TSTP Solution File: GEO222+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO222+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Fri Sep 16 20:35:51 EDT 2022
% Result : Theorem 0.66s 0.63s
% Output : Proof 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GEO222+3 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n004.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 31 06:59:04 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.66/0.63 % SZS status Theorem
% 0.66/0.63 % SZS output start Proof
% 0.66/0.63 tff(convergent_lines_type, type, (
% 0.66/0.63 convergent_lines: ( $i * $i ) > $o)).
% 0.66/0.63 tff(orthogonal_through_point_type, type, (
% 0.66/0.63 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.66/0.63 tff(intersection_point_type, type, (
% 0.66/0.63 intersection_point: ( $i * $i ) > $i)).
% 0.66/0.63 tff(tptp_fun_A_1_type, type, (
% 0.66/0.63 tptp_fun_A_1: $i)).
% 0.66/0.63 tff(tptp_fun_L_0_type, type, (
% 0.66/0.63 tptp_fun_L_0: $i)).
% 0.66/0.63 tff(distinct_lines_type, type, (
% 0.66/0.63 distinct_lines: ( $i * $i ) > $o)).
% 0.66/0.63 tff(apart_point_and_line_type, type, (
% 0.66/0.63 apart_point_and_line: ( $i * $i ) > $o)).
% 0.66/0.63 tff(unorthogonal_lines_type, type, (
% 0.66/0.63 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.66/0.63 tff(parallel_through_point_type, type, (
% 0.66/0.63 parallel_through_point: ( $i * $i ) > $i)).
% 0.66/0.63 tff(distinct_points_type, type, (
% 0.66/0.63 distinct_points: ( $i * $i ) > $o)).
% 0.66/0.63 tff(parallel_lines_type, type, (
% 0.66/0.63 parallel_lines: ( $i * $i ) > $o)).
% 0.66/0.63 tff(1,assumption,(~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))), introduced(assumption)).
% 0.66/0.63 tff(2,plain,
% 0.66/0.63 (^[A: $i, L: $i] : refl((~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> (~apart_point_and_line(A, orthogonal_through_point(L, A))))),
% 0.66/0.63 inference(bind,[status(th)],[])).
% 0.66/0.63 tff(3,plain,
% 0.66/0.63 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.66/0.63 inference(quant_intro,[status(thm)],[2])).
% 0.66/0.63 tff(4,plain,
% 0.66/0.63 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.66/0.63 inference(rewrite,[status(thm)],[])).
% 0.66/0.63 tff(5,axiom,(![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ooc2')).
% 0.66/0.63 tff(6,plain,
% 0.66/0.63 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.66/0.63 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.66/0.63 tff(7,plain,(
% 0.66/0.63 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.66/0.63 inference(skolemize,[status(sab)],[6])).
% 0.66/0.63 tff(8,plain,
% 0.66/0.63 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.66/0.63 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.66/0.63 tff(9,plain,
% 0.66/0.63 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.66/0.63 inference(quant_inst,[status(thm)],[])).
% 0.66/0.63 tff(10,plain,
% 0.66/0.63 (~apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.66/0.64 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.66/0.64 tff(11,plain,
% 0.66/0.64 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.66/0.64 inference(bind,[status(th)],[])).
% 0.66/0.64 tff(12,plain,
% 0.66/0.64 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.66/0.64 inference(quant_intro,[status(thm)],[11])).
% 0.66/0.64 tff(13,plain,
% 0.66/0.64 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.66/0.64 inference(rewrite,[status(thm)],[])).
% 0.66/0.64 tff(14,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.66/0.64 tff(15,plain,
% 0.66/0.64 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.66/0.64 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.66/0.64 tff(16,plain,(
% 0.66/0.64 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.66/0.64 inference(skolemize,[status(sab)],[15])).
% 0.66/0.64 tff(17,plain,
% 0.66/0.64 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.66/0.64 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.66/0.64 tff(18,plain,
% 0.66/0.64 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))),
% 0.66/0.64 inference(quant_inst,[status(thm)],[])).
% 0.66/0.64 tff(19,plain,
% 0.66/0.64 (~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)),
% 0.66/0.64 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.66/0.64 tff(20,plain,
% 0.66/0.64 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.66/0.64 inference(quant_inst,[status(thm)],[])).
% 0.66/0.64 tff(21,plain,
% 0.66/0.64 (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.66/0.64 inference(unit_resolution,[status(thm)],[20, 17])).
% 0.66/0.64 tff(22,plain,
% 0.66/0.64 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.66/0.64 inference(bind,[status(th)],[])).
% 0.66/0.64 tff(23,plain,
% 0.66/0.64 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.66/0.64 inference(quant_intro,[status(thm)],[22])).
% 0.66/0.64 tff(24,plain,
% 0.66/0.64 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.66/0.64 inference(rewrite,[status(thm)],[])).
% 0.66/0.64 tff(25,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.66/0.64 tff(26,plain,
% 0.66/0.64 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.66/0.64 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.66/0.64 tff(27,plain,(
% 0.66/0.64 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.66/0.64 inference(skolemize,[status(sab)],[26])).
% 0.66/0.64 tff(28,plain,
% 0.66/0.64 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.66/0.64 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.66/0.64 tff(29,plain,
% 0.66/0.64 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.66/0.64 inference(rewrite,[status(thm)],[])).
% 0.66/0.64 tff(30,plain,
% 0.66/0.64 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.66/0.64 inference(quant_inst,[status(thm)],[])).
% 0.66/0.64 tff(31,plain,
% 0.66/0.64 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.66/0.64 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.66/0.64 tff(32,plain,
% 0.66/0.64 (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.67/0.64 inference(unit_resolution,[status(thm)],[31, 28, 21])).
% 0.67/0.64 tff(33,plain,
% 0.67/0.64 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.67/0.64 inference(bind,[status(th)],[])).
% 0.67/0.64 tff(34,plain,
% 0.67/0.64 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.67/0.64 inference(quant_intro,[status(thm)],[33])).
% 0.67/0.64 tff(35,plain,
% 0.67/0.64 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.67/0.64 inference(rewrite,[status(thm)],[])).
% 0.67/0.64 tff(36,plain,
% 0.67/0.64 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.67/0.64 inference(bind,[status(th)],[])).
% 0.67/0.64 tff(37,plain,
% 0.67/0.64 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.67/0.64 inference(quant_intro,[status(thm)],[36])).
% 0.67/0.64 tff(38,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.67/0.64 tff(39,plain,
% 0.67/0.64 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.67/0.64 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.67/0.64 tff(40,plain,
% 0.67/0.64 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.67/0.64 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.67/0.64 tff(41,plain,(
% 0.67/0.64 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.67/0.64 inference(skolemize,[status(sab)],[40])).
% 0.67/0.64 tff(42,plain,
% 0.67/0.64 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.67/0.64 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.67/0.64 tff(43,plain,
% 0.67/0.64 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.64 inference(rewrite,[status(thm)],[])).
% 0.67/0.64 tff(44,plain,
% 0.67/0.64 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.64 inference(quant_inst,[status(thm)],[])).
% 0.67/0.64 tff(45,plain,
% 0.67/0.64 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1)))),
% 0.67/0.64 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.67/0.64 tff(46,plain,
% 0.67/0.64 (~apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1))),
% 0.67/0.64 inference(unit_resolution,[status(thm)],[45, 42, 32])).
% 0.67/0.64 tff(47,plain,
% 0.67/0.64 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.67/0.64 inference(quant_inst,[status(thm)],[])).
% 0.67/0.64 tff(48,plain,
% 0.67/0.64 (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.67/0.64 inference(unit_resolution,[status(thm)],[47, 17])).
