TSTP Solution File: GEO067-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO067-2 : TPTP v8.1.2. Released v1.0.0.
% 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 : n004.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 : Wed Aug 30 23:27:11 EDT 2023
% Result : Unsatisfiable 0.20s 0.43s
% 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
% 0.07/0.12 % Problem : GEO067-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 23:30:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.43 Command-line arguments: --no-flatten-goal
% 0.20/0.43
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 Take the following subset of the input axioms:
% 0.20/0.44 fof(colinearity1, axiom, ![X, Y, Z]: (~between(X, Y, Z) | colinear(X, Y, Z))).
% 0.20/0.44 fof(colinearity2, axiom, ![X2, Y2, Z2]: (~between(Y2, Z2, X2) | colinear(X2, Y2, Z2))).
% 0.20/0.44 fof(colinearity3, axiom, ![X2, Y2, Z2]: (~between(Z2, X2, Y2) | colinear(X2, Y2, Z2))).
% 0.20/0.44 fof(identity_for_equidistance, axiom, ![X2, Y2, Z2]: (~equidistant(X2, Y2, Z2, Z2) | X2=Y2)).
% 0.20/0.44 fof(part_1, negated_conjecture, ~colinear(x, x, y) | (~colinear(x, y, x) | (~colinear(y, x, x) | x=y))).
% 0.20/0.44 fof(part_2, negated_conjecture, ~colinear(x, x, y) | (~colinear(x, y, x) | (~colinear(y, x, x) | ~colinear(x, z, y)))).
% 0.20/0.44 fof(segment_construction1, axiom, ![V, W, X2, Y2]: between(X2, Y2, extension(X2, Y2, W, V))).
% 0.20/0.44 fof(segment_construction2, axiom, ![V2, X2, Y2, W2]: equidistant(Y2, extension(X2, Y2, W2, V2), W2, V2)).
% 0.20/0.44
% 0.20/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.44 fresh(y, y, x1...xn) = u
% 0.20/0.44 C => fresh(s, t, x1...xn) = v
% 0.20/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.44 variables of u and v.
% 0.20/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.44 input problem has no model of domain size 1).
% 0.20/0.44
% 0.20/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.44
% 0.20/0.44 Axiom 1 (part_1): fresh16(X, X) = y.
% 0.20/0.44 Axiom 2 (part_1): fresh5(X, X) = x.
% 0.20/0.44 Axiom 3 (identity_for_equidistance): fresh(X, X, Y, Z) = Z.
% 0.20/0.44 Axiom 4 (part_1): fresh15(X, X) = fresh16(colinear(x, x, y), true).
% 0.20/0.44 Axiom 5 (colinearity2): fresh14(X, X, Y, Z, W) = true.
% 0.20/0.44 Axiom 6 (colinearity1): fresh13(X, X, Y, Z, W) = true.
% 0.20/0.44 Axiom 7 (colinearity3): fresh12(X, X, Y, Z, W) = true.
% 0.20/0.44 Axiom 8 (part_1): fresh15(colinear(y, x, x), true) = fresh5(colinear(x, y, x), true).
% 0.20/0.44 Axiom 9 (segment_construction1): between(X, Y, extension(X, Y, Z, W)) = true.
% 0.20/0.44 Axiom 10 (identity_for_equidistance): fresh(equidistant(X, Y, Z, Z), true, X, Y) = X.
% 0.20/0.44 Axiom 11 (colinearity2): fresh14(between(X, Y, Z), true, X, Y, Z) = colinear(Z, X, Y).
% 0.20/0.44 Axiom 12 (colinearity1): fresh13(between(X, Y, Z), true, X, Y, Z) = colinear(X, Y, Z).
% 0.20/0.44 Axiom 13 (colinearity3): fresh12(between(X, Y, Z), true, X, Y, Z) = colinear(Y, Z, X).
% 0.20/0.44 Axiom 14 (segment_construction2): equidistant(X, extension(Y, X, Z, W), Z, W) = true.
% 0.20/0.44
% 0.20/0.44 Lemma 15: between(X, Y, Y) = true.
