TSTP Solution File: GEO037-3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO037-3 : 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 : n010.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 23:26:59 EDT 2023
% Result : Unsatisfiable 3.65s 0.82s
% Output : Proof 3.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO037-3 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13 % 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 : n010.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 21:18:33 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.65/0.82 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.65/0.82
% 3.65/0.82 % SZS status Unsatisfiable
% 3.65/0.82
% 3.70/0.83 % SZS output start Proof
% 3.70/0.83 Take the following subset of the input axioms:
% 3.70/0.83 fof(d2, axiom, ![X, V, W, U]: (~equidistant(U, V, W, X) | equidistant(W, X, U, V))).
% 3.70/0.83 fof(d5, axiom, ![Y, Z, V2, X2, W2, U2]: (~equidistant(U2, V2, W2, X2) | (~equidistant(W2, X2, Y, Z) | equidistant(U2, V2, Y, Z)))).
% 3.70/0.83 fof(e1, axiom, ![V2, W2, U2]: V2=extension(U2, V2, W2, W2)).
% 3.70/0.83 fof(e2_1, axiom, lower_dimension_point_1!=lower_dimension_point_2).
% 3.70/0.83 fof(identity_for_equidistance, axiom, ![X2, Y2, Z2]: (~equidistant(X2, Y2, Z2, Z2) | X2=Y2)).
% 3.70/0.83 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)))).
% 3.70/0.83 fof(segment_construction1, axiom, ![V2, X2, Y2, W2]: between(X2, Y2, extension(X2, Y2, W2, V2))).
% 3.70/0.83 fof(segment_construction2, axiom, ![V2, X2, Y2, W2]: equidistant(Y2, extension(X2, Y2, W2, V2), W2, V2)).
% 3.70/0.83
% 3.70/0.83 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.70/0.83 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.70/0.83 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.70/0.83 fresh(y, y, x1...xn) = u
% 3.70/0.83 C => fresh(s, t, x1...xn) = v
% 3.70/0.83 where fresh is a fresh function symbol and x1..xn are the free
% 3.70/0.83 variables of u and v.
% 3.70/0.83 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.70/0.83 input problem has no model of domain size 1).
% 3.70/0.83
% 3.70/0.83 The encoding turns the above axioms into the following unit equations and goals:
% 3.70/0.83
% 3.70/0.83 Axiom 1 (prove_lengthen): fresh11(X, X) = v.
% 3.70/0.83 Axiom 2 (e1): X = extension(Y, X, Z, Z).
% 3.70/0.83 Axiom 3 (prove_lengthen): fresh12(X, X) = extension(u, v, lower_dimension_point_1, lower_dimension_point_2).
% 3.70/0.83 Axiom 4 (identity_for_equidistance): fresh2(X, X, Y, Z) = Z.
% 3.70/0.83 Axiom 5 (d2): fresh26(X, X, Y, Z, W, V) = true.
% 3.70/0.83 Axiom 6 (d5): fresh18(X, X, Y, Z, W, V) = true.
% 3.70/0.83 Axiom 7 (segment_construction1): between(X, Y, extension(X, Y, Z, W)) = true.
% 3.70/0.83 Axiom 8 (segment_construction2): equidistant(X, extension(Y, X, Z, W), Z, W) = true.
% 3.70/0.83 Axiom 9 (d5): fresh19(X, X, Y, Z, W, V, U, T) = equidistant(Y, Z, U, T).
% 3.70/0.83 Axiom 10 (identity_for_equidistance): fresh2(equidistant(X, Y, Z, Z), true, X, Y) = X.
% 3.70/0.83 Axiom 11 (d2): fresh26(equidistant(X, Y, Z, W), true, X, Y, Z, W) = equidistant(Z, W, X, Y).
% 3.70/0.83 Axiom 12 (d5): fresh19(equidistant(X, Y, Z, W), true, V, U, X, Y, Z, W) = fresh18(equidistant(V, U, X, Y), true, V, U, Z, W).
% 3.70/0.83 Axiom 13 (prove_lengthen): fresh12(between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)), true) = fresh11(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).
% 3.70/0.83
% 3.70/0.83 Lemma 14: fresh19(equidistant(X, Y, Z, W), true, V, extension(U, V, X, Y), X, Y, Z, W) = true.
% 3.70/0.84 Proof:
% 3.70/0.84 fresh19(equidistant(X, Y, Z, W), true, V, extension(U, V, X, Y), X, Y, Z, W)
% 3.70/0.84 = { by axiom 12 (d5) }
% 3.70/0.84 fresh18(equidistant(V, extension(U, V, X, Y), X, Y), true, V, extension(U, V, X, Y), Z, W)
% 3.70/0.84 = { by axiom 8 (segment_construction2) }
% 3.70/0.84 fresh18(true, true, V, extension(U, V, X, Y), Z, W)
% 3.70/0.84 = { by axiom 6 (d5) }
% 3.70/0.84 true
% 3.70/0.84
% 3.70/0.84 Goal 1 (e2_1): lower_dimension_point_1 = lower_dimension_point_2.