% 0.67/0.64 tff(49,plain,
% 0.67/0.64 (^[A: $i, L: $i, M: $i, N: $i] : refl((apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))))),
% 0.67/0.64 inference(bind,[status(th)],[])).
% 0.67/0.64 tff(50,plain,
% 0.67/0.64 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.67/0.64 inference(quant_intro,[status(thm)],[49])).
% 0.67/0.64 tff(51,plain,
% 0.67/0.64 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.67/0.64 inference(rewrite,[status(thm)],[])).
% 0.67/0.64 tff(52,plain,
% 0.67/0.64 (^[A: $i, L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(A, L) | apart_point_and_line(A, M)) <=> (apart_point_and_line(A, M) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> ((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)))), rewrite(((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> ((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)))), rewrite(((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))))), rewrite((distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))))),
% 0.67/0.64 inference(bind,[status(th)],[])).
% 0.67/0.64 tff(53,plain,
% 0.67/0.64 (![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.67/0.64 inference(quant_intro,[status(thm)],[52])).
% 0.67/0.64 tff(54,axiom,(![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ouo1')).
% 0.67/0.64 tff(55,plain,
% 0.67/0.64 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.67/0.64 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.67/0.64 tff(56,plain,
% 0.67/0.64 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.67/0.64 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.67/0.64 tff(57,plain,(
% 0.67/0.64 ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.67/0.64 inference(skolemize,[status(sab)],[56])).
% 0.67/0.64 tff(58,plain,
% 0.67/0.64 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.67/0.64 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.67/0.64 tff(59,plain,
% 0.67/0.64 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.64 inference(rewrite,[status(thm)],[])).
% 0.67/0.64 tff(60,plain,
% 0.67/0.64 ((apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)))) <=> (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.64 inference(rewrite,[status(thm)],[])).
% 0.67/0.64 tff(61,plain,
% 0.67/0.64 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.67/0.65 inference(monotonicity,[status(thm)],[60])).
% 0.67/0.65 tff(62,plain,
% 0.67/0.65 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.65 inference(transitivity,[status(thm)],[61, 59])).
% 0.67/0.65 tff(63,plain,
% 0.67/0.65 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.65 inference(quant_inst,[status(thm)],[])).
% 0.67/0.65 tff(64,plain,
% 0.67/0.65 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.65 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.67/0.65 tff(65,plain,
% 0.67/0.65 ((~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.65 inference(unit_resolution,[status(thm)],[64, 58, 48, 46, 19])).
% 0.67/0.65 tff(66,plain,
% 0.67/0.65 (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))),
% 0.67/0.65 inference(unit_resolution,[status(thm)],[65, 10])).
% 0.67/0.65 tff(67,plain,
% 0.67/0.65 (^[L: $i, M: $i, N: $i] : refl((unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))))),
% 0.67/0.65 inference(bind,[status(th)],[])).
% 0.67/0.65 tff(68,plain,
% 0.67/0.65 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.67/0.65 inference(quant_intro,[status(thm)],[67])).
% 0.67/0.65 tff(69,plain,
% 0.67/0.65 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))))),
% 0.67/0.65 inference(bind,[status(th)],[])).
% 0.67/0.65 tff(70,plain,
% 0.67/0.65 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.67/0.65 inference(quant_intro,[status(thm)],[69])).
% 0.67/0.65 tff(71,plain,
% 0.67/0.65 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.67/0.65 inference(rewrite,[status(thm)],[])).
% 0.67/0.65 tff(72,plain,
% 0.67/0.65 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.67/0.65 inference(bind,[status(th)],[])).
% 0.67/0.65 tff(73,plain,
% 0.67/0.65 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.67/0.65 inference(quant_intro,[status(thm)],[72])).
% 0.67/0.65 tff(74,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.67/0.65 tff(75,plain,
% 0.67/0.65 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.67/0.65 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.67/0.65 tff(76,plain,
% 0.67/0.65 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.67/0.65 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.67/0.65 tff(77,plain,(
% 0.67/0.65 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.67/0.65 inference(skolemize,[status(sab)],[76])).
% 0.67/0.65 tff(78,plain,
% 0.67/0.65 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.67/0.65 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.67/0.65 tff(79,plain,
% 0.67/0.65 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.67/0.65 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.67/0.65 tff(80,plain,
% 0.67/0.65 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.65 inference(rewrite,[status(thm)],[])).
% 0.67/0.65 tff(81,plain,
% 0.67/0.65 ((unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.65 inference(rewrite,[status(thm)],[])).
% 0.67/0.65 tff(82,plain,
% 0.67/0.65 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.65 inference(monotonicity,[status(thm)],[81])).
% 0.67/0.65 tff(83,plain,
% 0.67/0.65 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.65 inference(transitivity,[status(thm)],[82, 80])).
% 0.67/0.65 tff(84,plain,
% 0.67/0.65 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.65 inference(quant_inst,[status(thm)],[])).
% 0.67/0.65 tff(85,plain,
% 0.67/0.65 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.67/0.65 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.67/0.65 tff(86,plain,
% 0.67/0.65 (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.67/0.65 inference(unit_resolution,[status(thm)],[85, 79, 21])).
% 0.67/0.65 tff(87,plain,
% 0.67/0.65 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.67/0.65 inference(bind,[status(th)],[])).
% 0.67/0.65 tff(88,plain,
% 0.67/0.65 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.67/0.65 inference(quant_intro,[status(thm)],[87])).
% 0.67/0.65 tff(89,plain,
% 0.67/0.65 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.67/0.65 inference(rewrite,[status(thm)],[])).
% 0.67/0.65 tff(90,plain,
% 0.67/0.65 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.67/0.65 inference(bind,[status(th)],[])).
% 0.67/0.65 tff(91,plain,
% 0.67/0.65 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.67/0.65 inference(quant_intro,[status(thm)],[90])).
% 0.67/0.65 tff(92,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.67/0.65 tff(93,plain,
% 0.67/0.65 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.67/0.65 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.67/0.65 tff(94,plain,
% 0.67/0.65 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.67/0.65 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.67/0.65 tff(95,plain,(
% 0.67/0.65 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.67/0.65 inference(skolemize,[status(sab)],[94])).
% 0.67/0.65 tff(96,plain,
% 0.67/0.65 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.67/0.65 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.67/0.65 tff(97,plain,
% 0.67/0.65 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.67/0.65 inference(rewrite,[status(thm)],[])).
% 0.67/0.65 tff(98,plain,
% 0.67/0.65 ((distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))) <=> (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.67/0.65 inference(rewrite,[status(thm)],[])).
% 0.67/0.65 tff(99,plain,
% 0.67/0.65 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))))),
% 0.67/0.65 inference(monotonicity,[status(thm)],[98])).
% 0.67/0.65 tff(100,plain,
% 0.67/0.65 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.67/0.66 inference(transitivity,[status(thm)],[99, 97])).
% 0.67/0.66 tff(101,plain,
% 0.67/0.66 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.67/0.66 inference(quant_inst,[status(thm)],[])).
% 0.67/0.66 tff(102,plain,
% 0.67/0.66 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.66 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.67/0.66 tff(103,plain,
% 0.67/0.66 (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.66 inference(unit_resolution,[status(thm)],[102, 96, 86, 66])).
% 0.67/0.66 tff(104,plain,
% 0.67/0.66 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.67/0.66 inference(rewrite,[status(thm)],[])).
% 0.67/0.66 tff(105,plain,
% 0.67/0.66 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.67/0.66 inference(quant_inst,[status(thm)],[])).
% 0.67/0.66 tff(106,plain,
% 0.67/0.66 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.67/0.66 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.67/0.66 tff(107,plain,
% 0.67/0.66 (convergent_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.67/0.66 inference(unit_resolution,[status(thm)],[106, 28, 48])).
