TSTP Solution File: KRS001-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS001-1 : 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 : n029.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 0.20s 0.40s
% Output : Proof 0.20s
% 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 : KRS001-1 : 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 : n029.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 02:17:56 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.40 Command-line arguments: --no-flatten-goal
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% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Take the following subset of the input axioms:
% 0.20/0.40 fof(clause_1, negated_conjecture, e(exist)).
% 0.20/0.40 fof(clause_10, axiom, ![X1, X3, X2]: (equalish(X3, X2) | (~r1most(X1) | (~r(X1, X3) | ~r(X1, X2))))).
% 0.20/0.40 fof(clause_14, axiom, ![X1_2]: (d(X1_2) | ~e(X1_2))).
% 0.20/0.40 fof(clause_15, axiom, ![X1_2]: (c(X1_2) | ~e(X1_2))).
% 0.20/0.40 fof(clause_2, axiom, ![X1_2]: (r2least(X1_2) | ~c(X1_2))).
% 0.20/0.40 fof(clause_4, axiom, ![X1_2]: (~r2least(X1_2) | ~equalish(u1r2(X1_2), u1r1(X1_2)))).
% 0.20/0.40 fof(clause_5, axiom, ![X1_2]: (r(X1_2, u1r1(X1_2)) | ~r2least(X1_2))).
% 0.20/0.40 fof(clause_6, axiom, ![X1_2]: (r(X1_2, u1r2(X1_2)) | ~r2least(X1_2))).
% 0.20/0.40 fof(clause_8, axiom, ![X1_2]: (r1most(X1_2) | ~d(X1_2))).
% 0.20/0.40
% 0.20/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40 fresh(y, y, x1...xn) = u
% 0.20/0.40 C => fresh(s, t, x1...xn) = v
% 0.20/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40 variables of u and v.
% 0.20/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40 input problem has no model of domain size 1).
% 0.20/0.40
% 0.20/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.40
% 0.20/0.40 Axiom 1 (clause_1): e(exist) = true2.
% 0.20/0.40 Axiom 2 (clause_14): fresh10(X, X, Y) = true2.
% 0.20/0.40 Axiom 3 (clause_15): fresh9(X, X, Y) = true2.
% 0.20/0.40 Axiom 4 (clause_2): fresh6(X, X, Y) = true2.
% 0.20/0.40 Axiom 5 (clause_5): fresh4(X, X, Y) = true2.
% 0.20/0.40 Axiom 6 (clause_6): fresh3(X, X, Y) = true2.
% 0.20/0.40 Axiom 7 (clause_8): fresh2(X, X, Y) = true2.
% 0.20/0.40 Axiom 8 (clause_10): fresh14(X, X, Y, Z) = true2.
% 0.20/0.40 Axiom 9 (clause_14): fresh10(e(X), true2, X) = d(X).
% 0.20/0.40 Axiom 10 (clause_15): fresh9(e(X), true2, X) = c(X).
% 0.20/0.40 Axiom 11 (clause_2): fresh6(c(X), true2, X) = r2least(X).
% 0.20/0.40 Axiom 12 (clause_5): fresh4(r2least(X), true2, X) = r(X, u1r1(X)).
% 0.20/0.40 Axiom 13 (clause_6): fresh3(r2least(X), true2, X) = r(X, u1r2(X)).
% 0.20/0.40 Axiom 14 (clause_8): fresh2(d(X), true2, X) = r1most(X).
% 0.20/0.40 Axiom 15 (clause_10): fresh12(X, X, Y, Z, W) = equalish(Y, Z).
% 0.20/0.40 Axiom 16 (clause_10): fresh13(X, X, Y, Z, W) = fresh14(r(W, Y), true2, Y, Z).
% 0.20/0.40 Axiom 17 (clause_10): fresh13(r1most(X), true2, Y, Z, X) = fresh12(r(X, Z), true2, Y, Z, X).
% 0.20/0.40
% 0.20/0.40 Lemma 18: r2least(exist) = true2.