% 3.70/0.84 Proof:
% 3.70/0.84 lower_dimension_point_1
% 3.70/0.84 = { by axiom 10 (identity_for_equidistance) R->L }
% 3.70/0.84 fresh2(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, X), true, lower_dimension_point_1, lower_dimension_point_2)
% 3.70/0.84 = { by axiom 2 (e1) }
% 3.70/0.84 fresh2(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, v)), true, lower_dimension_point_1, lower_dimension_point_2)
% 3.70/0.84 = { by axiom 1 (prove_lengthen) R->L }
% 3.70/0.84 fresh2(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh11(true, true))), true, lower_dimension_point_1, lower_dimension_point_2)
% 3.70/0.84 = { by lemma 14 R->L }
% 3.70/0.84 fresh2(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh11(fresh19(equidistant(lower_dimension_point_1, lower_dimension_point_2, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)), true, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), 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)
% 3.70/0.84 = { by axiom 11 (d2) R->L }
% 3.70/0.84 fresh2(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh11(fresh19(fresh26(equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2), true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2), true, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), 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)
% 3.70/0.84 = { by axiom 8 (segment_construction2) }
% 3.70/0.84 fresh2(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh11(fresh19(fresh26(true, true, x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2), true, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), 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)
% 3.70/0.84 = { by axiom 5 (d2) }
% 3.70/0.84 fresh2(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh11(fresh19(true, true, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), 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)
% 3.70/0.84 = { by axiom 9 (d5) }
% 3.70/0.84 fresh2(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh11(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)
% 3.70/0.84 = { by axiom 13 (prove_lengthen) R->L }
% 3.70/0.84 fresh2(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh12(between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)), true))), true, lower_dimension_point_1, lower_dimension_point_2)
% 3.70/0.84 = { by axiom 7 (segment_construction1) }
% 3.70/0.84 fresh2(equidistant(lower_dimension_point_1, lower_dimension_point_2, X, extension(Y, X, v, fresh12(true, true))), true, lower_dimension_point_1, lower_dimension_point_2)
% 3.70/0.84 = { by axiom 11 (d2) R->L }
% 3.70/0.84 fresh2(fresh26(equidistant(X, extension(Y, X, v, fresh12(true, true)), lower_dimension_point_1, lower_dimension_point_2), true, X, extension(Y, X, v, fresh12(true, true)), lower_dimension_point_1, lower_dimension_point_2), true, lower_dimension_point_1, lower_dimension_point_2)
% 3.70/0.84 = { by axiom 9 (d5) R->L }
% 3.70/0.84 fresh2(fresh26(fresh19(true, true, X, extension(Y, X, v, fresh12(true, true)), v, fresh12(true, true), lower_dimension_point_1, lower_dimension_point_2), true, X, extension(Y, X, v, fresh12(true, true)), lower_dimension_point_1, lower_dimension_point_2), true, lower_dimension_point_1, lower_dimension_point_2)
% 3.70/0.84 = { by axiom 8 (segment_construction2) R->L }
% 3.70/0.84 fresh2(fresh26(fresh19(equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2), true, X, extension(Y, X, v, fresh12(true, true)), v, fresh12(true, true), lower_dimension_point_1, lower_dimension_point_2), true, X, extension(Y, X, v, fresh12(true, true)), lower_dimension_point_1, lower_dimension_point_2), true, lower_dimension_point_1, lower_dimension_point_2)
% 3.70/0.84 = { by axiom 3 (prove_lengthen) R->L }
% 3.70/0.84 fresh2(fresh26(fresh19(equidistant(v, fresh12(true, true), lower_dimension_point_1, lower_dimension_point_2), true, X, extension(Y, X, v, fresh12(true, true)), v, fresh12(true, true), lower_dimension_point_1, lower_dimension_point_2), true, X, extension(Y, X, v, fresh12(true, true)), lower_dimension_point_1, lower_dimension_point_2), true, lower_dimension_point_1, lower_dimension_point_2)
% 3.70/0.84 = { by lemma 14 }
% 3.70/0.84 fresh2(fresh26(true, true, X, extension(Y, X, v, fresh12(true, true)), lower_dimension_point_1, lower_dimension_point_2), true, lower_dimension_point_1, lower_dimension_point_2)
% 3.70/0.84 = { by axiom 5 (d2) }
% 3.70/0.84 fresh2(true, true, lower_dimension_point_1, lower_dimension_point_2)
% 3.70/0.84 = { by axiom 4 (identity_for_equidistance) }
% 3.70/0.84 lower_dimension_point_2
% 3.70/0.84 % SZS output end Proof
% 3.70/0.84
% 3.70/0.84 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------