TSTP Solution File: GEO067-3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO067-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n005.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 0.19s 0.57s
% 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
% 0.10/0.12 % Problem : GEO067-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.10/0.13 % 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 : n005.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 : Tue Aug 29 21:58:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 Command-line arguments: --flatten
% 0.19/0.57
% 0.19/0.57 % SZS status Unsatisfiable
% 0.19/0.57
% 0.19/0.57 % SZS output start Proof
% 0.19/0.57 Take the following subset of the input axioms:
% 0.19/0.57 fof(c2_1, axiom, ![V, W, U]: (~between(W, V, U) | colinear(U, V, W))).
% 0.19/0.57 fof(c2_2, axiom, ![V2, U2, W2]: (~between(U2, W2, V2) | colinear(U2, V2, W2))).
% 0.19/0.57 fof(part_1, negated_conjecture, ~colinear(x, x, y) | (~colinear(x, y, x) | (~colinear(y, x, x) | x=y))).
% 0.19/0.57 fof(part_2, negated_conjecture, ~colinear(x, x, y) | (~colinear(x, y, x) | (~colinear(y, x, x) | ~colinear(x, z, y)))).
% 0.19/0.57 fof(t2, axiom, ![V2, U2]: between(U2, U2, V2)).
% 0.19/0.57 fof(t3, axiom, ![V2, U2]: between(U2, V2, V2)).
% 0.19/0.57
% 0.19/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.57 fresh(y, y, x1...xn) = u
% 0.19/0.57 C => fresh(s, t, x1...xn) = v
% 0.19/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.57 variables of u and v.
% 0.19/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.57 input problem has no model of domain size 1).
% 0.19/0.57
% 0.19/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.57
% 0.19/0.57 Axiom 1 (part_1): fresh59(X, X) = y.
% 0.19/0.57 Axiom 2 (part_1): fresh21(X, X) = x.
% 0.19/0.57 Axiom 3 (t2): between(X, X, Y) = true2.
% 0.19/0.57 Axiom 4 (t3): between(X, Y, Y) = true2.
% 0.19/0.57 Axiom 5 (c2_1): fresh49(X, X, Y, Z, W) = true2.
% 0.19/0.57 Axiom 6 (c2_2): fresh48(X, X, Y, Z, W) = true2.
% 0.19/0.57 Axiom 7 (part_1): fresh58(X, X) = fresh59(colinear(x, x, y), true2).
% 0.19/0.57 Axiom 8 (part_1): fresh58(colinear(y, x, x), true2) = fresh21(colinear(x, y, x), true2).
% 0.19/0.57 Axiom 9 (c2_1): fresh49(between(X, Y, Z), true2, X, Y, Z) = colinear(Z, Y, X).
% 0.19/0.57 Axiom 10 (c2_2): fresh48(between(X, Y, Z), true2, X, Y, Z) = colinear(X, Z, Y).
% 0.19/0.57
% 0.19/0.57 Lemma 11: colinear(X, Y, Y) = true2.
% 0.19/0.57 Proof:
% 0.19/0.57 colinear(X, Y, Y)
% 0.19/0.57 = { by axiom 9 (c2_1) R->L }
% 0.19/0.57 fresh49(between(Y, Y, X), true2, Y, Y, X)
% 0.19/0.57 = { by axiom 3 (t2) }
% 0.19/0.57 fresh49(true2, true2, Y, Y, X)
% 0.19/0.57 = { by axiom 5 (c2_1) }
% 0.19/0.57 true2
% 0.19/0.57
% 0.19/0.57 Lemma 12: colinear(Z, W, W) = colinear(X, X, Y).
% 0.19/0.57 Proof:
% 0.19/0.57 colinear(Z, W, W)
% 0.19/0.57 = { by lemma 11 }
% 0.19/0.57 true2
% 0.19/0.57 = { by axiom 5 (c2_1) R->L }
% 0.19/0.57 fresh49(true2, true2, Y, X, X)
% 0.19/0.57 = { by axiom 4 (t3) R->L }
% 0.19/0.57 fresh49(between(Y, X, X), true2, Y, X, X)
% 0.19/0.57 = { by axiom 9 (c2_1) }
% 0.19/0.57 colinear(X, X, Y)
% 0.19/0.57
% 0.19/0.57 Lemma 13: colinear(Z, Z, W) = colinear(X, Y, X).
