn) = u
% 0.18/0.38 C => fresh(s, t, x1...xn) = v
% 0.18/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.38 variables of u and v.
% 0.18/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.38 input problem has no model of domain size 1).
% 0.18/0.38
% 0.18/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.38
% 0.18/0.38 Axiom 1 (axiom_8): cUnsatisfiable(i2003_11_14_17_20_11330) = true2.
% 0.18/0.38 Axiom 2 (axiom_2): fresh4(X, X, Y) = true2.
% 0.18/0.38 Axiom 3 (axiom_5): fresh3(X, X, Y) = true2.
% 0.18/0.38 Axiom 4 (axiom_2): fresh4(cUnsatisfiable(X), true2, X) = cc1(X).
% 0.18/0.38 Axiom 5 (axiom_5): fresh3(cc1(X), true2, X) = cd1(X).
% 0.18/0.38
% 0.18/0.38 Lemma 6: cc1(i2003_11_14_17_20_11330) = true2.
% 0.18/0.38 Proof:
% 0.18/0.38 cc1(i2003_11_14_17_20_11330)
% 0.18/0.38 = { by axiom 4 (axiom_2) R->L }
% 0.18/0.38 fresh4(cUnsatisfiable(i2003_11_14_17_20_11330), true2, i2003_11_14_17_20_11330)
% 0.18/0.38 = { by axiom 1 (axiom_8) }
% 0.18/0.38 fresh4(true2, true2, i2003_11_14_17_20_11330)
% 0.18/0.38 = { by axiom 2 (axiom_2) }
% 0.18/0.38 true2
% 0.18/0.38
% 0.18/0.38 Goal 1 (axiom_4): tuple(cc1(X), cd1(X)) = tuple(true2, true2).
% 0.18/0.38 The goal is true when:
% 0.18/0.38 X = i2003_11_14_17_20_11330
% 0.18/0.38
% 0.18/0.38 Proof:
% 0.18/0.38 tuple(cc1(i2003_11_14_17_20_11330), cd1(i2003_11_14_17_20_11330))
% 0.18/0.38 = { by axiom 5 (axiom_5) R->L }
% 0.18/0.38 tuple(cc1(i2003_11_14_17_20_11330), fresh3(cc1(i2003_11_14_17_20_11330), true2, i2003_11_14_17_20_11330))
% 0.18/0.38 = { by lemma 6 }
% 0.18/0.38 tuple(cc1(i2003_11_14_17_20_11330), fresh3(true2, true2, i2003_11_14_17_20_11330))
% 0.18/0.38 = { by axiom 3 (axiom_5) }
% 0.18/0.39 tuple(cc1(i2003_11_14_17_20_11330), true2)
% 0.18/0.39 = { by lemma 6 }
% 0.18/0.39 tuple(true2, true2)
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39
% 0.18/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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