TSTP Solution File: KRS110+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : KRS110+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 : n032.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 05:52:55 EDT 2023
% Result : Unsatisfiable 0.17s 0.41s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : KRS110+1 : TPTP v8.1.2. Released v3.1.0.
% 0.10/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n032.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 01:16:00 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.41 Command-line arguments: --no-flatten-goal
% 0.17/0.41
% 0.17/0.41 % SZS status Unsatisfiable
% 0.17/0.41
% 0.17/0.41 % SZS output start Proof
% 0.17/0.41 Take the following subset of the input axioms:
% 0.17/0.41 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.17/0.41 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.17/0.41 fof(axiom_12, axiom, cUnsatisfiable(i2003_11_14_17_21_12565)).
% 0.17/0.41 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y]: (rs(X2, Y) & ca_Ax2(Y)) & ![Y2]: (rs(X2, Y2) => cpxcomp(Y2))))).
% 0.17/0.41 fof(axiom_3, axiom, ![X2]: (cp(X2) <=> ~?[Y2]: ra_Px1(X2, Y2))).
% 0.17/0.41 fof(axiom_4, axiom, ![X2]: (cpxcomp(X2) <=> ?[Y0]: ra_Px1(X2, Y0))).
% 0.17/0.41 fof(axiom_5, axiom, ![X2]: (ca_Ax2(X2) <=> (cp(X2) & ?[Y2]: (rinvS(X2, Y2) & cp(Y2))))).
% 0.17/0.41
% 0.17/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.17/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.17/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.17/0.41 fresh(y, y, x1...xn) = u
% 0.17/0.41 C => fresh(s, t, x1...xn) = v
% 0.17/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.17/0.41 variables of u and v.
% 0.17/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.17/0.41 input problem has no model of domain size 1).
% 0.17/0.41
% 0.17/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.17/0.41
% 0.17/0.41 Axiom 1 (axiom_12): cUnsatisfiable(i2003_11_14_17_21_12565) = true2.
% 0.17/0.41 Axiom 2 (axiom_2): fresh21(X, X, Y) = true2.
% 0.17/0.41 Axiom 3 (axiom_2_1): fresh20(X, X, Y) = true2.
% 0.17/0.41 Axiom 4 (axiom_2_2): fresh18(X, X, Y) = true2.
% 0.17/0.41 Axiom 5 (axiom_4): fresh16(X, X, Y) = true2.
% 0.17/0.41 Axiom 6 (axiom_5): fresh14(X, X, Y) = true2.
% 0.17/0.41 Axiom 7 (axiom_2): fresh21(cUnsatisfiable(X), true2, X) = ca_Ax2(y4(X)).
% 0.17/0.41 Axiom 8 (axiom_2_1): fresh20(cUnsatisfiable(X), true2, X) = rs(X, y4(X)).
% 0.17/0.41 Axiom 9 (axiom_2_2): fresh19(X, X, Y, Z) = cpxcomp(Z).
% 0.17/0.41 Axiom 10 (axiom_4): fresh16(cpxcomp(X), true2, X) = ra_Px1(X, y0(X)).
% 0.17/0.41 Axiom 11 (axiom_5): fresh14(ca_Ax2(X), true2, X) = cp(X).
% 0.17/0.42 Axiom 12 (axiom_2_2): fresh19(rs(X, Y), true2, X, Y) = fresh18(cUnsatisfiable(X), true2, Y).
% 0.17/0.42
% 0.17/0.42 Goal 1 (axiom_3_1): tuple(cp(X), ra_Px1(X, Y)) = tuple(true2, true2).
