TSTP Solution File: KRS070+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS070+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 : n031.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 05:52:47 EDT 2023
% Result : Unsatisfiable 0.23s 0.46s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : KRS070+1 : TPTP v8.1.2. Released v3.1.0.
% 0.15/0.16 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.38 % Computer : n031.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Mon Aug 28 01:56:39 EDT 2023
% 0.15/0.38 % CPUTime :
% 0.23/0.46 Command-line arguments: --no-flatten-goal
% 0.23/0.46
% 0.23/0.46 % SZS status Unsatisfiable
% 0.23/0.46
% 0.23/0.46 % SZS output start Proof
% 0.23/0.46 Take the following subset of the input axioms:
% 0.23/0.47 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.23/0.47 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.23/0.47 fof(axiom_16, axiom, ![Y, X2]: (rrx4(X2, Y) => rrx(X2, Y))).
% 0.23/0.47 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y2]: (rrx4(X2, Y2) & cc2(Y2)) & (~?[Y2]: (rrx3(X2, Y2) & (cc2(Y2) & cc1(Y2))) & ?[Y2]: (rrx3(X2, Y2) & cc1(Y2)))))).
% 0.23/0.47 fof(axiom_3, axiom, ![Z, X2, Y2]: ((rrx(X2, Y2) & rrx(X2, Z)) => Y2=Z)).
% 0.23/0.47 fof(axiom_8, axiom, cUnsatisfiable(i2003_11_14_17_18_32242)).
% 0.23/0.47 fof(axiom_9, axiom, ![X2, Y2]: (rrx3(X2, Y2) => rrx(X2, Y2))).
% 0.23/0.47
% 0.23/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.23/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.23/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.23/0.47 fresh(y, y, x1...xn) = u
% 0.23/0.47 C => fresh(s, t, x1...xn) = v
% 0.23/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.23/0.47 variables of u and v.
% 0.23/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.23/0.47 input problem has no model of domain size 1).
% 0.23/0.47
% 0.23/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.23/0.47
% 0.23/0.47 Axiom 1 (axiom_8): cUnsatisfiable(i2003_11_14_17_18_32242) = true2.
% 0.23/0.47 Axiom 2 (axiom_2): fresh15(X, X, Y) = true2.
% 0.23/0.47 Axiom 3 (axiom_2_1): fresh14(X, X, Y) = true2.
% 0.23/0.47 Axiom 4 (axiom_2_2): fresh13(X, X, Y) = true2.
% 0.23/0.47 Axiom 5 (axiom_2_3): fresh12(X, X, Y) = true2.
% 0.23/0.47 Axiom 6 (axiom_16): fresh16(X, X, Y, Z) = true2.
% 0.23/0.47 Axiom 7 (axiom_2): fresh15(cUnsatisfiable(X), true2, X) = cc1(y2(X)).
% 0.23/0.47 Axiom 8 (axiom_2_1): fresh14(cUnsatisfiable(X), true2, X) = cc2(y3(X)).
% 0.23/0.47 Axiom 9 (axiom_2_2): fresh13(cUnsatisfiable(X), true2, X) = rrx3(X, y2(X)).
% 0.23/0.47 Axiom 10 (axiom_2_3): fresh12(cUnsatisfiable(X), true2, X) = rrx4(X, y3(X)).
% 0.23/0.47 Axiom 11 (axiom_9): fresh11(X, X, Y, Z) = true2.
% 0.23/0.47 Axiom 12 (axiom_3): fresh9(X, X, Y, Z) = Z.
% 0.23/0.47 Axiom 13 (axiom_3): fresh10(X, X, Y, Z, W) = Z.
% 0.23/0.47 Axiom 14 (axiom_16): fresh16(rrx4(X, Y), true2, X, Y) = rrx(X, Y).
% 0.23/0.47 Axiom 15 (axiom_9): fresh11(rrx3(X, Y), true2, X, Y) = rrx(X, Y).
% 0.23/0.47 Axiom 16 (axiom_3): fresh10(rrx(X, Y), true2, X, Z, Y) = fresh9(rrx(X, Z), true2, Z, Y).
