TSTP Solution File: GEO058-3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO058-3 : 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 : n021.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 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO058-3 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13 % 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 : n021.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 20:41:29 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.44 Command-line arguments: --no-flatten-goal
% 0.20/0.44
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 Take the following subset of the input axioms:
% 0.20/0.44 fof(d2, axiom, ![X, V, W, U]: (~equidistant(U, V, W, X) | equidistant(W, X, U, V))).
% 0.20/0.44 fof(identity_for_equidistance, axiom, ![Y, Z, X2]: (~equidistant(X2, Y, Z, Z) | X2=Y)).
% 0.20/0.44 fof(prove_u_equals_v, negated_conjecture, u!=v).
% 0.20/0.44 fof(r2_2, axiom, ![V2, U2]: equidistant(V2, reflection(U2, V2), U2, V2)).
% 0.20/0.44 fof(v_equals_reflection, hypothesis, v=reflection(u, v)).
% 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 (v_equals_reflection): v = reflection(u, v).
% 0.20/0.44 Axiom 2 (identity_for_equidistance): fresh(X, X, Y, Z) = Z.
% 0.20/0.44 Axiom 3 (d2): fresh17(X, X, Y, Z, W, V) = true.
% 0.20/0.44 Axiom 4 (r2_2): equidistant(X, reflection(Y, X), Y, X) = true.
% 0.20/0.44 Axiom 5 (identity_for_equidistance): fresh(equidistant(X, Y, Z, Z), true, X, Y) = X.
% 0.20/0.44 Axiom 6 (d2): fresh17(equidistant(X, Y, Z, W), true, X, Y, Z, W) = equidistant(Z, W, X, Y).
% 0.20/0.44
% 0.20/0.44 Goal 1 (prove_u_equals_v): u = v.
% 0.20/0.44 Proof:
% 0.20/0.44 u
% 0.20/0.44 = { by axiom 5 (identity_for_equidistance) R->L }
% 0.20/0.44 fresh(equidistant(u, v, v, v), true, u, v)
% 0.20/0.44 = { by axiom 6 (d2) R->L }
% 0.20/0.44 fresh(fresh17(equidistant(v, v, u, v), true, v, v, u, v), true, u, v)
% 0.20/0.44 = { by axiom 1 (v_equals_reflection) }
% 0.20/0.44 fresh(fresh17(equidistant(v, reflection(u, v), u, v), true, v, v, u, v), true, u, v)
% 0.20/0.44 = { by axiom 4 (r2_2) }
% 0.20/0.44 fresh(fresh17(true, true, v, v, u, v), true, u, v)
% 0.20/0.44 = { by axiom 3 (d2) }
% 0.20/0.44 fresh(true, true, u, v)
% 0.20/0.44 = { by axiom 2 (identity_for_equidistance) }
% 0.20/0.44 v
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------