TSTP Solution File: KRS126+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS126+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 : n027.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 05:52:59 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% 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 : KRS126+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
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 02:46:51 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Take the following subset of the input axioms:
% 0.19/0.39 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.19/0.39 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.19/0.39 fof(axiom_11, axiom, cUnsatisfiable(i2003_11_14_17_22_23554)).
% 0.19/0.39 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) => cd1xcomp(X2))).
% 0.19/0.39 fof(axiom_3, axiom, ![X2]: (cUnsatisfiable(X2) => cd1(X2))).
% 0.19/0.39 fof(axiom_5, axiom, ![X2]: (cd(X2) <=> ~?[Y]: ra_Px1(X2, Y))).
% 0.19/0.39 fof(axiom_7, axiom, ![X2]: (cd1(X2) <=> ?[Y0]: ra_Px2(X2, Y0))).
% 0.19/0.39 fof(axiom_8, axiom, ![X2]: (cd1xcomp(X2) <=> ~?[Y2]: ra_Px2(X2, Y2))).
% 0.19/0.39
% 0.19/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.39 fresh(y, y, x1...xn) = u
% 0.19/0.39 C => fresh(s, t, x1...xn) = v
% 0.19/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.39 variables of u and v.
% 0.19/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.39 input problem has no model of domain size 1).
% 0.19/0.39
% 0.19/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.39
% 0.19/0.39 Axiom 1 (axiom_11): cUnsatisfiable(i2003_11_14_17_22_23554) = true2.
% 0.19/0.39 Axiom 2 (axiom_2): fresh9(X, X, Y) = true2.
% 0.19/0.39 Axiom 3 (axiom_3): fresh7(X, X, Y) = true2.
% 0.19/0.39 Axiom 4 (axiom_7): fresh3(X, X, Y) = true2.
% 0.19/0.39 Axiom 5 (axiom_2): fresh9(cUnsatisfiable(X), true2, X) = cd1xcomp(X).
% 0.19/0.39 Axiom 6 (axiom_3): fresh7(cUnsatisfiable(X), true2, X) = cd1(X).
% 0.19/0.39 Axiom 7 (axiom_7): fresh3(cd1(X), true2, X) = ra_Px2(X, y0(X)).
% 0.19/0.39
% 0.19/0.39 Goal 1 (axiom_8_1): tuple(cd1xcomp(X), ra_Px2(X, Y)) = tuple(true2, true2).
% 0.19/0.39 The goal is true when:
% 0.19/0.39 X = i2003_11_14_17_22_23554
% 0.19/0.39 Y = y0(i2003_11_14_17_22_23554)
% 0.19/0.39
% 0.19/0.39 Proof:
% 0.19/0.39 tuple(cd1xcomp(i2003_11_14_17_22_23554), ra_Px2(i2003_11_14_17_22_23554, y0(i2003_11_14_17_22_23554)))
% 0.19/0.39 = { by axiom 7 (axiom_7) R->L }
% 0.19/0.39 tuple(cd1xcomp(i2003_11_14_17_22_23554), fresh3(cd1(i2003_11_14_17_22_23554), true2, i2003_11_14_17_22_23554))
% 0.19/0.40 = { by axiom 6 (axiom_3) R->L }
% 0.19/0.40 tuple(cd1xcomp(i2003_11_14_17_22_23554), fresh3(fresh7(cUnsatisfiable(i2003_11_14_17_22_23554), true2, i2003_11_14_17_22_23554), true2, i2003_11_14_17_22_23554))
% 0.19/0.40 = { by axiom 1 (axiom_11) }
% 0.19/0.40 tuple(cd1xcomp(i2003_11_14_17_22_23554), fresh3(fresh7(true2, true2, i2003_11_14_17_22_23554), true2, i2003_11_14_17_22_23554))
% 0.19/0.40 = { by axiom 3 (axiom_3) }
% 0.19/0.40 tuple(cd1xcomp(i2003_11_14_17_22_23554), fresh3(true2, true2, i2003_11_14_17_22_23554))
% 0.19/0.40 = { by axiom 4 (axiom_7) }
% 0.19/0.40 tuple(cd1xcomp(i2003_11_14_17_22_23554), true2)
% 0.19/0.40 = { by axiom 5 (axiom_2) R->L }
% 0.19/0.40 tuple(fresh9(cUnsatisfiable(i2003_11_14_17_22_23554), true2, i2003_11_14_17_22_23554), true2)
% 0.19/0.40 = { by axiom 1 (axiom_11) }
% 0.19/0.40 tuple(fresh9(true2, true2, i2003_11_14_17_22_23554), true2)
% 0.19/0.40 = { by axiom 2 (axiom_2) }
% 0.19/0.40 tuple(true2, true2)
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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