TSTP Solution File: KRS114+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS114+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 : n021.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 05:52:56 EDT 2023
% Result : Unsatisfiable 0.19s 0.43s
% 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 : KRS114+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 : n021.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 01:14:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.43 Command-line arguments: --no-flatten-goal
% 0.19/0.43
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 Take the following subset of the input axioms:
% 0.19/0.44 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.19/0.44 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.19/0.44 fof(axiom_10, axiom, ![Y, X2]: (rinvR(X2, Y) <=> rr(Y, X2))).
% 0.19/0.44 fof(axiom_11, axiom, cUnsatisfiable(i2003_11_14_17_21_262)).
% 0.19/0.45 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y2]: (rr(X2, Y2) & ca_Ax4(Y2)) & ?[Y3]: (rs(X2, Y3) & ca_Ax3(Y3))))).
% 0.19/0.45 fof(axiom_3, axiom, ![X2]: (cp(X2) <=> ~?[Y3]: ra_Px1(X2, Y3))).
% 0.19/0.45 fof(axiom_4, axiom, ![X2]: (cpxcomp(X2) <=> ?[Y0]: ra_Px1(X2, Y0))).
% 0.19/0.45 fof(axiom_6, axiom, ![X2]: (cqxcomp(X2) <=> ~?[Y3]: ra_Px2(X2, Y3))).
% 0.19/0.45 fof(axiom_7, axiom, ![X2]: (ca_Ax3(X2) <=> (cqxcomp(X2) & cpxcomp(X2)))).
% 0.19/0.45 fof(axiom_8, axiom, ![X2]: (ca_Ax4(X2) <=> (![Y1, Y0_2]: ((rinvR(X2, Y0_2) & rinvR(X2, Y1)) => Y0_2=Y1) & ?[Y3]: (rinvR(X2, Y3) & ca_Vx5(Y3))))).
% 0.19/0.45 fof(axiom_9, axiom, ![X2]: (ca_Vx5(X2) <=> ![Y3]: (rs(X2, Y3) => cp(Y3)))).
% 0.19/0.45
% 0.19/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.45 fresh(y, y, x1...xn) = u
% 0.19/0.45 C => fresh(s, t, x1...xn) = v
% 0.19/0.45 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.45 variables of u and v.
% 0.19/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.45 input problem has no model of domain size 1).
% 0.19/0.45
% 0.19/0.45 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.45
% 0.19/0.45 Axiom 1 (axiom_11): cUnsatisfiable(i2003_11_14_17_21_262) = true2.
% 0.19/0.45 Axiom 2 (axiom_2): fresh19(X, X, Y) = true2.
% 0.19/0.45 Axiom 3 (axiom_2_1): fresh18(X, X, Y) = true2.
% 0.19/0.45 Axiom 4 (axiom_2_2): fresh17(X, X, Y) = true2.
% 0.19/0.45 Axiom 5 (axiom_2_3): fresh16(X, X, Y) = true2.
% 0.19/0.45 Axiom 6 (axiom_4): fresh15(X, X, Y) = true2.
% 0.19/0.45 Axiom 7 (axiom_7): fresh11(X, X, Y) = true2.
% 0.19/0.45 Axiom 8 (axiom_8_1): fresh6(X, X, Y) = true2.
% 0.19/0.45 Axiom 9 (axiom_8_2): fresh5(X, X, Y) = true2.
% 0.19/0.45 Axiom 10 (axiom_9_1): fresh3(X, X, Y) = true2.
% 0.19/0.45 Axiom 11 (axiom_8_3): fresh25(X, X, Y, Z) = Z.
% 0.19/0.45 Axiom 12 (axiom_10_1): fresh21(X, X, Y, Z) = true2.
% 0.19/0.45 Axiom 13 (axiom_2): fresh19(cUnsatisfiable(X), true2, X) = ca_Ax3(y5(X)).
% 0.19/0.45 Axiom 14 (axiom_2_1): fresh18(cUnsatisfiable(X), true2, X) = ca_Ax4(y6(X)).
% 0.19/0.45 Axiom 15 (axiom_2_2): fresh17(cUnsatisfiable(X), true2, X) = rr(X, y6(X)).
% 0.19/0.45 Axiom 16 (axiom_2_3): fresh16(cUnsatisfiable(X), true2, X) = rs(X, y5(X)).
