TSTP Solution File: GEO207+3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO207+3 : TPTP v8.1.2. Released v4.0.0.
% 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 : n028.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 23:28:03 EDT 2023
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO207+3 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n028.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
% 0.13/0.34 % DateTime : Tue Aug 29 21:15:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.40 Command-line arguments: --no-flatten-goal
% 0.13/0.40
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 Take the following subset of the input axioms:
% 0.19/0.40 fof(a3, axiom, ![X, Y]: (parallel_lines(X, Y) <=> ~convergent_lines(X, Y))).
% 0.19/0.40 fof(a4, axiom, ![X2, Y2]: (incident_point_and_line(X2, Y2) <=> ~apart_point_and_line(X2, Y2))).
% 0.19/0.40 fof(a5, axiom, ![X2, Y2]: (orthogonal_lines(X2, Y2) <=> ~unorthogonal_lines(X2, Y2))).
% 0.19/0.40 fof(apart1, axiom, ![X2]: ~distinct_points(X2, X2)).
% 0.19/0.40 fof(apart2, axiom, ![X2]: ~distinct_lines(X2, X2)).
% 0.19/0.40 fof(apart3, axiom, ![X2]: ~convergent_lines(X2, X2)).
% 0.19/0.40 fof(ax1, axiom, ![X2, Y2]: (equal_points(X2, Y2) <=> ~distinct_points(X2, Y2))).
% 0.19/0.40 fof(ax2, axiom, ![X2, Y2]: (equal_lines(X2, Y2) <=> ~distinct_lines(X2, Y2))).
% 0.19/0.40 fof(ci1, axiom, ![X2, Y2]: (distinct_points(X2, Y2) => ~apart_point_and_line(X2, line_connecting(X2, Y2)))).
% 0.19/0.40 fof(ci2, axiom, ![X2, Y2]: (distinct_points(X2, Y2) => ~apart_point_and_line(Y2, line_connecting(X2, Y2)))).
% 0.19/0.40 fof(ci3, axiom, ![X2, Y2]: (convergent_lines(X2, Y2) => ~apart_point_and_line(intersection_point(X2, Y2), X2))).
% 0.19/0.40 fof(ci4, axiom, ![X2, Y2]: (convergent_lines(X2, Y2) => ~apart_point_and_line(intersection_point(X2, Y2), Y2))).
% 0.19/0.40 fof(con, conjecture, ![X2]: ~convergent_lines(X2, X2)).
% 0.19/0.40 fof(cp1, axiom, ![X2, Y2]: ~convergent_lines(parallel_through_point(Y2, X2), Y2)).
% 0.19/0.40 fof(cp2, axiom, ![X2, Y2]: ~apart_point_and_line(X2, parallel_through_point(Y2, X2))).
% 0.19/0.41 fof(ooc1, axiom, ![L, A]: ~unorthogonal_lines(orthogonal_through_point(L, A), L)).
% 0.19/0.41 fof(ooc2, axiom, ![A2, L2]: ~apart_point_and_line(A2, orthogonal_through_point(L2, A2))).
% 0.19/0.41
% 0.19/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.41 fresh(y, y, x1...xn) = u
% 0.19/0.41 C => fresh(s, t, x1...xn) = v
% 0.19/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.41 variables of u and v.
% 0.19/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.41 input problem has no model of domain size 1).
% 0.19/0.41
% 0.19/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.41
% 0.19/0.41 Axiom 1 (con): convergent_lines(x, x) = true2.
% 0.19/0.41
% 0.19/0.41 Goal 1 (apart3): convergent_lines(X, X) = true2.
% 0.19/0.41 The goal is true when:
% 0.19/0.41 X = x
% 0.19/0.41
% 0.19/0.41 Proof:
% 0.19/0.41 convergent_lines(x, x)
% 0.19/0.41 = { by axiom 1 (con) }
% 0.19/0.41 true2
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------