% 0.19/0.57 Proof:
% 0.19/0.57 colinear(Z, Z, W)
% 0.19/0.57 = { by lemma 12 R->L }
% 0.19/0.57 colinear(V, U, U)
% 0.19/0.57 = { by lemma 11 }
% 0.19/0.57 true2
% 0.19/0.57 = { by axiom 6 (c2_2) R->L }
% 0.19/0.57 fresh48(true2, true2, X, X, Y)
% 0.19/0.57 = { by axiom 3 (t2) R->L }
% 0.19/0.57 fresh48(between(X, X, Y), true2, X, X, Y)
% 0.19/0.57 = { by axiom 10 (c2_2) }
% 0.19/0.57 colinear(X, Y, X)
% 0.19/0.57
% 0.19/0.57 Goal 1 (part_2): tuple(colinear(x, x, y), colinear(x, y, x), colinear(x, z, y), colinear(y, x, x)) = tuple(true2, true2, true2, true2).
% 0.19/0.57 Proof:
% 0.19/0.57 tuple(colinear(x, x, y), colinear(x, y, x), colinear(x, z, y), colinear(y, x, x))
% 0.19/0.57 = { by lemma 12 }
% 0.19/0.57 tuple(colinear(x, x, y), colinear(x, y, x), colinear(x, z, y), colinear(X, X, X))
% 0.19/0.57 = { by lemma 13 R->L }
% 0.19/0.57 tuple(colinear(x, x, y), colinear(Y, Y, Y), colinear(x, z, y), colinear(X, X, X))
% 0.19/0.57 = { by axiom 1 (part_1) R->L }
% 0.19/0.57 tuple(colinear(x, x, y), colinear(Y, Y, Y), colinear(x, z, fresh59(colinear(x, x, y), colinear(x, x, y))), colinear(X, X, X))
% 0.19/0.58 = { by lemma 12 R->L }
% 0.19/0.58 tuple(colinear(x, x, y), colinear(Y, Y, Y), colinear(x, z, fresh59(colinear(x, x, y), colinear(Z, W, W))), colinear(X, X, X))
% 0.19/0.58 = { by lemma 11 }
% 0.19/0.58 tuple(colinear(x, x, y), colinear(Y, Y, Y), colinear(x, z, fresh59(colinear(x, x, y), true2)), colinear(X, X, X))
% 0.19/0.58 = { by axiom 2 (part_1) R->L }
% 0.19/0.58 tuple(colinear(x, x, y), colinear(Y, Y, Y), colinear(fresh21(colinear(V, V, V), colinear(V, V, V)), z, fresh59(colinear(x, x, y), true2)), colinear(X, X, X))
% 0.19/0.58 = { by lemma 11 }
% 0.19/0.58 tuple(colinear(x, x, y), colinear(Y, Y, Y), colinear(fresh21(colinear(V, V, V), true2), z, fresh59(colinear(x, x, y), true2)), colinear(X, X, X))
% 0.19/0.58 = { by lemma 13 }
% 0.19/0.58 tuple(colinear(x, x, y), colinear(Y, Y, Y), colinear(fresh21(colinear(x, y, x), true2), z, fresh59(colinear(x, x, y), true2)), colinear(X, X, X))
% 0.19/0.58 = { by axiom 8 (part_1) R->L }
% 0.19/0.58 tuple(colinear(x, x, y), colinear(Y, Y, Y), colinear(fresh58(colinear(y, x, x), true2), z, fresh59(colinear(x, x, y), true2)), colinear(X, X, X))
% 0.19/0.58 = { by lemma 11 R->L }
% 0.19/0.58 tuple(colinear(x, x, y), colinear(Y, Y, Y), colinear(fresh58(colinear(y, x, x), colinear(y, x, x)), z, fresh59(colinear(x, x, y), true2)), colinear(X, X, X))
% 0.19/0.58 = { by axiom 7 (part_1) }
% 0.19/0.58 tuple(colinear(x, x, y), colinear(Y, Y, Y), colinear(fresh59(colinear(x, x, y), true2), z, fresh59(colinear(x, x, y), true2)), colinear(X, X, X))
% 0.19/0.58 = { by lemma 13 R->L }
% 0.19/0.58 tuple(colinear(x, x, y), colinear(Y, Y, Y), colinear(U, U, U), colinear(X, X, X))
% 0.19/0.58 = { by lemma 11 }
% 0.19/0.58 tuple(colinear(x, x, y), true2, colinear(U, U, U), colinear(X, X, X))
% 0.19/0.58 = { by lemma 11 }
% 0.19/0.58 tuple(colinear(x, x, y), true2, true2, colinear(X, X, X))
% 0.19/0.58 = { by lemma 11 }
% 0.19/0.58 tuple(colinear(x, x, y), true2, true2, true2)
% 0.19/0.58 = { by lemma 12 R->L }
% 0.19/0.58 tuple(colinear(T, S, S), true2, true2, true2)
% 0.19/0.58 = { by lemma 11 }
% 0.19/0.58 tuple(true2, true2, true2, true2)
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58
% 0.19/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
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