TSTP Solution File: GEO235+3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO235+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 : n018.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 23:28:15 EDT 2023
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO235+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % 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 : n018.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 21:15:33 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.45 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.45
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 Take the following subset of the input axioms:
% 0.19/0.46 fof(a4_defns, axiom, ![X, Y]: (equally_directed_lines(X, Y) <=> ~unequally_directed_lines(X, Y))).
% 0.19/0.46 fof(a5_defns, axiom, ![X2, Y2]: (equally_directed_opposite_lines(X2, Y2) <=> ~unequally_directed_opposite_lines(X2, Y2))).
% 0.19/0.46 fof(ax10_basics, axiom, ![A, L]: ~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))).
% 0.19/0.46 fof(ax11_basics, axiom, ![M, L2]: ~(left_convergent_lines(L2, M) | left_convergent_lines(L2, reverse_line(M)))).
% 0.19/0.46 fof(ax1_basics, axiom, ![A2]: ~distinct_points(A2, A2)).
% 0.19/0.46 fof(ax3_basics, axiom, ![L2]: ~distinct_lines(L2, L2)).
% 0.19/0.46 fof(ax5_cons_objs, axiom, ![B, A2]: (distinct_points(A2, B) => (~apart_point_and_line(A2, line_connecting(A2, B)) & ~apart_point_and_line(B, line_connecting(A2, B))))).
% 0.19/0.46 fof(ax6_cons_objs, 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)))).
% 0.19/0.46 fof(ax7_cons_objs, axiom, ![A2, L2]: ~apart_point_and_line(A2, parallel_through_point(L2, A2))).
% 0.19/0.46 fof(ax8_cons_objs, axiom, ![L2]: ~distinct_lines(L2, reverse_line(L2))).
% 0.19/0.46 fof(con, conjecture, ![A2, L2, B2]: ((left_apart_point(A2, L2) & right_apart_point(B2, L2)) => distinct_points(A2, B2))).
% 0.19/0.46
% 0.19/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.46 fresh(y, y, x1...xn) = u
% 0.19/0.46 C => fresh(s, t, x1...xn) = v
% 0.19/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.46 variables of u and v.
% 0.19/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.46 input problem has no model of domain size 1).
% 0.19/0.46
% 0.19/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.46
% 0.19/0.46 Axiom 1 (con_1): left_apart_point(a, l) = true2.
% 0.19/0.46
% 0.19/0.46 Goal 1 (ax10_basics): left_apart_point(X, Y) = true2.
% 0.19/0.46 The goal is true when:
% 0.19/0.46 X = a
% 0.19/0.46 Y = l
% 0.19/0.46
% 0.19/0.46 Proof:
% 0.19/0.46 left_apart_point(a, l)
% 0.19/0.46 = { by axiom 1 (con_1) }
% 0.19/0.46 true2
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46
% 0.19/0.46 RESULT: Theorem (the conjecture is true).
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