% 0.20/0.44 Proof:
% 0.20/0.44 between(X, Y, Y)
% 0.20/0.44 = { by axiom 10 (identity_for_equidistance) R->L }
% 0.20/0.44 between(X, Y, fresh(equidistant(Y, extension(X, Y, Z, Z), Z, Z), true, Y, extension(X, Y, Z, Z)))
% 0.20/0.44 = { by axiom 14 (segment_construction2) }
% 0.20/0.44 between(X, Y, fresh(true, true, Y, extension(X, Y, Z, Z)))
% 0.20/0.44 = { by axiom 3 (identity_for_equidistance) }
% 0.20/0.44 between(X, Y, extension(X, Y, Z, Z))
% 0.20/0.44 = { by axiom 9 (segment_construction1) }
% 0.20/0.44 true
% 0.20/0.44
% 0.20/0.44 Lemma 16: colinear(X, X, Y) = true.
% 0.20/0.44 Proof:
% 0.20/0.44 colinear(X, X, Y)
% 0.20/0.44 = { by axiom 13 (colinearity3) R->L }
% 0.20/0.44 fresh12(between(Y, X, X), true, Y, X, X)
% 0.20/0.44 = { by lemma 15 }
% 0.20/0.44 fresh12(true, true, Y, X, X)
% 0.20/0.44 = { by axiom 7 (colinearity3) }
% 0.20/0.44 true
% 0.20/0.44
% 0.20/0.44 Lemma 17: colinear(X, Y, X) = true.
% 0.20/0.44 Proof:
% 0.20/0.44 colinear(X, Y, X)
% 0.20/0.44 = { by axiom 11 (colinearity2) R->L }
% 0.20/0.44 fresh14(between(Y, X, X), true, Y, X, X)
% 0.20/0.44 = { by lemma 15 }
% 0.20/0.44 fresh14(true, true, Y, X, X)
% 0.20/0.44 = { by axiom 5 (colinearity2) }
% 0.20/0.44 true
% 0.20/0.44
% 0.20/0.44 Lemma 18: colinear(X, Y, Y) = true.
% 0.20/0.44 Proof:
% 0.20/0.44 colinear(X, Y, Y)
% 0.20/0.44 = { by axiom 12 (colinearity1) R->L }
% 0.20/0.44 fresh13(between(X, Y, Y), true, X, Y, Y)
% 0.20/0.44 = { by lemma 15 }
% 0.20/0.44 fresh13(true, true, X, Y, Y)
% 0.20/0.44 = { by axiom 6 (colinearity1) }
% 0.20/0.44 true
% 0.20/0.44
% 0.20/0.44 Goal 1 (part_2): tuple(colinear(x, x, y), colinear(x, y, x), colinear(x, z, y), colinear(y, x, x)) = tuple(true, true, true, true).
% 0.20/0.44 Proof:
% 0.20/0.44 tuple(colinear(x, x, y), colinear(x, y, x), colinear(x, z, y), colinear(y, x, x))
% 0.20/0.44 = { by lemma 17 }
% 0.20/0.44 tuple(colinear(x, x, y), true, colinear(x, z, y), colinear(y, x, x))
% 0.20/0.44 = { by lemma 18 }
% 0.20/0.44 tuple(colinear(x, x, y), true, colinear(x, z, y), true)
% 0.20/0.44 = { by lemma 16 }
% 0.20/0.44 tuple(true, true, colinear(x, z, y), true)
% 0.20/0.44 = { by axiom 2 (part_1) R->L }
% 0.20/0.44 tuple(true, true, colinear(fresh5(true, true), z, y), true)
% 0.20/0.44 = { by lemma 17 R->L }
% 0.20/0.44 tuple(true, true, colinear(fresh5(colinear(x, y, x), true), z, y), true)
% 0.20/0.44 = { by axiom 8 (part_1) R->L }
% 0.20/0.44 tuple(true, true, colinear(fresh15(colinear(y, x, x), true), z, y), true)
% 0.20/0.44 = { by lemma 18 }
% 0.20/0.44 tuple(true, true, colinear(fresh15(true, true), z, y), true)
% 0.20/0.44 = { by axiom 4 (part_1) }
% 0.20/0.44 tuple(true, true, colinear(fresh16(colinear(x, x, y), true), z, y), true)
% 0.20/0.44 = { by lemma 16 }
% 0.20/0.44 tuple(true, true, colinear(fresh16(true, true), z, y), true)
% 0.20/0.44 = { by axiom 1 (part_1) }
% 0.20/0.44 tuple(true, true, colinear(y, z, y), true)
% 0.20/0.44 = { by lemma 17 }
% 0.20/0.44 tuple(true, true, true, true)
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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