% 0.19/0.45 Axiom 17 (axiom_4): fresh15(cpxcomp(X), true2, X) = ra_Px1(X, y0_3(X)).
% 0.19/0.45 Axiom 18 (axiom_7): fresh11(ca_Ax3(X), true2, X) = cpxcomp(X).
% 0.19/0.45 Axiom 19 (axiom_8_1): fresh6(ca_Ax4(X), true2, X) = ca_Vx5(y2(X)).
% 0.19/0.45 Axiom 20 (axiom_8_2): fresh5(ca_Ax4(X), true2, X) = rinvR(X, y2(X)).
% 0.19/0.45 Axiom 21 (axiom_9_1): fresh4(X, X, Y, Z) = cp(Z).
% 0.19/0.45 Axiom 22 (axiom_8_3): fresh(X, X, Y, Z, W) = Z.
% 0.19/0.45 Axiom 23 (axiom_8_3): fresh24(X, X, Y, Z, W) = fresh25(ca_Ax4(Y), true2, Z, W).
% 0.19/0.45 Axiom 24 (axiom_10_1): fresh21(rr(X, Y), true2, Y, X) = rinvR(Y, X).
% 0.19/0.45 Axiom 25 (axiom_9_1): fresh4(rs(X, Y), true2, X, Y) = fresh3(ca_Vx5(X), true2, Y).
% 0.19/0.45 Axiom 26 (axiom_8_3): fresh24(rinvR(X, Y), true2, X, Z, Y) = fresh(rinvR(X, Z), true2, X, Z, Y).
% 0.19/0.45
% 0.19/0.45 Lemma 27: ca_Ax4(y6(i2003_11_14_17_21_262)) = true2.
% 0.19/0.45 Proof:
% 0.19/0.45 ca_Ax4(y6(i2003_11_14_17_21_262))
% 0.19/0.45 = { by axiom 14 (axiom_2_1) R->L }
% 0.19/0.45 fresh18(cUnsatisfiable(i2003_11_14_17_21_262), true2, i2003_11_14_17_21_262)
% 0.19/0.45 = { by axiom 1 (axiom_11) }
% 0.19/0.45 fresh18(true2, true2, i2003_11_14_17_21_262)
% 0.19/0.45 = { by axiom 3 (axiom_2_1) }
% 0.19/0.45 true2
% 0.19/0.45
% 0.19/0.45 Goal 1 (axiom_3_1): tuple(cp(X), ra_Px1(X, Y)) = tuple(true2, true2).
% 0.19/0.45 The goal is true when:
% 0.19/0.45 X = y5(i2003_11_14_17_21_262)
% 0.19/0.45 Y = y0_3(y5(i2003_11_14_17_21_262))
% 0.19/0.45
% 0.19/0.45 Proof:
% 0.19/0.45 tuple(cp(y5(i2003_11_14_17_21_262)), ra_Px1(y5(i2003_11_14_17_21_262), y0_3(y5(i2003_11_14_17_21_262))))
% 0.19/0.45 = { by axiom 17 (axiom_4) R->L }
% 0.19/0.45 tuple(cp(y5(i2003_11_14_17_21_262)), fresh15(cpxcomp(y5(i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)))
% 0.19/0.45 = { by axiom 18 (axiom_7) R->L }
% 0.19/0.45 tuple(cp(y5(i2003_11_14_17_21_262)), fresh15(fresh11(ca_Ax3(y5(i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)))
% 0.19/0.45 = { by axiom 13 (axiom_2) R->L }
% 0.19/0.45 tuple(cp(y5(i2003_11_14_17_21_262)), fresh15(fresh11(fresh19(cUnsatisfiable(i2003_11_14_17_21_262), true2, i2003_11_14_17_21_262), true2, y5(i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)))
% 0.19/0.45 = { by axiom 1 (axiom_11) }
% 0.19/0.45 tuple(cp(y5(i2003_11_14_17_21_262)), fresh15(fresh11(fresh19(true2, true2, i2003_11_14_17_21_262), true2, y5(i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)))
% 0.19/0.45 = { by axiom 2 (axiom_2) }
% 0.19/0.45 tuple(cp(y5(i2003_11_14_17_21_262)), fresh15(fresh11(true2, true2, y5(i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)))
% 0.19/0.45 = { by axiom 7 (axiom_7) }
% 0.19/0.45 tuple(cp(y5(i2003_11_14_17_21_262)), fresh15(true2, true2, y5(i2003_11_14_17_21_262)))
% 0.19/0.45 = { by axiom 6 (axiom_4) }
% 0.19/0.45 tuple(cp(y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 21 (axiom_9_1) R->L }
% 0.19/0.45 tuple(fresh4(true2, true2, i2003_11_14_17_21_262, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 5 (axiom_2_3) R->L }
% 0.19/0.45 tuple(fresh4(fresh16(true2, true2, i2003_11_14_17_21_262), true2, i2003_11_14_17_21_262, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 1 (axiom_11) R->L }
% 0.19/0.45 tuple(fresh4(fresh16(cUnsatisfiable(i2003_11_14_17_21_262), true2, i2003_11_14_17_21_262), true2, i2003_11_14_17_21_262, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 16 (axiom_2_3) }
% 0.19/0.45 tuple(fresh4(rs(i2003_11_14_17_21_262, y5(i2003_11_14_17_21_262)), true2, i2003_11_14_17_21_262, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 25 (axiom_9_1) }