% 0.67/0.66 tff(108,plain,
% 0.67/0.66 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.66 inference(rewrite,[status(thm)],[])).
% 0.67/0.66 tff(109,plain,
% 0.67/0.66 ((distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0))) <=> ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.66 inference(rewrite,[status(thm)],[])).
% 0.67/0.66 tff(110,plain,
% 0.67/0.66 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.67/0.66 inference(monotonicity,[status(thm)],[109])).
% 0.67/0.66 tff(111,plain,
% 0.67/0.66 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.66 inference(transitivity,[status(thm)],[110, 108])).
% 0.67/0.66 tff(112,plain,
% 0.67/0.66 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.67/0.66 inference(quant_inst,[status(thm)],[])).
% 0.67/0.66 tff(113,plain,
% 0.67/0.66 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.66 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.67/0.66 tff(114,plain,
% 0.67/0.66 ($false),
% 0.67/0.66 inference(unit_resolution,[status(thm)],[113, 96, 107, 103, 1])).
% 0.67/0.66 tff(115,plain,(distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.66 tff(116,plain,
% 0.67/0.66 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.67/0.66 inference(bind,[status(th)],[])).
% 0.67/0.66 tff(117,plain,
% 0.67/0.66 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.67/0.66 inference(quant_intro,[status(thm)],[116])).
% 0.67/0.66 tff(118,plain,
% 0.67/0.66 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.67/0.66 inference(rewrite,[status(thm)],[])).
% 0.67/0.66 tff(119,plain,
% 0.67/0.66 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.67/0.66 inference(bind,[status(th)],[])).
% 0.67/0.66 tff(120,plain,
% 0.67/0.66 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.67/0.66 inference(quant_intro,[status(thm)],[119])).
% 0.67/0.66 tff(121,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.67/0.66 tff(122,plain,
% 0.67/0.66 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.67/0.66 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.67/0.66 tff(123,plain,
% 0.67/0.66 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.67/0.66 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.67/0.66 tff(124,plain,(
% 0.67/0.66 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.67/0.66 inference(skolemize,[status(sab)],[123])).
% 0.67/0.66 tff(125,plain,
% 0.67/0.66 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.67/0.66 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.67/0.66 tff(126,plain,
% 0.67/0.66 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.66 inference(rewrite,[status(thm)],[])).
% 0.67/0.66 tff(127,plain,
% 0.67/0.66 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.66 inference(quant_inst,[status(thm)],[])).
% 0.67/0.66 tff(128,plain,
% 0.67/0.66 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.66 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.67/0.66 tff(129,plain,
% 0.67/0.66 (convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.66 inference(unit_resolution,[status(thm)],[128, 125, 115])).
% 0.67/0.66 tff(130,plain,
% 0.67/0.66 (((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.67/0.66 inference(tautology,[status(thm)],[])).
% 0.67/0.66 tff(131,plain,
% 0.67/0.66 ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.67/0.66 inference(unit_resolution,[status(thm)],[130, 86])).
% 0.67/0.66 tff(132,plain,
% 0.67/0.66 (((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.67/0.66 inference(tautology,[status(thm)],[])).
% 0.67/0.66 tff(133,plain,
% 0.67/0.66 ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.67/0.66 inference(unit_resolution,[status(thm)],[132, 48])).
% 0.67/0.66 tff(134,plain,
% 0.67/0.66 (((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.67/0.66 inference(tautology,[status(thm)],[])).
% 0.67/0.66 tff(135,plain,
% 0.67/0.66 ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.67/0.66 inference(unit_resolution,[status(thm)],[134, 21])).
% 0.67/0.66 tff(136,plain,
% 0.67/0.66 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.67/0.66 inference(bind,[status(th)],[])).
% 0.67/0.66 tff(137,plain,
% 0.67/0.66 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.67/0.66 inference(quant_intro,[status(thm)],[136])).
% 0.67/0.66 tff(138,plain,
% 0.67/0.66 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.67/0.67 inference(rewrite,[status(thm)],[])).
% 0.67/0.67 tff(139,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.67/0.67 tff(140,plain,
% 0.67/0.67 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.67/0.67 tff(141,plain,(
% 0.67/0.67 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.67/0.67 inference(skolemize,[status(sab)],[140])).
% 0.67/0.67 tff(142,plain,
% 0.67/0.67 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.67/0.67 tff(143,plain,
% 0.67/0.67 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.67/0.67 inference(quant_inst,[status(thm)],[])).
% 0.67/0.67 tff(144,plain,
% 0.67/0.67 (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.67/0.67 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.67/0.67 tff(145,plain,
% 0.67/0.67 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.67/0.67 inference(rewrite,[status(thm)],[])).
% 0.67/0.67 tff(146,plain,
% 0.67/0.67 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.67/0.67 inference(quant_inst,[status(thm)],[])).
% 0.67/0.67 tff(147,plain,
% 0.67/0.67 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.67/0.67 tff(148,plain,
% 0.67/0.67 (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.67/0.67 inference(unit_resolution,[status(thm)],[147, 125, 144])).
% 0.67/0.67 tff(149,assumption,(convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))), introduced(assumption)).
% 0.67/0.67 tff(150,plain,
% 0.67/0.67 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.67/0.67 inference(bind,[status(th)],[])).
% 0.67/0.67 tff(151,plain,
% 0.67/0.67 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.67/0.67 inference(quant_intro,[status(thm)],[150])).
% 0.67/0.67 tff(152,plain,
% 0.67/0.67 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.67/0.67 inference(rewrite,[status(thm)],[])).
% 0.67/0.67 tff(153,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.67/0.67 tff(154,plain,
% 0.67/0.67 (![X: $i] : (~convergent_lines(X, X))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.67/0.67 tff(155,plain,(
% 0.67/0.67 ![X: $i] : (~convergent_lines(X, X))),
% 0.67/0.67 inference(skolemize,[status(sab)],[154])).
% 0.67/0.67 tff(156,plain,
% 0.67/0.67 (![X: $i] : (~convergent_lines(X, X))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.67/0.67 tff(157,plain,
% 0.67/0.67 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.67/0.67 inference(quant_inst,[status(thm)],[])).
% 0.67/0.67 tff(158,plain,
% 0.67/0.67 ($false),
% 0.67/0.67 inference(unit_resolution,[status(thm)],[157, 156, 149])).
% 0.67/0.67 tff(159,plain,(~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.67 tff(160,plain,
% 0.67/0.67 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.67/0.67 inference(rewrite,[status(thm)],[])).
% 0.67/0.67 tff(161,plain,
% 0.67/0.67 ((distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))) <=> (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.67/0.67 inference(rewrite,[status(thm)],[])).
% 0.67/0.67 tff(162,plain,
% 0.67/0.67 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))))),
% 0.67/0.67 inference(monotonicity,[status(thm)],[161])).
% 0.67/0.67 tff(163,plain,
% 0.67/0.67 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.67/0.67 inference(transitivity,[status(thm)],[162, 160])).
% 0.67/0.67 tff(164,plain,
% 0.67/0.67 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.67/0.67 inference(quant_inst,[status(thm)],[])).
% 0.67/0.67 tff(165,plain,
% 0.67/0.67 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.67/0.67 tff(166,plain,
% 0.67/0.67 (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))),
% 0.67/0.67 inference(unit_resolution,[status(thm)],[165, 96, 159, 148])).
% 0.67/0.67 tff(167,plain,
% 0.67/0.67 (((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))),
% 0.67/0.67 inference(tautology,[status(thm)],[])).
% 0.67/0.67 tff(168,plain,
% 0.67/0.67 ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))),
% 0.67/0.67 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.67/0.67 tff(169,assumption,(unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))), introduced(assumption)).
