TSTP Solution File: GEO037-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO037-2 : 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 : n002.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 23:26:58 EDT 2023
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO037-2 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 20:14:50 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.49 Command-line arguments: --no-flatten-goal
% 0.20/0.49
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 Take the following subset of the input axioms:
% 0.20/0.51 fof(identity_for_equidistance, axiom, ![X, Y, Z]: (~equidistant(X, Y, Z, Z) | X=Y)).
% 0.20/0.51 fof(lower_dimension3, axiom, ~between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2)).
% 0.20/0.51 fof(prove_lengthen, negated_conjecture, v=extension(u, v, lower_dimension_point_1, lower_dimension_point_2) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)) | ~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)))).
% 0.20/0.51 fof(reflexivity_for_equidistance, axiom, ![X2, Y2]: equidistant(X2, Y2, Y2, X2)).
% 0.20/0.51 fof(segment_construction1, axiom, ![V, W, X2, Y2]: between(X2, Y2, extension(X2, Y2, W, V))).
% 0.20/0.51 fof(segment_construction2, axiom, ![X2, Y2, V3, W2]: equidistant(Y2, extension(X2, Y2, W2, V3), W2, V3)).
% 0.20/0.51 fof(transitivity_for_equidistance, axiom, ![V2, X2, Y2, Z2, V3, W2]: (~equidistant(X2, Y2, Z2, V3) | (~equidistant(X2, Y2, V2, W2) | equidistant(Z2, V3, V2, W2)))).
% 0.20/0.51
% 0.20/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.51 fresh(y, y, x1...xn) = u
% 0.20/0.51 C => fresh(s, t, x1...xn) = v
% 0.20/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.51 variables of u and v.
% 0.20/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.51 input problem has no model of domain size 1).
% 0.20/0.51
% 0.20/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.51
% 0.20/0.51 Axiom 1 (prove_lengthen): fresh5(X, X) = v.
% 0.20/0.51 Axiom 2 (identity_for_equidistance): fresh(X, X, Y, Z) = Z.
% 0.20/0.51 Axiom 3 (prove_lengthen): fresh6(X, X) = extension(u, v, lower_dimension_point_1, lower_dimension_point_2).
% 0.20/0.51 Axiom 4 (reflexivity_for_equidistance): equidistant(X, Y, Y, X) = true.
% 0.20/0.51 Axiom 5 (transitivity_for_equidistance): fresh3(X, X, Y, Z, W, V) = true.
% 0.20/0.51 Axiom 6 (segment_construction1): between(X, Y, extension(X, Y, Z, W)) = true.
% 0.20/0.51 Axiom 7 (identity_for_equidistance): fresh(equidistant(X, Y, Z, Z), true, X, Y) = X.
% 0.20/0.51 Axiom 8 (transitivity_for_equidistance): fresh4(X, X, Y, Z, W, V, U, T) = equidistant(W, V, U, T).
% 0.20/0.51 Axiom 9 (segment_construction2): equidistant(X, extension(Y, X, Z, W), Z, W) = true.
% 0.20/0.51 Axiom 10 (transitivity_for_equidistance): fresh4(equidistant(X, Y, Z, W), true, X, Y, V, U, Z, W) = fresh3(equidistant(X, Y, V, U), true, V, U, Z, W).
% 0.20/0.51 Axiom 11 (prove_lengthen): fresh6(between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)), true) = fresh5(equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true).
% 0.20/0.51
% 0.20/0.51 Lemma 12: extension(X, Y, Z, Z) = Y.
% 0.20/0.51 Proof:
% 0.20/0.51 extension(X, Y, Z, Z)
% 0.20/0.51 = { by axiom 2 (identity_for_equidistance) R->L }
% 0.20/0.51 fresh(true, true, Y, extension(X, Y, Z, Z))
% 0.20/0.51 = { by axiom 9 (segment_construction2) R->L }
% 0.20/0.51 fresh(equidistant(Y, extension(X, Y, Z, Z), Z, Z), true, Y, extension(X, Y, Z, Z))
% 0.20/0.51 = { by axiom 7 (identity_for_equidistance) }
% 0.20/0.51 Y
% 0.20/0.51
% 0.20/0.51 Lemma 13: equidistant(v, fresh6(X, X), lower_dimension_point_1, lower_dimension_point_2) = true.
