TSTP Solution File: KRS002-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS002-1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n014.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 05:52:34 EDT 2023
% Result : Unsatisfiable 0.19s 0.38s
% 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 : KRS002-1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n014.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 01:12:31 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.38 Command-line arguments: --ground-connectedness --complete-subsets
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38
% 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(clause_1, negated_conjecture, e(exist)).
% 0.19/0.39 fof(clause_10, axiom, ![X1, X3, X2]: (equalish(X3, X2) | (~s1most(X1) | (~s(X1, X3) | ~s(X1, X2))))).
% 0.19/0.39 fof(clause_14, axiom, ![X1_2]: (r(X1_2, u4r2(X1_2)) | ~e(X1_2))).
% 0.19/0.39 fof(clause_15, axiom, ![X1_2, X2_2]: (d(X2_2) | (~e(X1_2) | ~r(X1_2, X2_2)))).
% 0.19/0.39 fof(clause_16, axiom, ![X1_2, X2_2]: (c(X2_2) | (~e(X1_2) | ~r(X1_2, X2_2)))).
% 0.19/0.39 fof(clause_2, axiom, ![X1_2]: (s2least(X1_2) | ~c(X1_2))).
% 0.19/0.39 fof(clause_4, axiom, ![X1_2]: (~s2least(X1_2) | ~equalish(u1r2(X1_2), u1r1(X1_2)))).
% 0.19/0.39 fof(clause_5, axiom, ![X1_2]: (s(X1_2, u1r1(X1_2)) | ~s2least(X1_2))).
% 0.19/0.39 fof(clause_6, axiom, ![X1_2]: (s(X1_2, u1r2(X1_2)) | ~s2least(X1_2))).
% 0.19/0.39 fof(clause_8, axiom, ![X1_2]: (s1most(X1_2) | ~d(X1_2))).
% 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 (clause_1): e(exist) = true2.
% 0.19/0.39 Axiom 2 (clause_14): fresh12(X, X, Y) = true2.
% 0.19/0.39 Axiom 3 (clause_15): fresh10(X, X, Y) = true2.
% 0.19/0.39 Axiom 4 (clause_16): fresh8(X, X, Y) = true2.
% 0.19/0.39 Axiom 5 (clause_2): fresh6(X, X, Y) = true2.
% 0.19/0.39 Axiom 6 (clause_5): fresh4(X, X, Y) = true2.
% 0.19/0.39 Axiom 7 (clause_6): fresh3(X, X, Y) = true2.
% 0.19/0.39 Axiom 8 (clause_8): fresh2(X, X, Y) = true2.
% 0.19/0.39 Axiom 9 (clause_10): fresh18(X, X, Y, Z) = true2.
% 0.19/0.39 Axiom 10 (clause_14): fresh12(e(X), true2, X) = r(X, u4r2(X)).
% 0.19/0.39 Axiom 11 (clause_15): fresh11(X, X, Y, Z) = d(Y).
% 0.19/0.39 Axiom 12 (clause_16): fresh9(X, X, Y, Z) = c(Y).
% 0.19/0.39 Axiom 13 (clause_2): fresh6(c(X), true2, X) = s2least(X).
% 0.19/0.39 Axiom 14 (clause_5): fresh4(s2least(X), true2, X) = s(X, u1r1(X)).
% 0.19/0.39 Axiom 15 (clause_6): fresh3(s2least(X), true2, X) = s(X, u1r2(X)).
% 0.19/0.39 Axiom 16 (clause_8): fresh2(d(X), true2, X) = s1most(X).
% 0.19/0.39 Axiom 17 (clause_10): fresh14(X, X, Y, Z, W) = equalish(Y, Z).
% 0.19/0.39 Axiom 18 (clause_10): fresh17(X, X, Y, Z, W) = fresh18(s(W, Y), true2, Y, Z).
% 0.19/0.39 Axiom 19 (clause_15): fresh11(r(X, Y), true2, Y, X) = fresh10(e(X), true2, Y).
% 0.19/0.39 Axiom 20 (clause_16): fresh9(r(X, Y), true2, Y, X) = fresh8(e(X), true2, Y).
% 0.19/0.39 Axiom 21 (clause_10): fresh17(s1most(X), true2, Y, Z, X) = fresh14(s(X, Z), true2, Y, Z, X).
% 0.19/0.39
% 0.19/0.39 Lemma 22: r(exist, u4r2(exist)) = true2.