% 0.67/0.67 tff(170,plain,
% 0.67/0.67 (((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.67 inference(tautology,[status(thm)],[])).
% 0.67/0.67 tff(171,plain,
% 0.67/0.67 ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.67 inference(unit_resolution,[status(thm)],[170, 103])).
% 0.67/0.67 tff(172,plain,
% 0.67/0.67 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))),
% 0.67/0.67 inference(rewrite,[status(thm)],[])).
% 0.67/0.67 tff(173,plain,
% 0.67/0.67 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))),
% 0.67/0.67 inference(quant_inst,[status(thm)],[])).
% 0.67/0.67 tff(174,plain,
% 0.67/0.67 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.67/0.67 tff(175,plain,
% 0.67/0.67 (convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)),
% 0.67/0.68 inference(unit_resolution,[status(thm)],[174, 28, 19])).
% 0.67/0.68 tff(176,plain,
% 0.67/0.68 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(177,plain,
% 0.67/0.68 ((unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))) <=> (unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(178,plain,
% 0.67/0.68 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.67/0.68 inference(monotonicity,[status(thm)],[177])).
% 0.67/0.68 tff(179,plain,
% 0.67/0.68 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.68 inference(transitivity,[status(thm)],[178, 176])).
% 0.67/0.68 tff(180,plain,
% 0.67/0.68 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)))),
% 0.67/0.68 inference(quant_inst,[status(thm)],[])).
% 0.67/0.68 tff(181,plain,
% 0.67/0.68 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.67/0.68 tff(182,plain,
% 0.67/0.68 (unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.68 inference(unit_resolution,[status(thm)],[181, 79, 19, 175])).
% 0.67/0.68 tff(183,plain,
% 0.67/0.68 (^[L: $i, M: $i, N: $i] : refl(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))),
% 0.67/0.68 inference(bind,[status(th)],[])).
% 0.67/0.68 tff(184,plain,
% 0.67/0.68 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.67/0.68 inference(quant_intro,[status(thm)],[183])).
% 0.67/0.68 tff(185,plain,
% 0.67/0.68 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) <=> (~((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> (~(~((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))))), rewrite((~(~((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))) <=> ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))))), rewrite(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))))),
% 0.67/0.68 inference(bind,[status(th)],[])).
% 0.67/0.68 tff(186,plain,
% 0.67/0.68 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.67/0.68 inference(quant_intro,[status(thm)],[185])).
% 0.67/0.68 tff(187,plain,
% 0.67/0.68 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(188,plain,
% 0.67/0.68 (^[L: $i, M: $i, N: $i] : rewrite(((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.67/0.68 inference(bind,[status(th)],[])).
% 0.67/0.68 tff(189,plain,
% 0.67/0.68 (![L: $i, M: $i, N: $i] : ((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.67/0.68 inference(quant_intro,[status(thm)],[188])).
% 0.67/0.68 tff(190,axiom,(![L: $i, M: $i, N: $i] : ((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax','cotno1')).
% 0.67/0.68 tff(191,plain,
% 0.67/0.68 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.67/0.68 tff(192,plain,
% 0.67/0.68 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.67/0.68 tff(193,plain,(
% 0.67/0.68 ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.67/0.68 inference(skolemize,[status(sab)],[192])).
% 0.67/0.68 tff(194,plain,
% 0.67/0.68 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.67/0.68 tff(195,plain,
% 0.67/0.68 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[194, 184])).
% 0.67/0.68 tff(196,plain,
% 0.67/0.68 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(197,plain,
% 0.67/0.68 (((~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))))) <=> ((~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(198,plain,
% 0.67/0.69 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))))))),
% 0.67/0.69 inference(monotonicity,[status(thm)],[197])).
% 0.67/0.69 tff(199,plain,
% 0.67/0.69 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))))),
% 0.67/0.69 inference(transitivity,[status(thm)],[198, 196])).
% 0.67/0.69 tff(200,plain,
% 0.67/0.69 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))))),
% 0.67/0.69 inference(quant_inst,[status(thm)],[])).
% 0.67/0.69 tff(201,plain,
% 0.67/0.69 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.67/0.69 tff(202,plain,
% 0.67/0.69 (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[201, 195, 182, 171])).
% 0.67/0.69 tff(203,plain,
% 0.67/0.69 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)))),
% 0.67/0.69 inference(quant_inst,[status(thm)],[])).
% 0.67/0.69 tff(204,plain,
% 0.67/0.69 (~apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1))),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[203, 8])).
% 0.67/0.69 tff(205,plain,
% 0.67/0.69 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(206,plain,
% 0.67/0.69 ((apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(207,plain,
% 0.67/0.69 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.69 inference(monotonicity,[status(thm)],[206])).
% 0.67/0.69 tff(208,plain,
% 0.67/0.69 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.69 inference(transitivity,[status(thm)],[207, 205])).
% 0.67/0.69 tff(209,plain,
% 0.67/0.69 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.69 inference(quant_inst,[status(thm)],[])).
% 0.67/0.69 tff(210,plain,
% 0.67/0.69 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.67/0.69 tff(211,plain,
% 0.67/0.69 (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[210, 58, 48, 204])).
% 0.67/0.69 tff(212,plain,
% 0.67/0.69 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.67/0.69 inference(bind,[status(th)],[])).
% 0.67/0.69 tff(213,plain,
% 0.67/0.69 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.67/0.69 inference(quant_intro,[status(thm)],[212])).
% 0.67/0.69 tff(214,plain,
% 0.67/0.69 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(215,plain,
% 0.67/0.69 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.67/0.70 inference(bind,[status(th)],[])).
% 0.67/0.70 tff(216,plain,
% 0.67/0.70 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.67/0.70 inference(quant_intro,[status(thm)],[215])).
% 0.67/0.70 tff(217,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.67/0.70 tff(218,plain,
% 0.67/0.70 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.67/0.70 tff(219,plain,
% 0.67/0.70 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.67/0.70 tff(220,plain,(
% 0.67/0.70 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.67/0.70 inference(skolemize,[status(sab)],[219])).
% 0.67/0.70 tff(221,plain,
% 0.67/0.70 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.67/0.70 tff(222,plain,
% 0.67/0.70 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(223,plain,
% 0.67/0.70 ((distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))) <=> (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(224,plain,
% 0.67/0.70 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))))),
% 0.67/0.70 inference(monotonicity,[status(thm)],[223])).
% 0.67/0.70 tff(225,plain,
% 0.67/0.70 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.67/0.70 inference(transitivity,[status(thm)],[224, 222])).
% 0.67/0.70 tff(226,plain,
% 0.67/0.70 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.67/0.70 inference(quant_inst,[status(thm)],[])).
% 0.67/0.70 tff(227,plain,
% 0.67/0.70 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.67/0.70 tff(228,plain,
% 0.67/0.70 (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[227, 221, 211, 66])).
% 0.67/0.70 tff(229,plain,
% 0.67/0.70 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(230,plain,
% 0.67/0.70 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))))),
% 0.67/0.70 inference(quant_inst,[status(thm)],[])).
% 0.67/0.70 tff(231,plain,
% 0.67/0.70 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)))),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.67/0.70 tff(232,plain,
% 0.67/0.70 (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1))),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[231, 96, 228, 202])).
% 0.67/0.70 tff(233,assumption,(~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))), introduced(assumption)).
% 0.67/0.70 tff(234,plain,
% 0.67/0.70 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.67/0.70 inference(quant_inst,[status(thm)],[])).
% 0.67/0.70 tff(235,plain,
% 0.67/0.70 (~apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[234, 8])).
