TSTP Solution File: KRS124+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS124+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 05:52:59 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% 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 : KRS124+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
% 0.17/0.34 % Computer : n026.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon Aug 28 01:44:49 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --no-flatten-goal
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Take the following subset of the input axioms:
% 0.19/0.41 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.19/0.41 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.19/0.41 fof(axiom_12, axiom, ![X2]: (ca_Ax3(X2) <=> (cd(X2) & cc(X2)))).
% 0.19/0.41 fof(axiom_13, axiom, cUnsatisfiable(i2003_11_14_17_22_10903)).
% 0.19/0.41 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y]: (rr(X2, Y) & cowlThing(Y)) & ![Y2]: (rr(X2, Y2) => ca_Ax3(Y2))))).
% 0.19/0.41 fof(axiom_3, axiom, ![X2]: (cc(X2) => cdxcomp(X2))).
% 0.19/0.41 fof(axiom_6, axiom, ![X2]: (cd(X2) <=> ~?[Y2]: ra_Px1(X2, Y2))).
% 0.19/0.41 fof(axiom_7, axiom, ![X2]: (cdxcomp(X2) <=> ?[Y0]: ra_Px1(X2, Y0))).
% 0.19/0.41 fof(axiom_9, axiom, ![X2]: (cd1xcomp(X2) <=> ~?[Y2]: ra_Px2(X2, Y2))).
% 0.19/0.41
% 0.19/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.41 fresh(y, y, x1...xn) = u
% 0.19/0.41 C => fresh(s, t, x1...xn) = v
% 0.19/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.41 variables of u and v.
% 0.19/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.41 input problem has no model of domain size 1).
% 0.19/0.41
% 0.19/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.41
% 0.19/0.41 Axiom 1 (axiom_13): cUnsatisfiable(i2003_11_14_17_22_10903) = true2.
% 0.19/0.41 Axiom 2 (axiom_12): fresh16(X, X, Y) = true2.
% 0.19/0.41 Axiom 3 (axiom_12_1): fresh15(X, X, Y) = true2.
% 0.19/0.41 Axiom 4 (axiom_2_3): fresh10(X, X, Y) = true2.
% 0.19/0.41 Axiom 5 (axiom_2_4): fresh8(X, X, Y) = true2.
% 0.19/0.41 Axiom 6 (axiom_3): fresh7(X, X, Y) = true2.
% 0.19/0.41 Axiom 7 (axiom_7): fresh4(X, X, Y) = true2.
% 0.19/0.41 Axiom 8 (axiom_12): fresh16(ca_Ax3(X), true2, X) = cc(X).
% 0.19/0.41 Axiom 9 (axiom_12_1): fresh15(ca_Ax3(X), true2, X) = cd(X).
% 0.19/0.41 Axiom 10 (axiom_2_3): fresh10(cUnsatisfiable(X), true2, X) = rr(X, y4(X)).
% 0.19/0.41 Axiom 11 (axiom_2_4): fresh9(X, X, Y, Z) = ca_Ax3(Z).
% 0.19/0.41 Axiom 12 (axiom_3): fresh7(cc(X), true2, X) = cdxcomp(X).
% 0.19/0.41 Axiom 13 (axiom_7): fresh4(cdxcomp(X), true2, X) = ra_Px1(X, y0_2(X)).
% 0.19/0.41 Axiom 14 (axiom_2_4): fresh9(rr(X, Y), true2, X, Y) = fresh8(cUnsatisfiable(X), true2, Y).
% 0.19/0.41
% 0.19/0.41 Lemma 15: ca_Ax3(y4(i2003_11_14_17_22_10903)) = true2.