% 0.19/0.45 tuple(fresh3(ca_Vx5(i2003_11_14_17_21_262), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 11 (axiom_8_3) R->L }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh25(true2, true2, y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by lemma 27 R->L }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh25(ca_Ax4(y6(i2003_11_14_17_21_262)), true2, y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 23 (axiom_8_3) R->L }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh24(true2, true2, y6(i2003_11_14_17_21_262), y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 12 (axiom_10_1) R->L }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh24(fresh21(true2, true2, y6(i2003_11_14_17_21_262), i2003_11_14_17_21_262), true2, y6(i2003_11_14_17_21_262), y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 4 (axiom_2_2) R->L }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh24(fresh21(fresh17(true2, true2, i2003_11_14_17_21_262), true2, y6(i2003_11_14_17_21_262), i2003_11_14_17_21_262), true2, y6(i2003_11_14_17_21_262), y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 1 (axiom_11) R->L }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh24(fresh21(fresh17(cUnsatisfiable(i2003_11_14_17_21_262), true2, i2003_11_14_17_21_262), true2, y6(i2003_11_14_17_21_262), i2003_11_14_17_21_262), true2, y6(i2003_11_14_17_21_262), y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 15 (axiom_2_2) }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh24(fresh21(rr(i2003_11_14_17_21_262, y6(i2003_11_14_17_21_262)), true2, y6(i2003_11_14_17_21_262), i2003_11_14_17_21_262), true2, y6(i2003_11_14_17_21_262), y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 24 (axiom_10_1) }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh24(rinvR(y6(i2003_11_14_17_21_262), i2003_11_14_17_21_262), true2, y6(i2003_11_14_17_21_262), y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 26 (axiom_8_3) }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh(rinvR(y6(i2003_11_14_17_21_262), y2(y6(i2003_11_14_17_21_262))), true2, y6(i2003_11_14_17_21_262), y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 20 (axiom_8_2) R->L }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh(fresh5(ca_Ax4(y6(i2003_11_14_17_21_262)), true2, y6(i2003_11_14_17_21_262)), true2, y6(i2003_11_14_17_21_262), y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by lemma 27 }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh(fresh5(true2, true2, y6(i2003_11_14_17_21_262)), true2, y6(i2003_11_14_17_21_262), y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 9 (axiom_8_2) }
% 0.19/0.45 tuple(fresh3(ca_Vx5(fresh(true2, true2, y6(i2003_11_14_17_21_262), y2(y6(i2003_11_14_17_21_262)), i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 22 (axiom_8_3) }
% 0.19/0.45 tuple(fresh3(ca_Vx5(y2(y6(i2003_11_14_17_21_262))), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 19 (axiom_8_1) R->L }
% 0.19/0.45 tuple(fresh3(fresh6(ca_Ax4(y6(i2003_11_14_17_21_262)), true2, y6(i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by lemma 27 }
% 0.19/0.45 tuple(fresh3(fresh6(true2, true2, y6(i2003_11_14_17_21_262)), true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 8 (axiom_8_1) }
% 0.19/0.45 tuple(fresh3(true2, true2, y5(i2003_11_14_17_21_262)), true2)
% 0.19/0.45 = { by axiom 10 (axiom_9_1) }
% 0.19/0.45 tuple(true2, true2)
% 0.19/0.45 % SZS output end Proof
% 0.19/0.45
% 0.19/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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