% 0.67/0.70 tff(236,plain,
% 0.67/0.70 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(237,plain,
% 0.67/0.70 ((apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(238,plain,
% 0.67/0.70 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))))),
% 0.73/0.71 inference(monotonicity,[status(thm)],[237])).
% 0.73/0.71 tff(239,plain,
% 0.73/0.71 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.73/0.71 inference(transitivity,[status(thm)],[238, 236])).
% 0.73/0.71 tff(240,plain,
% 0.73/0.71 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.73/0.71 inference(quant_inst,[status(thm)],[])).
% 0.73/0.71 tff(241,plain,
% 0.73/0.71 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.73/0.71 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.73/0.71 tff(242,plain,
% 0.73/0.71 (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.73/0.71 inference(unit_resolution,[status(thm)],[241, 58, 21, 235])).
% 0.73/0.71 tff(243,plain,
% 0.73/0.71 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.73/0.71 inference(rewrite,[status(thm)],[])).
% 0.73/0.71 tff(244,plain,
% 0.73/0.71 ((distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))) <=> (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.73/0.71 inference(rewrite,[status(thm)],[])).
% 0.73/0.71 tff(245,plain,
% 0.73/0.71 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))))),
% 0.73/0.71 inference(monotonicity,[status(thm)],[244])).
% 0.73/0.71 tff(246,plain,
% 0.73/0.71 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.73/0.71 inference(transitivity,[status(thm)],[245, 243])).
% 0.73/0.71 tff(247,plain,
% 0.73/0.71 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.73/0.71 inference(quant_inst,[status(thm)],[])).
% 0.73/0.71 tff(248,plain,
% 0.73/0.71 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))),
% 0.73/0.71 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.73/0.71 tff(249,plain,
% 0.73/0.71 (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))),
% 0.73/0.71 inference(unit_resolution,[status(thm)],[248, 221, 242, 148])).
% 0.73/0.71 tff(250,plain,
% 0.73/0.71 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.73/0.71 inference(bind,[status(th)],[])).
% 0.73/0.71 tff(251,plain,
% 0.73/0.71 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.73/0.71 inference(quant_intro,[status(thm)],[250])).
% 0.73/0.71 tff(252,plain,
% 0.73/0.71 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.73/0.71 inference(rewrite,[status(thm)],[])).
% 0.73/0.71 tff(253,plain,
% 0.73/0.71 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.73/0.71 inference(bind,[status(th)],[])).
% 0.73/0.71 tff(254,plain,
% 0.73/0.71 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.73/0.71 inference(quant_intro,[status(thm)],[253])).
% 0.73/0.71 tff(255,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.73/0.71 tff(256,plain,
% 0.73/0.71 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.73/0.71 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.73/0.71 tff(257,plain,
% 0.73/0.71 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.73/0.71 inference(modus_ponens,[status(thm)],[256, 252])).
% 0.73/0.71 tff(258,plain,(
% 0.73/0.71 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.73/0.71 inference(skolemize,[status(sab)],[257])).
% 0.73/0.71 tff(259,plain,
% 0.73/0.71 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.73/0.71 inference(modus_ponens,[status(thm)],[258, 251])).
% 0.73/0.71 tff(260,plain,
% 0.73/0.71 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.73/0.71 inference(rewrite,[status(thm)],[])).
% 0.73/0.71 tff(261,plain,
% 0.73/0.71 ((convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.73/0.71 inference(rewrite,[status(thm)],[])).
% 0.73/0.71 tff(262,plain,
% 0.73/0.71 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.73/0.71 inference(monotonicity,[status(thm)],[261])).
% 0.73/0.71 tff(263,plain,
% 0.73/0.71 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.73/0.72 inference(transitivity,[status(thm)],[262, 260])).
% 0.73/0.72 tff(264,plain,
% 0.73/0.72 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.73/0.72 inference(quant_inst,[status(thm)],[])).
% 0.73/0.72 tff(265,plain,
% 0.73/0.72 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.73/0.72 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.73/0.72 tff(266,plain,
% 0.73/0.72 (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[265, 259, 32])).
% 0.73/0.72 tff(267,plain,
% 0.73/0.72 (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[266, 159])).
% 0.73/0.72 tff(268,plain,
% 0.73/0.72 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(269,plain,
% 0.73/0.72 ((distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(270,plain,
% 0.73/0.72 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.73/0.72 inference(monotonicity,[status(thm)],[269])).
% 0.73/0.72 tff(271,plain,
% 0.73/0.72 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))),
% 0.73/0.72 inference(transitivity,[status(thm)],[270, 268])).
% 0.73/0.72 tff(272,plain,
% 0.73/0.72 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.73/0.72 inference(quant_inst,[status(thm)],[])).
% 0.73/0.72 tff(273,plain,
% 0.73/0.72 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))),
% 0.73/0.72 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.73/0.72 tff(274,plain,
% 0.73/0.72 ($false),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[273, 96, 267, 249, 233])).
% 0.73/0.72 tff(275,plain,(convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.72 tff(276,assumption,(~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))), introduced(assumption)).
% 0.73/0.72 tff(277,plain,
% 0.73/0.72 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(278,plain,
% 0.73/0.72 ((distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))) <=> (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(279,plain,
% 0.73/0.72 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))))),
% 0.73/0.72 inference(monotonicity,[status(thm)],[278])).
% 0.73/0.72 tff(280,plain,
% 0.73/0.72 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.73/0.72 inference(transitivity,[status(thm)],[279, 277])).
% 0.73/0.72 tff(281,plain,
% 0.73/0.72 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.73/0.72 inference(quant_inst,[status(thm)],[])).
% 0.73/0.72 tff(282,plain,
% 0.73/0.72 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))),
% 0.73/0.72 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.73/0.72 tff(283,plain,
% 0.73/0.72 ($false),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[282, 96, 103, 276, 275])).
% 0.73/0.72 tff(284,plain,(distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.73 tff(285,plain,
% 0.73/0.73 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.73/0.73 inference(rewrite,[status(thm)],[])).
% 0.73/0.73 tff(286,plain,
% 0.73/0.73 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.73/0.73 inference(quant_inst,[status(thm)],[])).
% 0.73/0.73 tff(287,plain,
% 0.73/0.73 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.73/0.73 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.73/0.73 tff(288,plain,
% 0.73/0.73 (convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.73/0.73 inference(unit_resolution,[status(thm)],[287, 125, 284])).
% 0.73/0.73 tff(289,plain,
% 0.73/0.73 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.73 inference(rewrite,[status(thm)],[])).
% 0.73/0.73 tff(290,plain,
% 0.73/0.73 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.73 inference(quant_inst,[status(thm)],[])).
% 0.73/0.73 tff(291,plain,
% 0.73/0.73 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.73/0.73 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.73/0.73 tff(292,plain,
% 0.73/0.73 (convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.73/0.73 inference(unit_resolution,[status(thm)],[291, 259, 288])).
% 0.73/0.73 tff(293,plain,
% 0.73/0.73 (convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.73/0.73 inference(unit_resolution,[status(thm)],[292, 232])).
% 0.73/0.73 tff(294,plain,
% 0.73/0.73 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) | (~unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) | (~unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.73 inference(rewrite,[status(thm)],[])).
% 0.73/0.73 tff(295,plain,
% 0.73/0.73 (((~unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))))) <=> ((~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) | (~unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.73 inference(rewrite,[status(thm)],[])).
% 0.73/0.73 tff(296,plain,
% 0.73/0.73 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) | (~unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))))),
% 0.73/0.73 inference(monotonicity,[status(thm)],[295])).
% 0.73/0.73 tff(297,plain,
% 0.73/0.73 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) | (~unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.73 inference(transitivity,[status(thm)],[296, 294])).