% 0.20/0.40 Proof:
% 0.20/0.40 r2least(exist)
% 0.20/0.40 = { by axiom 11 (clause_2) R->L }
% 0.20/0.40 fresh6(c(exist), true2, exist)
% 0.20/0.40 = { by axiom 10 (clause_15) R->L }
% 0.20/0.40 fresh6(fresh9(e(exist), true2, exist), true2, exist)
% 0.20/0.40 = { by axiom 1 (clause_1) }
% 0.20/0.40 fresh6(fresh9(true2, true2, exist), true2, exist)
% 0.20/0.40 = { by axiom 3 (clause_15) }
% 0.20/0.40 fresh6(true2, true2, exist)
% 0.20/0.40 = { by axiom 4 (clause_2) }
% 0.20/0.40 true2
% 0.20/0.40
% 0.20/0.40 Goal 1 (clause_4): tuple(r2least(X), equalish(u1r2(X), u1r1(X))) = tuple(true2, true2).
% 0.20/0.40 The goal is true when:
% 0.20/0.40 X = exist
% 0.20/0.40
% 0.20/0.40 Proof:
% 0.20/0.40 tuple(r2least(exist), equalish(u1r2(exist), u1r1(exist)))
% 0.20/0.40 = { by axiom 15 (clause_10) R->L }
% 0.20/0.40 tuple(r2least(exist), fresh12(true2, true2, u1r2(exist), u1r1(exist), exist))
% 0.20/0.40 = { by axiom 5 (clause_5) R->L }
% 0.20/0.40 tuple(r2least(exist), fresh12(fresh4(true2, true2, exist), true2, u1r2(exist), u1r1(exist), exist))
% 0.20/0.40 = { by lemma 18 R->L }
% 0.20/0.40 tuple(r2least(exist), fresh12(fresh4(r2least(exist), true2, exist), true2, u1r2(exist), u1r1(exist), exist))
% 0.20/0.40 = { by axiom 12 (clause_5) }
% 0.20/0.40 tuple(r2least(exist), fresh12(r(exist, u1r1(exist)), true2, u1r2(exist), u1r1(exist), exist))
% 0.20/0.40 = { by axiom 17 (clause_10) R->L }
% 0.20/0.40 tuple(r2least(exist), fresh13(r1most(exist), true2, u1r2(exist), u1r1(exist), exist))
% 0.20/0.40 = { by axiom 14 (clause_8) R->L }
% 0.20/0.40 tuple(r2least(exist), fresh13(fresh2(d(exist), true2, exist), true2, u1r2(exist), u1r1(exist), exist))
% 0.20/0.40 = { by axiom 9 (clause_14) R->L }
% 0.20/0.41 tuple(r2least(exist), fresh13(fresh2(fresh10(e(exist), true2, exist), true2, exist), true2, u1r2(exist), u1r1(exist), exist))
% 0.20/0.41 = { by axiom 1 (clause_1) }
% 0.20/0.41 tuple(r2least(exist), fresh13(fresh2(fresh10(true2, true2, exist), true2, exist), true2, u1r2(exist), u1r1(exist), exist))
% 0.20/0.41 = { by axiom 2 (clause_14) }
% 0.20/0.41 tuple(r2least(exist), fresh13(fresh2(true2, true2, exist), true2, u1r2(exist), u1r1(exist), exist))
% 0.20/0.41 = { by axiom 7 (clause_8) }
% 0.20/0.41 tuple(r2least(exist), fresh13(true2, true2, u1r2(exist), u1r1(exist), exist))
% 0.20/0.41 = { by axiom 16 (clause_10) }
% 0.20/0.41 tuple(r2least(exist), fresh14(r(exist, u1r2(exist)), true2, u1r2(exist), u1r1(exist)))
% 0.20/0.41 = { by axiom 13 (clause_6) R->L }
% 0.20/0.41 tuple(r2least(exist), fresh14(fresh3(r2least(exist), true2, exist), true2, u1r2(exist), u1r1(exist)))
% 0.20/0.41 = { by lemma 18 }
% 0.20/0.41 tuple(r2least(exist), fresh14(fresh3(true2, true2, exist), true2, u1r2(exist), u1r1(exist)))
% 0.20/0.41 = { by axiom 6 (clause_6) }
% 0.20/0.41 tuple(r2least(exist), fresh14(true2, true2, u1r2(exist), u1r1(exist)))
% 0.20/0.41 = { by axiom 8 (clause_10) }
% 0.20/0.41 tuple(r2least(exist), true2)
% 0.20/0.41 = { by lemma 18 }
% 0.20/0.41 tuple(true2, true2)
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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