TSTP Solution File: GEO242+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO242+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 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 : n006.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 23:28:18 EDT 2023
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO242+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 0.07/0.13 % 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 : n006.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 20:31:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.43 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.43
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 Take the following subset of the input axioms:
% 0.21/0.44 fof(bf_def, axiom, ![L, B, A2]: (before_on_line(L, A2, B) <=> (distinct_points(A2, B) & (~(left_apart_point(A2, L) | left_apart_point(A2, reverse_line(L))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L))) & ~unequally_directed_lines(L, line_connecting(A2, B))))))).
% 0.21/0.44 fof(con, conjecture, ![A, B2, L2]: ((~apart_point_and_line(A, L2) & (distinct_points(A, B2) & left_convergent_lines(L2, reverse_line(line_connecting(A, B2))))) => left_apart_point(B2, reverse_line(L2)))).
% 0.21/0.44 fof(oag1, axiom, ![A3]: ~distinct_points(A3, A3)).
% 0.21/0.44 fof(oag10, axiom, ![A3, L2]: ~(left_apart_point(A3, L2) | left_apart_point(A3, reverse_line(L2)))).
% 0.21/0.44 fof(oag11, axiom, ![M, L2]: ~(left_convergent_lines(L2, M) | left_convergent_lines(L2, reverse_line(M)))).
% 0.21/0.44 fof(oag3, axiom, ![L2]: ~distinct_lines(L2, L2)).
% 0.21/0.44 fof(oag5, axiom, ![L2]: ~unequally_directed_lines(L2, L2)).
% 0.21/0.44 fof(oagco10, axiom, ![A3, L2]: ~unequally_directed_lines(parallel_through_point(L2, A3), L2)).
% 0.21/0.44 fof(oagco5, axiom, ![A3, B2]: (distinct_points(A3, B2) => (~apart_point_and_line(A3, line_connecting(A3, B2)) & ~apart_point_and_line(B2, line_connecting(A3, B2))))).
% 0.21/0.44 fof(oagco6, axiom, ![L2, M2]: ((unequally_directed_lines(L2, M2) & unequally_directed_lines(L2, reverse_line(M2))) => (~apart_point_and_line(intersection_point(L2, M2), L2) & ~apart_point_and_line(intersection_point(L2, M2), M2)))).
% 0.21/0.44 fof(oagco7, axiom, ![A3, L2]: ~apart_point_and_line(A3, parallel_through_point(L2, A3))).
% 0.21/0.44 fof(oagco8, axiom, ![L2]: ~distinct_lines(L2, reverse_line(L2))).
% 0.21/0.44 fof(oagco9, axiom, ![A3, B2]: ~unequally_directed_lines(line_connecting(A3, B2), reverse_line(line_connecting(B2, A3)))).
% 0.21/0.44
% 0.21/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.44 fresh(y, y, x1...xn) = u
% 0.21/0.44 C => fresh(s, t, x1...xn) = v
% 0.21/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.44 variables of u and v.
% 0.21/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.44 input problem has no model of domain size 1).
% 0.21/0.44
% 0.21/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.44
% 0.21/0.44 Axiom 1 (con_1): left_convergent_lines(l, reverse_line(line_connecting(a, b))) = true2.
% 0.21/0.44
% 0.21/0.44 Goal 1 (oag11): left_convergent_lines(X, Y) = true2.
% 0.21/0.44 The goal is true when:
% 0.21/0.44 X = l
% 0.21/0.44 Y = reverse_line(line_connecting(a, b))
% 0.21/0.44
% 0.21/0.44 Proof:
% 0.21/0.44 left_convergent_lines(l, reverse_line(line_connecting(a, b)))
% 0.21/0.44 = { by axiom 1 (con_1) }
% 0.21/0.44 true2
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44
% 0.21/0.44 RESULT: Theorem (the conjecture is true).
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