% 0.73/0.73 tff(298,plain,
% 0.73/0.73 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))))),
% 0.73/0.74 inference(quant_inst,[status(thm)],[])).
% 0.73/0.74 tff(299,plain,
% 0.73/0.74 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) | (~unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.73/0.74 tff(300,plain,
% 0.73/0.74 ($false),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[299, 195, 293, 169, 168, 135])).
% 0.73/0.74 tff(301,plain,(~unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.74 tff(302,plain,
% 0.73/0.74 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.73/0.74 inference(bind,[status(th)],[])).
% 0.73/0.74 tff(303,plain,
% 0.73/0.74 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.73/0.74 inference(quant_intro,[status(thm)],[302])).
% 0.73/0.74 tff(304,plain,
% 0.73/0.74 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(305,plain,
% 0.73/0.74 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.73/0.74 inference(bind,[status(th)],[])).
% 0.73/0.74 tff(306,plain,
% 0.73/0.74 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.73/0.74 inference(quant_intro,[status(thm)],[305])).
% 0.73/0.74 tff(307,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.73/0.74 tff(308,plain,
% 0.73/0.74 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.73/0.74 tff(309,plain,
% 0.73/0.74 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[308, 304])).
% 0.73/0.74 tff(310,plain,(
% 0.73/0.74 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.73/0.74 inference(skolemize,[status(sab)],[309])).
% 0.73/0.74 tff(311,plain,
% 0.73/0.74 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[310, 303])).
% 0.73/0.74 tff(312,plain,
% 0.73/0.74 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(313,plain,
% 0.73/0.74 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.73/0.74 inference(quant_inst,[status(thm)],[])).
% 0.73/0.74 tff(314,plain,
% 0.73/0.74 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.73/0.74 tff(315,plain,
% 0.73/0.74 (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[314, 311, 288])).
% 0.73/0.74 tff(316,plain,
% 0.73/0.74 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.73/0.74 inference(bind,[status(th)],[])).
% 0.73/0.74 tff(317,plain,
% 0.73/0.74 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.73/0.74 inference(quant_intro,[status(thm)],[316])).
% 0.73/0.74 tff(318,plain,
% 0.73/0.74 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(319,plain,
% 0.73/0.74 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.73/0.74 inference(bind,[status(th)],[])).
% 0.73/0.74 tff(320,plain,
% 0.73/0.74 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.73/0.74 inference(quant_intro,[status(thm)],[319])).
% 0.73/0.74 tff(321,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.73/0.74 tff(322,plain,
% 0.73/0.74 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.73/0.74 tff(323,plain,
% 0.73/0.74 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[322, 318])).
% 0.73/0.74 tff(324,plain,(
% 0.73/0.74 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.73/0.74 inference(skolemize,[status(sab)],[323])).
% 0.73/0.74 tff(325,plain,
% 0.73/0.74 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[324, 317])).
% 0.73/0.74 tff(326,plain,
% 0.73/0.74 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(327,plain,
% 0.73/0.74 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.73/0.74 inference(quant_inst,[status(thm)],[])).
% 0.73/0.74 tff(328,plain,
% 0.73/0.74 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.73/0.74 tff(329,plain,
% 0.73/0.74 (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[328, 325, 249, 315])).
% 0.73/0.74 tff(330,plain,
% 0.73/0.74 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(331,plain,
% 0.73/0.74 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.74 inference(quant_inst,[status(thm)],[])).
% 0.73/0.74 tff(332,plain,
% 0.73/0.74 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.73/0.74 tff(333,plain,
% 0.73/0.74 (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[332, 42, 288])).
% 0.73/0.74 tff(334,plain,
% 0.73/0.74 (^[X: $i, Y: $i] : refl((~apart_point_and_line(X, parallel_through_point(Y, X))) <=> (~apart_point_and_line(X, parallel_through_point(Y, X))))),
% 0.73/0.74 inference(bind,[status(th)],[])).
% 0.73/0.74 tff(335,plain,
% 0.73/0.74 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[334])).
% 0.73/0.75 tff(336,plain,
% 0.73/0.75 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(337,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.73/0.75 tff(338,plain,
% 0.73/0.75 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.73/0.75 tff(339,plain,(
% 0.73/0.75 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.73/0.75 inference(skolemize,[status(sab)],[338])).
% 0.73/0.75 tff(340,plain,
% 0.73/0.75 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[339, 335])).
% 0.73/0.75 tff(341,plain,
% 0.73/0.75 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(342,plain,
% 0.73/0.75 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[341, 340])).
% 0.73/0.75 tff(343,plain,
% 0.73/0.75 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(344,plain,
% 0.73/0.75 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(345,plain,
% 0.73/0.75 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.73/0.75 tff(346,plain,
% 0.73/0.75 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[345, 311, 175])).
% 0.73/0.75 tff(347,plain,
% 0.73/0.75 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0)))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(348,plain,
% 0.73/0.75 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0)))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(349,plain,
% 0.73/0.75 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.73/0.75 tff(350,plain,
% 0.73/0.75 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0)),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[349, 42, 175])).
% 0.73/0.75 tff(351,plain,
% 0.73/0.75 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(352,plain,
% 0.73/0.75 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1))))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(353,plain,
% 0.73/0.75 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.73/0.75 tff(354,plain,
% 0.73/0.75 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[353, 311, 107])).
% 0.73/0.75 tff(355,plain,
% 0.73/0.75 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(356,plain,
% 0.73/0.75 ((distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))) <=> (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(357,plain,
% 0.73/0.75 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))))),
% 0.73/0.75 inference(monotonicity,[status(thm)],[356])).
% 0.73/0.75 tff(358,plain,
% 0.73/0.75 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.75 inference(transitivity,[status(thm)],[357, 355])).
% 0.73/0.75 tff(359,plain,
% 0.73/0.75 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(360,plain,
% 0.73/0.75 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.73/0.75 tff(361,plain,
% 0.73/0.75 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[360, 325, 354, 66])).
% 0.73/0.76 tff(362,plain,
% 0.73/0.76 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0)))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(363,plain,
% 0.73/0.76 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0)))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(364,plain,
% 0.73/0.76 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.73/0.76 tff(365,plain,
% 0.73/0.76 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[364, 42, 107])).
% 0.73/0.76 tff(366,plain,
% 0.73/0.76 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(367,plain,
% 0.73/0.76 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[366])).
% 0.73/0.76 tff(368,plain,
% 0.73/0.76 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))))), rewrite((~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(369,plain,
% 0.73/0.76 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[368])).
% 0.73/0.76 tff(370,plain,
% 0.73/0.76 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(371,plain,
% 0.73/0.76 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(372,plain,
% 0.73/0.76 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[371])).
% 0.73/0.76 tff(373,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.73/0.76 tff(374,plain,
% 0.73/0.76 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.73/0.76 tff(375,plain,
% 0.73/0.76 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[374, 370])).
% 0.73/0.76 tff(376,plain,(
% 0.73/0.76 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.73/0.76 inference(skolemize,[status(sab)],[375])).
% 0.73/0.76 tff(377,plain,
% 0.73/0.76 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[376, 369])).
% 0.73/0.76 tff(378,plain,
% 0.73/0.76 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[377, 367])).
% 0.73/0.76 tff(379,plain,
% 0.73/0.76 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(380,plain,
% 0.73/0.76 ((apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))) <=> (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(381,plain,
% 0.73/0.76 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.79/0.76 inference(monotonicity,[status(thm)],[380])).
% 0.79/0.76 tff(382,plain,
% 0.79/0.76 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.79/0.77 inference(transitivity,[status(thm)],[381, 379])).