% 0.19/0.39 Proof:
% 0.19/0.39 r(exist, u4r2(exist))
% 0.19/0.39 = { by axiom 10 (clause_14) R->L }
% 0.19/0.39 fresh12(e(exist), true2, exist)
% 0.19/0.39 = { by axiom 1 (clause_1) }
% 0.19/0.39 fresh12(true2, true2, exist)
% 0.19/0.39 = { by axiom 2 (clause_14) }
% 0.19/0.39 true2
% 0.19/0.39
% 0.19/0.39 Lemma 23: s2least(u4r2(exist)) = true2.
% 0.19/0.39 Proof:
% 0.19/0.39 s2least(u4r2(exist))
% 0.19/0.39 = { by axiom 13 (clause_2) R->L }
% 0.19/0.39 fresh6(c(u4r2(exist)), true2, u4r2(exist))
% 0.19/0.39 = { by axiom 12 (clause_16) R->L }
% 0.19/0.39 fresh6(fresh9(true2, true2, u4r2(exist), exist), true2, u4r2(exist))
% 0.19/0.39 = { by lemma 22 R->L }
% 0.19/0.39 fresh6(fresh9(r(exist, u4r2(exist)), true2, u4r2(exist), exist), true2, u4r2(exist))
% 0.19/0.39 = { by axiom 20 (clause_16) }
% 0.19/0.39 fresh6(fresh8(e(exist), true2, u4r2(exist)), true2, u4r2(exist))
% 0.19/0.39 = { by axiom 1 (clause_1) }
% 0.19/0.39 fresh6(fresh8(true2, true2, u4r2(exist)), true2, u4r2(exist))
% 0.19/0.39 = { by axiom 4 (clause_16) }
% 0.19/0.39 fresh6(true2, true2, u4r2(exist))
% 0.19/0.39 = { by axiom 5 (clause_2) }
% 0.19/0.39 true2
% 0.19/0.39
% 0.19/0.39 Goal 1 (clause_4): tuple(s2least(X), equalish(u1r2(X), u1r1(X))) = tuple(true2, true2).
% 0.19/0.39 The goal is true when:
% 0.19/0.39 X = u4r2(exist)
% 0.19/0.39
% 0.19/0.39 Proof:
% 0.19/0.39 tuple(s2least(u4r2(exist)), equalish(u1r2(u4r2(exist)), u1r1(u4r2(exist))))
% 0.19/0.39 = { by axiom 17 (clause_10) R->L }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh14(true2, true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by axiom 6 (clause_5) R->L }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh14(fresh4(true2, true2, u4r2(exist)), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by lemma 23 R->L }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh14(fresh4(s2least(u4r2(exist)), true2, u4r2(exist)), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by axiom 14 (clause_5) }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh14(s(u4r2(exist), u1r1(u4r2(exist))), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by axiom 21 (clause_10) R->L }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh17(s1most(u4r2(exist)), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by axiom 16 (clause_8) R->L }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh17(fresh2(d(u4r2(exist)), true2, u4r2(exist)), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by axiom 11 (clause_15) R->L }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh17(fresh2(fresh11(true2, true2, u4r2(exist), exist), true2, u4r2(exist)), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by lemma 22 R->L }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh17(fresh2(fresh11(r(exist, u4r2(exist)), true2, u4r2(exist), exist), true2, u4r2(exist)), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by axiom 19 (clause_15) }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh17(fresh2(fresh10(e(exist), true2, u4r2(exist)), true2, u4r2(exist)), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by axiom 1 (clause_1) }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh17(fresh2(fresh10(true2, true2, u4r2(exist)), true2, u4r2(exist)), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by axiom 3 (clause_15) }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh17(fresh2(true2, true2, u4r2(exist)), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by axiom 8 (clause_8) }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh17(true2, true2, u1r2(u4r2(exist)), u1r1(u4r2(exist)), u4r2(exist)))
% 0.19/0.39 = { by axiom 18 (clause_10) }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh18(s(u4r2(exist), u1r2(u4r2(exist))), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist))))
% 0.19/0.39 = { by axiom 15 (clause_6) R->L }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh18(fresh3(s2least(u4r2(exist)), true2, u4r2(exist)), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist))))
% 0.19/0.39 = { by lemma 23 }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh18(fresh3(true2, true2, u4r2(exist)), true2, u1r2(u4r2(exist)), u1r1(u4r2(exist))))
% 0.19/0.39 = { by axiom 7 (clause_6) }
% 0.19/0.39 tuple(s2least(u4r2(exist)), fresh18(true2, true2, u1r2(u4r2(exist)), u1r1(u4r2(exist))))
% 0.19/0.39 = { by axiom 9 (clause_10) }
% 0.19/0.39 tuple(s2least(u4r2(exist)), true2)
% 0.19/0.39 = { by lemma 23 }
% 0.19/0.39 tuple(true2, true2)
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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