% 0.23/0.47
% 0.23/0.47 Lemma 17: rrx3(i2003_11_14_17_18_32242, y2(i2003_11_14_17_18_32242)) = true2.
% 0.23/0.47 Proof:
% 0.23/0.47 rrx3(i2003_11_14_17_18_32242, y2(i2003_11_14_17_18_32242))
% 0.23/0.47 = { by axiom 9 (axiom_2_2) R->L }
% 0.23/0.47 fresh13(cUnsatisfiable(i2003_11_14_17_18_32242), true2, i2003_11_14_17_18_32242)
% 0.23/0.47 = { by axiom 1 (axiom_8) }
% 0.23/0.47 fresh13(true2, true2, i2003_11_14_17_18_32242)
% 0.23/0.47 = { by axiom 4 (axiom_2_2) }
% 0.23/0.47 true2
% 0.23/0.47
% 0.23/0.47 Lemma 18: y2(i2003_11_14_17_18_32242) = y3(i2003_11_14_17_18_32242).
% 0.23/0.47 Proof:
% 0.23/0.47 y2(i2003_11_14_17_18_32242)
% 0.23/0.47 = { by axiom 12 (axiom_3) R->L }
% 0.23/0.47 fresh9(true2, true2, y3(i2003_11_14_17_18_32242), y2(i2003_11_14_17_18_32242))
% 0.23/0.47 = { by axiom 6 (axiom_16) R->L }
% 0.23/0.47 fresh9(fresh16(true2, true2, i2003_11_14_17_18_32242, y3(i2003_11_14_17_18_32242)), true2, y3(i2003_11_14_17_18_32242), y2(i2003_11_14_17_18_32242))
% 0.23/0.47 = { by axiom 5 (axiom_2_3) R->L }
% 0.23/0.47 fresh9(fresh16(fresh12(true2, true2, i2003_11_14_17_18_32242), true2, i2003_11_14_17_18_32242, y3(i2003_11_14_17_18_32242)), true2, y3(i2003_11_14_17_18_32242), y2(i2003_11_14_17_18_32242))
% 0.23/0.47 = { by axiom 1 (axiom_8) R->L }
% 0.23/0.47 fresh9(fresh16(fresh12(cUnsatisfiable(i2003_11_14_17_18_32242), true2, i2003_11_14_17_18_32242), true2, i2003_11_14_17_18_32242, y3(i2003_11_14_17_18_32242)), true2, y3(i2003_11_14_17_18_32242), y2(i2003_11_14_17_18_32242))
% 0.23/0.47 = { by axiom 10 (axiom_2_3) }
% 0.23/0.47 fresh9(fresh16(rrx4(i2003_11_14_17_18_32242, y3(i2003_11_14_17_18_32242)), true2, i2003_11_14_17_18_32242, y3(i2003_11_14_17_18_32242)), true2, y3(i2003_11_14_17_18_32242), y2(i2003_11_14_17_18_32242))
% 0.23/0.47 = { by axiom 14 (axiom_16) }
% 0.23/0.47 fresh9(rrx(i2003_11_14_17_18_32242, y3(i2003_11_14_17_18_32242)), true2, y3(i2003_11_14_17_18_32242), y2(i2003_11_14_17_18_32242))
% 0.23/0.47 = { by axiom 16 (axiom_3) R->L }
% 0.23/0.47 fresh10(rrx(i2003_11_14_17_18_32242, y2(i2003_11_14_17_18_32242)), true2, i2003_11_14_17_18_32242, y3(i2003_11_14_17_18_32242), y2(i2003_11_14_17_18_32242))
% 0.23/0.47 = { by axiom 15 (axiom_9) R->L }
% 0.23/0.47 fresh10(fresh11(rrx3(i2003_11_14_17_18_32242, y2(i2003_11_14_17_18_32242)), true2, i2003_11_14_17_18_32242, y2(i2003_11_14_17_18_32242)), true2, i2003_11_14_17_18_32242, y3(i2003_11_14_17_18_32242), y2(i2003_11_14_17_18_32242))
% 0.23/0.47 = { by lemma 17 }
% 0.23/0.47 fresh10(fresh11(true2, true2, i2003_11_14_17_18_32242, y2(i2003_11_14_17_18_32242)), true2, i2003_11_14_17_18_32242, y3(i2003_11_14_17_18_32242), y2(i2003_11_14_17_18_32242))
% 0.23/0.47 = { by axiom 11 (axiom_9) }
% 0.23/0.47 fresh10(true2, true2, i2003_11_14_17_18_32242, y3(i2003_11_14_17_18_32242), y2(i2003_11_14_17_18_32242))
% 0.23/0.47 = { by axiom 13 (axiom_3) }
% 0.23/0.47 y3(i2003_11_14_17_18_32242)
% 0.23/0.47
% 0.23/0.47 Goal 1 (axiom_2_4): tuple(cUnsatisfiable(X), cc1(Y), cc2(Y), rrx3(X, Y)) = tuple(true2, true2, true2, true2).