% 0.79/0.77 tff(383,plain,
% 0.79/0.77 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.79/0.77 inference(quant_inst,[status(thm)],[])).
% 0.79/0.77 tff(384,plain,
% 0.79/0.77 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.79/0.77 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.79/0.77 tff(385,plain,
% 0.79/0.77 ((~distinct_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.79/0.77 inference(unit_resolution,[status(thm)],[384, 378, 365, 361, 350, 346])).
% 0.79/0.77 tff(386,plain,
% 0.79/0.77 (~distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0))),
% 0.79/0.77 inference(unit_resolution,[status(thm)],[385, 115])).
% 0.79/0.77 tff(387,plain,
% 0.79/0.77 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))))),
% 0.79/0.77 inference(bind,[status(th)],[])).
% 0.79/0.77 tff(388,plain,
% 0.79/0.77 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.79/0.77 inference(quant_intro,[status(thm)],[387])).
% 0.79/0.77 tff(389,plain,
% 0.79/0.77 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.79/0.77 inference(rewrite,[status(thm)],[])).
% 0.79/0.77 tff(390,plain,
% 0.79/0.77 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | apart_point_and_line(Z, Y)) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))))), rewrite((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))))),
% 0.79/0.77 inference(bind,[status(th)],[])).
% 0.79/0.77 tff(391,plain,
% 0.79/0.77 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.79/0.77 inference(quant_intro,[status(thm)],[390])).
% 0.79/0.77 tff(392,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.79/0.77 tff(393,plain,
% 0.79/0.77 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.79/0.77 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.79/0.77 tff(394,plain,
% 0.79/0.77 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.79/0.77 inference(modus_ponens,[status(thm)],[393, 389])).
% 0.79/0.77 tff(395,plain,(
% 0.79/0.77 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.79/0.77 inference(skolemize,[status(sab)],[394])).
% 0.79/0.77 tff(396,plain,
% 0.79/0.77 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.79/0.77 inference(modus_ponens,[status(thm)],[395, 388])).
% 0.79/0.77 tff(397,plain,
% 0.79/0.77 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.79/0.77 inference(rewrite,[status(thm)],[])).
% 0.79/0.77 tff(398,plain,
% 0.79/0.77 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.79/0.77 inference(quant_inst,[status(thm)],[])).
% 0.79/0.77 tff(399,plain,
% 0.79/0.77 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), intersection_point(orthogonal_through_point(L!0, A!1), L!0)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.79/0.77 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.79/0.77 tff(400,plain,
% 0.79/0.77 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.79/0.77 inference(unit_resolution,[status(thm)],[399, 396, 386, 342])).
% 0.79/0.77 tff(401,plain,
% 0.79/0.77 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.79/0.77 inference(quant_inst,[status(thm)],[])).
% 0.79/0.77 tff(402,plain,
% 0.79/0.77 (~convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.79/0.77 inference(unit_resolution,[status(thm)],[401, 142])).
% 0.79/0.77 tff(403,plain,
% 0.79/0.77 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.79/0.77 inference(rewrite,[status(thm)],[])).
% 0.79/0.77 tff(404,plain,
% 0.79/0.77 ((convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))) <=> (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.79/0.78 inference(rewrite,[status(thm)],[])).
% 0.79/0.78 tff(405,plain,
% 0.79/0.78 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))))),
% 0.79/0.78 inference(monotonicity,[status(thm)],[404])).
% 0.79/0.78 tff(406,plain,
% 0.79/0.78 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.79/0.78 inference(transitivity,[status(thm)],[405, 403])).
% 0.79/0.78 tff(407,plain,
% 0.79/0.78 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.79/0.78 inference(quant_inst,[status(thm)],[])).
% 0.79/0.78 tff(408,plain,
% 0.79/0.78 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.79/0.78 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.79/0.78 tff(409,plain,
% 0.79/0.78 (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.79/0.78 inference(unit_resolution,[status(thm)],[408, 259, 159, 402])).
% 0.79/0.78 tff(410,plain,
% 0.79/0.78 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.79/0.78 inference(rewrite,[status(thm)],[])).
% 0.79/0.78 tff(411,plain,
% 0.79/0.78 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.79/0.78 inference(quant_inst,[status(thm)],[])).
% 0.79/0.78 tff(412,plain,
% 0.79/0.78 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.79/0.78 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.79/0.78 tff(413,plain,
% 0.79/0.78 (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.79/0.78 inference(unit_resolution,[status(thm)],[412, 125, 409])).
% 0.79/0.78 tff(414,plain,
% 0.79/0.78 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.79/0.78 inference(rewrite,[status(thm)],[])).
% 0.79/0.78 tff(415,plain,
% 0.79/0.78 ((distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.79/0.78 inference(rewrite,[status(thm)],[])).
% 0.79/0.78 tff(416,plain,
% 0.79/0.78 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.79/0.78 inference(monotonicity,[status(thm)],[415])).
% 0.79/0.78 tff(417,plain,
% 0.79/0.78 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.79/0.78 inference(transitivity,[status(thm)],[416, 414])).
% 0.79/0.78 tff(418,plain,
% 0.79/0.78 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.79/0.79 inference(quant_inst,[status(thm)],[])).
% 0.79/0.79 tff(419,plain,
% 0.79/0.79 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), intersection_point(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.79/0.79 tff(420,plain,
% 0.79/0.79 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.79/0.79 inference(unit_resolution,[status(thm)],[419, 325, 413, 400])).
% 0.79/0.79 tff(421,plain,
% 0.79/0.79 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(422,plain,
% 0.79/0.79 ((distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))) <=> (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(423,plain,
% 0.79/0.79 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))))),
% 0.79/0.79 inference(monotonicity,[status(thm)],[422])).
% 0.79/0.79 tff(424,plain,
% 0.79/0.79 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.79/0.79 inference(transitivity,[status(thm)],[423, 421])).
% 0.79/0.79 tff(425,plain,
% 0.79/0.79 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.79/0.79 inference(quant_inst,[status(thm)],[])).
% 0.79/0.79 tff(426,plain,
% 0.79/0.79 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.79/0.79 tff(427,plain,
% 0.79/0.79 (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.79/0.79 inference(unit_resolution,[status(thm)],[426, 221, 148, 284])).
% 0.79/0.79 tff(428,plain,
% 0.79/0.79 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(429,plain,
% 0.79/0.79 ((apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)))) <=> (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(430,plain,
% 0.79/0.80 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)))))),
% 0.79/0.80 inference(monotonicity,[status(thm)],[429])).
% 0.79/0.80 tff(431,plain,
% 0.79/0.80 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))))),
% 0.79/0.81 inference(transitivity,[status(thm)],[430, 428])).
% 0.79/0.81 tff(432,plain,
% 0.79/0.81 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(433,plain,
% 0.79/0.81 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | (~distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[432, 431])).
% 0.79/0.81 tff(434,plain,
% 0.79/0.81 (~distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0))),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[433, 378, 346, 427, 420, 333, 329])).
% 0.79/0.81 tff(435,plain,
% 0.79/0.81 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(436,plain,
% 0.79/0.81 ((distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0))) <=> (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(437,plain,
% 0.79/0.81 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0))))),
% 0.79/0.81 inference(monotonicity,[status(thm)],[436])).
% 0.79/0.81 tff(438,plain,
% 0.79/0.81 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0)))),
% 0.79/0.81 inference(transitivity,[status(thm)],[437, 435])).
% 0.79/0.81 tff(439,plain,
% 0.79/0.81 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0)))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(440,plain,
% 0.79/0.81 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0), L!0) | distinct_points(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), intersection_point(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), L!0)) | (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.79/0.82 tff(441,plain,
% 0.79/0.82 (~apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[440, 396, 350, 434])).