% 0.20/0.51 Proof:
% 0.20/0.51 equidistant(v, fresh6(X, X), lower_dimension_point_1, lower_dimension_point_2)
% 0.20/0.51 = { by axiom 3 (prove_lengthen) }
% 0.20/0.51 equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)
% 0.20/0.51 = { by axiom 9 (segment_construction2) }
% 0.20/0.51 true
% 0.20/0.51
% 0.20/0.51 Lemma 14: fresh3(equidistant(X, Y, Z, W), true, Z, W, Y, X) = equidistant(Z, W, Y, X).
% 0.20/0.51 Proof:
% 0.20/0.51 fresh3(equidistant(X, Y, Z, W), true, Z, W, Y, X)
% 0.20/0.51 = { by axiom 10 (transitivity_for_equidistance) R->L }
% 0.20/0.51 fresh4(equidistant(X, Y, Y, X), true, X, Y, Z, W, Y, X)
% 0.20/0.51 = { by axiom 4 (reflexivity_for_equidistance) }
% 0.20/0.51 fresh4(true, true, X, Y, Z, W, Y, X)
% 0.20/0.51 = { by axiom 8 (transitivity_for_equidistance) }
% 0.20/0.51 equidistant(Z, W, Y, X)
% 0.20/0.51
% 0.20/0.51 Lemma 15: equidistant(X, Y, extension(Z, W, X, Y), W) = true.
% 0.20/0.51 Proof:
% 0.20/0.51 equidistant(X, Y, extension(Z, W, X, Y), W)
% 0.20/0.51 = { by lemma 14 R->L }
% 0.20/0.51 fresh3(equidistant(W, extension(Z, W, X, Y), X, Y), true, X, Y, extension(Z, W, X, Y), W)
% 0.20/0.51 = { by axiom 9 (segment_construction2) }
% 0.20/0.51 fresh3(true, true, X, Y, extension(Z, W, X, Y), W)
% 0.20/0.51 = { by axiom 5 (transitivity_for_equidistance) }
% 0.20/0.51 true
% 0.20/0.51
% 0.20/0.51 Goal 1 (lower_dimension3): between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2) = true.
% 0.20/0.51 Proof:
% 0.20/0.51 between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_2)
% 0.20/0.51 = { by axiom 2 (identity_for_equidistance) R->L }
% 0.20/0.51 between(lower_dimension_point_3, lower_dimension_point_1, fresh(true, true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.51 = { by axiom 5 (transitivity_for_equidistance) R->L }
% 0.20/0.51 between(lower_dimension_point_3, lower_dimension_point_1, fresh(fresh3(true, true, lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh6(true, true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.51 = { by axiom 5 (transitivity_for_equidistance) R->L }
% 0.20/0.51 between(lower_dimension_point_3, lower_dimension_point_1, fresh(fresh3(fresh3(true, true, extension(Y, X, v, fresh6(true, true)), X, lower_dimension_point_1, lower_dimension_point_2), true, lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh6(true, true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.51 = { by lemma 15 R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(fresh3(fresh3(equidistant(v, fresh6(true, true), extension(Y, X, v, fresh6(true, true)), X), true, extension(Y, X, v, fresh6(true, true)), X, lower_dimension_point_1, lower_dimension_point_2), true, lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh6(true, true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 10 (transitivity_for_equidistance) R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(fresh3(fresh4(equidistant(v, fresh6(true, true), lower_dimension_point_1, lower_dimension_point_2), true, v, fresh6(true, true), extension(Y, X, v, fresh6(true, true)), X, lower_dimension_point_1, lower_dimension_point_2), true, lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh6(true, true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by lemma 13 }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(fresh3(fresh4(true, true, v, fresh6(true, true), extension(Y, X, v, fresh6(true, true)), X, lower_dimension_point_1, lower_dimension_point_2), true, lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh6(true, true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 8 (transitivity_for_equidistance) }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(fresh3(equidistant(extension(Y, X, v, fresh6(true, true)), X, lower_dimension_point_1, lower_dimension_point_2), true, lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh6(true, true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by lemma 14 }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh6(true, true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 6 (segment_construction1) R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh6(between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 11 (prove_lengthen) }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 3 (prove_lengthen) R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(equidistant(v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 8 (transitivity_for_equidistance) R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh4(true, true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 5 (transitivity_for_equidistance) R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh4(fresh3(true, true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 4 (reflexivity_for_equidistance) R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh4(fresh3(equidistant(extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by lemma 14 }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh4(equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 10 (transitivity_for_equidistance) }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z)), true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by lemma 14 R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(fresh3(equidistant(fresh6(Z, Z), v, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z)), true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by lemma 14 R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(fresh3(fresh3(equidistant(extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x, fresh6(Z, Z), v), true, fresh6(Z, Z), v, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z)), true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 8 (transitivity_for_equidistance) R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(fresh3(fresh3(fresh4(true, true, lower_dimension_point_1, lower_dimension_point_2, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x, fresh6(Z, Z), v), true, fresh6(Z, Z), v, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z)), true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 5 (transitivity_for_equidistance) R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(fresh3(fresh3(fresh4(fresh3(true, true, lower_dimension_point_1, lower_dimension_point_2, fresh6(Z, Z), v), true, lower_dimension_point_1, lower_dimension_point_2, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x, fresh6(Z, Z), v), true, fresh6(Z, Z), v, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z)), true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by lemma 13 R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(fresh3(fresh3(fresh4(fresh3(equidistant(v, fresh6(Z, Z), lower_dimension_point_1, lower_dimension_point_2), true, lower_dimension_point_1, lower_dimension_point_2, fresh6(Z, Z), v), true, lower_dimension_point_1, lower_dimension_point_2, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x, fresh6(Z, Z), v), true, fresh6(Z, Z), v, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z)), true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by lemma 14 }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(fresh3(fresh3(fresh4(equidistant(lower_dimension_point_1, lower_dimension_point_2, fresh6(Z, Z), v), true, lower_dimension_point_1, lower_dimension_point_2, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x, fresh6(Z, Z), v), true, fresh6(Z, Z), v, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z)), true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 10 (transitivity_for_equidistance) }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(fresh3(fresh3(fresh3(equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x), true, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x, fresh6(Z, Z), v), true, fresh6(Z, Z), v, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z)), true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by lemma 15 }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(fresh3(fresh3(fresh3(true, true, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), x, fresh6(Z, Z), v), true, fresh6(Z, Z), v, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z)), true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 5 (transitivity_for_equidistance) }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(fresh3(fresh3(true, true, fresh6(Z, Z), v, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z)), true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 5 (transitivity_for_equidistance) }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(fresh3(true, true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), v, fresh6(Z, Z)), true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 5 (transitivity_for_equidistance) }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(fresh3(true, true, v, fresh6(Z, Z), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 5 (transitivity_for_equidistance) }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh5(true, true))), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 1 (prove_lengthen) }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, v)), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by lemma 12 }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, fresh(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, X), true, lower_dimension_point_1, lower_dimension_point_2))
% 0.20/0.52 = { by axiom 7 (identity_for_equidistance) }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, lower_dimension_point_1)
% 0.20/0.52 = { by lemma 12 R->L }
% 0.20/0.52 between(lower_dimension_point_3, lower_dimension_point_1, extension(lower_dimension_point_3, lower_dimension_point_1, W, W))
% 0.20/0.52 = { by axiom 6 (segment_construction1) }
% 0.20/0.52 true
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52
% 0.20/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
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