TSTP Solution File: GEO058-2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO058-2 : 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 : n025.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 23:27:08 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO058-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 23:37:40 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.39 Command-line arguments: --ground-connectedness --complete-subsets
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Take the following subset of the input axioms:
% 0.19/0.40 fof(identity_for_equidistance, axiom, ![X, Y, Z]: (~equidistant(X, Y, Z, Z) | X=Y)).
% 0.19/0.40 fof(prove_u_equals_v, negated_conjecture, u!=v).
% 0.19/0.40 fof(reflection, axiom, ![V, U]: reflection(U, V)=extension(U, V, U, V)).
% 0.19/0.40 fof(reflexivity_for_equidistance, axiom, ![X2, Y2]: equidistant(X2, Y2, Y2, X2)).
% 0.19/0.40 fof(segment_construction2, axiom, ![W, X2, Y2, V3]: equidistant(Y2, extension(X2, Y2, W, V3), W, V3)).
% 0.19/0.40 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)))).
% 0.19/0.40 fof(v_equals_reflection, hypothesis, v=reflection(u, v)).
% 0.19/0.40
% 0.19/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.40 fresh(y, y, x1...xn) = u
% 0.19/0.40 C => fresh(s, t, x1...xn) = v
% 0.19/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.40 variables of u and v.
% 0.19/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.40 input problem has no model of domain size 1).
% 0.19/0.40
% 0.19/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.40
% 0.19/0.40 Axiom 1 (v_equals_reflection): v = reflection(u, v).
% 0.19/0.40 Axiom 2 (identity_for_equidistance): fresh(X, X, Y, Z) = Z.
% 0.19/0.40 Axiom 3 (reflection): reflection(X, Y) = extension(X, Y, X, Y).
% 0.19/0.40 Axiom 4 (reflexivity_for_equidistance): equidistant(X, Y, Y, X) = true.
% 0.19/0.40 Axiom 5 (transitivity_for_equidistance): fresh3(X, X, Y, Z, W, V) = true.
% 0.19/0.40 Axiom 6 (identity_for_equidistance): fresh(equidistant(X, Y, Z, Z), true, X, Y) = X.
% 0.19/0.40 Axiom 7 (transitivity_for_equidistance): fresh4(X, X, Y, Z, W, V, U, T) = equidistant(W, V, U, T).
% 0.19/0.40 Axiom 8 (segment_construction2): equidistant(X, extension(Y, X, Z, W), Z, W) = true.
% 0.19/0.40 Axiom 9 (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).
% 0.19/0.40
% 0.19/0.40 Goal 1 (prove_u_equals_v): u = v.
% 0.19/0.40 Proof:
% 0.19/0.40 u
% 0.19/0.40 = { by axiom 6 (identity_for_equidistance) R->L }
% 0.19/0.40 fresh(equidistant(u, v, v, v), true, u, v)
% 0.19/0.40 = { by axiom 7 (transitivity_for_equidistance) R->L }
% 0.19/0.40 fresh(fresh4(true, true, v, v, u, v, v, v), true, u, v)
% 0.19/0.40 = { by axiom 4 (reflexivity_for_equidistance) R->L }
% 0.19/0.40 fresh(fresh4(equidistant(v, v, v, v), true, v, v, u, v, v, v), true, u, v)
% 0.19/0.40 = { by axiom 9 (transitivity_for_equidistance) }
% 0.19/0.40 fresh(fresh3(equidistant(v, v, u, v), true, u, v, v, v), true, u, v)
% 0.19/0.40 = { by axiom 1 (v_equals_reflection) }
% 0.19/0.40 fresh(fresh3(equidistant(v, reflection(u, v), u, v), true, u, v, v, v), true, u, v)
% 0.19/0.40 = { by axiom 3 (reflection) }
% 0.19/0.40 fresh(fresh3(equidistant(v, extension(u, v, u, v), u, v), true, u, v, v, v), true, u, v)
% 0.19/0.40 = { by axiom 8 (segment_construction2) }
% 0.19/0.40 fresh(fresh3(true, true, u, v, v, v), true, u, v)
% 0.19/0.40 = { by axiom 5 (transitivity_for_equidistance) }
% 0.19/0.40 fresh(true, true, u, v)
% 0.19/0.40 = { by axiom 2 (identity_for_equidistance) }
% 0.19/0.40 v
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------