% 0.79/0.82 tff(442,assumption,(~distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))), introduced(assumption)).
% 0.79/0.82 tff(443,assumption,(~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)), introduced(assumption)).
% 0.79/0.82 tff(444,plain,
% 0.79/0.82 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(445,plain,
% 0.79/0.82 ((unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0))) <=> (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(446,plain,
% 0.79/0.82 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0))))),
% 0.79/0.82 inference(monotonicity,[status(thm)],[445])).
% 0.79/0.82 tff(447,plain,
% 0.79/0.82 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0)))),
% 0.79/0.82 inference(transitivity,[status(thm)],[446, 444])).
% 0.79/0.82 tff(448,plain,
% 0.79/0.82 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(449,plain,
% 0.79/0.82 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.79/0.82 tff(450,plain,
% 0.79/0.82 (~convergent_lines(L!0, L!0)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[449, 79, 48])).
% 0.79/0.82 tff(451,plain,
% 0.79/0.82 (^[X: $i, Y: $i] : refl((parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(452,plain,
% 0.79/0.82 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[451])).
% 0.79/0.82 tff(453,plain,
% 0.79/0.82 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(454,axiom,(![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a3')).
% 0.79/0.82 tff(455,plain,
% 0.79/0.82 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.79/0.82 tff(456,plain,(
% 0.79/0.82 ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.79/0.82 inference(skolemize,[status(sab)],[455])).
% 0.79/0.82 tff(457,plain,
% 0.79/0.82 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[456, 452])).
% 0.79/0.82 tff(458,plain,
% 0.79/0.82 ((~![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))) | (parallel_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) <=> (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(459,plain,
% 0.79/0.82 (parallel_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) <=> (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[458, 457])).
% 0.79/0.82 tff(460,plain,
% 0.79/0.82 ((~![A: $i, L: $i] : parallel_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A))) <=> (~![A: $i, L: $i] : parallel_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(461,axiom,(~![A: $i, L: $i] : parallel_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.79/0.82 tff(462,plain,
% 0.79/0.82 (~![A: $i, L: $i] : parallel_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.79/0.82 tff(463,plain,
% 0.79/0.82 (~![A: $i, L: $i] : parallel_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[462, 460])).
% 0.79/0.82 tff(464,plain,
% 0.79/0.82 (~![A: $i, L: $i] : parallel_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[463, 460])).
% 0.79/0.82 tff(465,plain,
% 0.79/0.82 (~![A: $i, L: $i] : parallel_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[464, 460])).
% 0.79/0.82 tff(466,plain,
% 0.79/0.82 (~![A: $i, L: $i] : parallel_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[465, 460])).
% 0.79/0.82 tff(467,plain,
% 0.79/0.82 (~![A: $i, L: $i] : parallel_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[466, 460])).
% 0.79/0.82 tff(468,plain,
% 0.79/0.82 (~![A: $i, L: $i] : parallel_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[467, 460])).
% 0.79/0.82 tff(469,plain,(
% 0.79/0.82 ~parallel_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.79/0.82 inference(skolemize,[status(sab)],[468])).
% 0.79/0.82 tff(470,plain,
% 0.79/0.82 ((~(parallel_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) <=> (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | parallel_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.79/0.82 inference(tautology,[status(thm)],[])).
% 0.79/0.82 tff(471,plain,
% 0.79/0.82 ((~(parallel_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) <=> (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[470, 469])).
% 0.79/0.82 tff(472,plain,
% 0.79/0.82 (convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[471, 459])).
% 0.79/0.82 tff(473,plain,
% 0.79/0.82 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(474,plain,
% 0.79/0.82 ((distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(475,plain,
% 0.79/0.82 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.79/0.82 inference(monotonicity,[status(thm)],[474])).
% 0.79/0.82 tff(476,plain,
% 0.79/0.82 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.79/0.82 inference(transitivity,[status(thm)],[475, 473])).
% 0.79/0.82 tff(477,plain,
% 0.79/0.82 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(478,plain,
% 0.79/0.82 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.79/0.82 tff(479,plain,
% 0.79/0.82 ($false),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[478, 96, 472, 450, 443])).
% 0.79/0.82 tff(480,plain,(distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.82 tff(481,plain,
% 0.79/0.82 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(482,plain,
% 0.79/0.82 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(483,plain,
% 0.79/0.82 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.79/0.82 tff(484,plain,
% 0.79/0.82 (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[483, 125, 480])).
% 0.79/0.82 tff(485,plain,
% 0.79/0.82 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(486,plain,
% 0.79/0.82 ((distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))) <=> (distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(487,plain,
% 0.79/0.82 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.79/0.83 inference(monotonicity,[status(thm)],[486])).
% 0.79/0.83 tff(488,plain,
% 0.79/0.83 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))),
% 0.79/0.83 inference(transitivity,[status(thm)],[487, 485])).
% 0.79/0.83 tff(489,plain,
% 0.79/0.83 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(490,plain,
% 0.79/0.83 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.79/0.83 tff(491,plain,
% 0.79/0.83 ($false),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[490, 96, 484, 442, 166])).
% 0.79/0.83 tff(492,plain,(distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.83 tff(493,plain,
% 0.79/0.83 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(494,plain,
% 0.79/0.83 ((apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0) | (~distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)))) <=> (unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(495,plain,
% 0.79/0.83 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0) | (~distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.79/0.83 inference(monotonicity,[status(thm)],[494])).
% 0.79/0.83 tff(496,plain,
% 0.79/0.83 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0) | (~distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.79/0.83 inference(transitivity,[status(thm)],[495, 493])).
% 0.79/0.83 tff(497,plain,
% 0.79/0.83 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0) | (~distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(498,plain,
% 0.79/0.83 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1))) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.79/0.83 tff(499,plain,
% 0.79/0.83 (unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))), L!0) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[498, 58, 492, 315])).
% 0.79/0.83 tff(500,plain,
% 0.79/0.83 (unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(parallel_through_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[499, 441])).
% 0.79/0.83 tff(501,plain,
% 0.79/0.83 (unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[500, 301])).
% 0.79/0.83 tff(502,plain,
% 0.79/0.83 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(503,plain,
% 0.79/0.84 (((~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))))) <=> ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(504,plain,
% 0.79/0.84 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))))))),
% 0.79/0.84 inference(monotonicity,[status(thm)],[503])).
% 0.79/0.84 tff(505,plain,
% 0.79/0.84 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.79/0.84 inference(transitivity,[status(thm)],[504, 502])).
% 0.79/0.84 tff(506,plain,
% 0.79/0.84 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(507,plain,
% 0.79/0.84 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.79/0.84 tff(508,plain,
% 0.79/0.84 (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[507, 195, 501, 133, 131])).
% 0.79/0.84 tff(509,plain,
% 0.79/0.84 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(510,plain,
% 0.79/0.84 ((distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))) <=> (convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(511,plain,
% 0.79/0.85 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))))),
% 0.79/0.85 inference(monotonicity,[status(thm)],[510])).
% 0.79/0.85 tff(512,plain,
% 0.79/0.85 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.79/0.85 inference(transitivity,[status(thm)],[511, 509])).
% 0.79/0.85 tff(513,plain,
% 0.79/0.85 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))))),
% 0.79/0.85 inference(quant_inst,[status(thm)],[])).
% 0.79/0.85 tff(514,plain,
% 0.79/0.85 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(L!0, orthogonal_through_point(L!0, intersection_point(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.79/0.85 tff(515,plain,
% 0.79/0.85 ($false),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[514, 96, 508, 66, 129])).
% 0.79/0.85 % SZS output end Proof
%------------------------------------------------------------------------------