% 0.17/0.42 The goal is true when:
% 0.17/0.42 X = y4(i2003_11_14_17_21_12565)
% 0.17/0.42 Y = y0(y4(i2003_11_14_17_21_12565))
% 0.17/0.42
% 0.17/0.42 Proof:
% 0.17/0.42 tuple(cp(y4(i2003_11_14_17_21_12565)), ra_Px1(y4(i2003_11_14_17_21_12565), y0(y4(i2003_11_14_17_21_12565))))
% 0.17/0.42 = { by axiom 10 (axiom_4) R->L }
% 0.17/0.42 tuple(cp(y4(i2003_11_14_17_21_12565)), fresh16(cpxcomp(y4(i2003_11_14_17_21_12565)), true2, y4(i2003_11_14_17_21_12565)))
% 0.17/0.42 = { by axiom 9 (axiom_2_2) R->L }
% 0.17/0.42 tuple(cp(y4(i2003_11_14_17_21_12565)), fresh16(fresh19(true2, true2, i2003_11_14_17_21_12565, y4(i2003_11_14_17_21_12565)), true2, y4(i2003_11_14_17_21_12565)))
% 0.17/0.42 = { by axiom 3 (axiom_2_1) R->L }
% 0.17/0.42 tuple(cp(y4(i2003_11_14_17_21_12565)), fresh16(fresh19(fresh20(true2, true2, i2003_11_14_17_21_12565), true2, i2003_11_14_17_21_12565, y4(i2003_11_14_17_21_12565)), true2, y4(i2003_11_14_17_21_12565)))
% 0.17/0.42 = { by axiom 1 (axiom_12) R->L }
% 0.17/0.42 tuple(cp(y4(i2003_11_14_17_21_12565)), fresh16(fresh19(fresh20(cUnsatisfiable(i2003_11_14_17_21_12565), true2, i2003_11_14_17_21_12565), true2, i2003_11_14_17_21_12565, y4(i2003_11_14_17_21_12565)), true2, y4(i2003_11_14_17_21_12565)))
% 0.17/0.42 = { by axiom 8 (axiom_2_1) }
% 0.17/0.42 tuple(cp(y4(i2003_11_14_17_21_12565)), fresh16(fresh19(rs(i2003_11_14_17_21_12565, y4(i2003_11_14_17_21_12565)), true2, i2003_11_14_17_21_12565, y4(i2003_11_14_17_21_12565)), true2, y4(i2003_11_14_17_21_12565)))
% 0.17/0.42 = { by axiom 12 (axiom_2_2) }
% 0.17/0.42 tuple(cp(y4(i2003_11_14_17_21_12565)), fresh16(fresh18(cUnsatisfiable(i2003_11_14_17_21_12565), true2, y4(i2003_11_14_17_21_12565)), true2, y4(i2003_11_14_17_21_12565)))
% 0.17/0.42 = { by axiom 1 (axiom_12) }
% 0.17/0.42 tuple(cp(y4(i2003_11_14_17_21_12565)), fresh16(fresh18(true2, true2, y4(i2003_11_14_17_21_12565)), true2, y4(i2003_11_14_17_21_12565)))
% 0.17/0.42 = { by axiom 4 (axiom_2_2) }
% 0.17/0.42 tuple(cp(y4(i2003_11_14_17_21_12565)), fresh16(true2, true2, y4(i2003_11_14_17_21_12565)))
% 0.17/0.42 = { by axiom 5 (axiom_4) }
% 0.17/0.42 tuple(cp(y4(i2003_11_14_17_21_12565)), true2)
% 0.17/0.42 = { by axiom 11 (axiom_5) R->L }
% 0.17/0.42 tuple(fresh14(ca_Ax2(y4(i2003_11_14_17_21_12565)), true2, y4(i2003_11_14_17_21_12565)), true2)
% 0.17/0.42 = { by axiom 7 (axiom_2) R->L }
% 0.17/0.42 tuple(fresh14(fresh21(cUnsatisfiable(i2003_11_14_17_21_12565), true2, i2003_11_14_17_21_12565), true2, y4(i2003_11_14_17_21_12565)), true2)
% 0.17/0.42 = { by axiom 1 (axiom_12) }
% 0.17/0.42 tuple(fresh14(fresh21(true2, true2, i2003_11_14_17_21_12565), true2, y4(i2003_11_14_17_21_12565)), true2)
% 0.17/0.42 = { by axiom 2 (axiom_2) }
% 0.17/0.42 tuple(fresh14(true2, true2, y4(i2003_11_14_17_21_12565)), true2)
% 0.17/0.42 = { by axiom 6 (axiom_5) }
% 0.17/0.42 tuple(true2, true2)
% 0.17/0.42 % SZS output end Proof
% 0.17/0.42
% 0.17/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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