% 0.23/0.47 The goal is true when:
% 0.23/0.47 X = i2003_11_14_17_18_32242
% 0.23/0.47 Y = y3(i2003_11_14_17_18_32242)
% 0.23/0.47
% 0.23/0.47 Proof:
% 0.23/0.47 tuple(cUnsatisfiable(i2003_11_14_17_18_32242), cc1(y3(i2003_11_14_17_18_32242)), cc2(y3(i2003_11_14_17_18_32242)), rrx3(i2003_11_14_17_18_32242, y3(i2003_11_14_17_18_32242)))
% 0.23/0.47 = { by lemma 18 R->L }
% 0.23/0.47 tuple(cUnsatisfiable(i2003_11_14_17_18_32242), cc1(y3(i2003_11_14_17_18_32242)), cc2(y3(i2003_11_14_17_18_32242)), rrx3(i2003_11_14_17_18_32242, y2(i2003_11_14_17_18_32242)))
% 0.23/0.47 = { by lemma 17 }
% 0.23/0.47 tuple(cUnsatisfiable(i2003_11_14_17_18_32242), cc1(y3(i2003_11_14_17_18_32242)), cc2(y3(i2003_11_14_17_18_32242)), true2)
% 0.23/0.47 = { by axiom 1 (axiom_8) }
% 0.23/0.47 tuple(true2, cc1(y3(i2003_11_14_17_18_32242)), cc2(y3(i2003_11_14_17_18_32242)), true2)
% 0.23/0.47 = { by lemma 18 R->L }
% 0.23/0.47 tuple(true2, cc1(y2(i2003_11_14_17_18_32242)), cc2(y3(i2003_11_14_17_18_32242)), true2)
% 0.23/0.47 = { by axiom 7 (axiom_2) R->L }
% 0.23/0.47 tuple(true2, fresh15(cUnsatisfiable(i2003_11_14_17_18_32242), true2, i2003_11_14_17_18_32242), cc2(y3(i2003_11_14_17_18_32242)), true2)
% 0.23/0.47 = { by axiom 1 (axiom_8) }
% 0.23/0.47 tuple(true2, fresh15(true2, true2, i2003_11_14_17_18_32242), cc2(y3(i2003_11_14_17_18_32242)), true2)
% 0.23/0.47 = { by axiom 2 (axiom_2) }
% 0.23/0.47 tuple(true2, true2, cc2(y3(i2003_11_14_17_18_32242)), true2)
% 0.23/0.47 = { by axiom 8 (axiom_2_1) R->L }
% 0.23/0.47 tuple(true2, true2, fresh14(cUnsatisfiable(i2003_11_14_17_18_32242), true2, i2003_11_14_17_18_32242), true2)
% 0.23/0.47 = { by axiom 1 (axiom_8) }
% 0.23/0.47 tuple(true2, true2, fresh14(true2, true2, i2003_11_14_17_18_32242), true2)
% 0.23/0.47 = { by axiom 3 (axiom_2_1) }
% 0.23/0.47 tuple(true2, true2, true2, true2)
% 0.23/0.47 % SZS output end Proof
% 0.23/0.47
% 0.23/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
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