% 0.19/0.41 Proof:
% 0.19/0.41 ca_Ax3(y4(i2003_11_14_17_22_10903))
% 0.19/0.41 = { by axiom 11 (axiom_2_4) R->L }
% 0.19/0.41 fresh9(true2, true2, i2003_11_14_17_22_10903, y4(i2003_11_14_17_22_10903))
% 0.19/0.41 = { by axiom 4 (axiom_2_3) R->L }
% 0.19/0.41 fresh9(fresh10(true2, true2, i2003_11_14_17_22_10903), true2, i2003_11_14_17_22_10903, y4(i2003_11_14_17_22_10903))
% 0.19/0.41 = { by axiom 1 (axiom_13) R->L }
% 0.19/0.41 fresh9(fresh10(cUnsatisfiable(i2003_11_14_17_22_10903), true2, i2003_11_14_17_22_10903), true2, i2003_11_14_17_22_10903, y4(i2003_11_14_17_22_10903))
% 0.19/0.41 = { by axiom 10 (axiom_2_3) }
% 0.19/0.41 fresh9(rr(i2003_11_14_17_22_10903, y4(i2003_11_14_17_22_10903)), true2, i2003_11_14_17_22_10903, y4(i2003_11_14_17_22_10903))
% 0.19/0.41 = { by axiom 14 (axiom_2_4) }
% 0.19/0.41 fresh8(cUnsatisfiable(i2003_11_14_17_22_10903), true2, y4(i2003_11_14_17_22_10903))
% 0.19/0.41 = { by axiom 1 (axiom_13) }
% 0.19/0.41 fresh8(true2, true2, y4(i2003_11_14_17_22_10903))
% 0.19/0.41 = { by axiom 5 (axiom_2_4) }
% 0.19/0.41 true2
% 0.19/0.41
% 0.19/0.41 Goal 1 (axiom_6_1): tuple(cd(X), ra_Px1(X, Y)) = tuple(true2, true2).
% 0.19/0.41 The goal is true when:
% 0.19/0.41 X = y4(i2003_11_14_17_22_10903)
% 0.19/0.41 Y = y0_2(y4(i2003_11_14_17_22_10903))
% 0.19/0.41
% 0.19/0.41 Proof:
% 0.19/0.41 tuple(cd(y4(i2003_11_14_17_22_10903)), ra_Px1(y4(i2003_11_14_17_22_10903), y0_2(y4(i2003_11_14_17_22_10903))))
% 0.19/0.41 = { by axiom 13 (axiom_7) R->L }
% 0.19/0.41 tuple(cd(y4(i2003_11_14_17_22_10903)), fresh4(cdxcomp(y4(i2003_11_14_17_22_10903)), true2, y4(i2003_11_14_17_22_10903)))
% 0.19/0.41 = { by axiom 12 (axiom_3) R->L }
% 0.19/0.41 tuple(cd(y4(i2003_11_14_17_22_10903)), fresh4(fresh7(cc(y4(i2003_11_14_17_22_10903)), true2, y4(i2003_11_14_17_22_10903)), true2, y4(i2003_11_14_17_22_10903)))
% 0.19/0.41 = { by axiom 8 (axiom_12) R->L }
% 0.19/0.41 tuple(cd(y4(i2003_11_14_17_22_10903)), fresh4(fresh7(fresh16(ca_Ax3(y4(i2003_11_14_17_22_10903)), true2, y4(i2003_11_14_17_22_10903)), true2, y4(i2003_11_14_17_22_10903)), true2, y4(i2003_11_14_17_22_10903)))
% 0.19/0.41 = { by lemma 15 }
% 0.19/0.41 tuple(cd(y4(i2003_11_14_17_22_10903)), fresh4(fresh7(fresh16(true2, true2, y4(i2003_11_14_17_22_10903)), true2, y4(i2003_11_14_17_22_10903)), true2, y4(i2003_11_14_17_22_10903)))
% 0.19/0.41 = { by axiom 2 (axiom_12) }
% 0.19/0.41 tuple(cd(y4(i2003_11_14_17_22_10903)), fresh4(fresh7(true2, true2, y4(i2003_11_14_17_22_10903)), true2, y4(i2003_11_14_17_22_10903)))
% 0.19/0.41 = { by axiom 6 (axiom_3) }
% 0.19/0.41 tuple(cd(y4(i2003_11_14_17_22_10903)), fresh4(true2, true2, y4(i2003_11_14_17_22_10903)))
% 0.19/0.41 = { by axiom 7 (axiom_7) }
% 0.19/0.41 tuple(cd(y4(i2003_11_14_17_22_10903)), true2)
% 0.19/0.41 = { by axiom 9 (axiom_12_1) R->L }
% 0.19/0.41 tuple(fresh15(ca_Ax3(y4(i2003_11_14_17_22_10903)), true2, y4(i2003_11_14_17_22_10903)), true2)
% 0.19/0.41 = { by lemma 15 }
% 0.19/0.41 tuple(fresh15(true2, true2, y4(i2003_11_14_17_22_10903)), true2)
% 0.19/0.41 = { by axiom 3 (axiom_12_1) }
% 0.19/0.41 tuple(true2, true2)
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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