%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n008.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 20:35:50 EDT 2022

% Result   : Theorem 0.20s 0.43s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 31 07:05:55 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  % SZS output start Proof
% 0.20/0.43  tff(convergent_lines_type, type, (
% 0.20/0.43     convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.43  tff(orthogonal_through_point_type, type, (
% 0.20/0.43     orthogonal_through_point: ( $i * $i ) > $i)).
% 0.20/0.43  tff(tptp_fun_A_1_type, type, (
% 0.20/0.43     tptp_fun_A_1: $i)).
% 0.20/0.43  tff(tptp_fun_L_0_type, type, (
% 0.20/0.43     tptp_fun_L_0: $i)).
% 0.20/0.43  tff(distinct_lines_type, type, (
% 0.20/0.43     distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.43  tff(unorthogonal_lines_type, type, (
% 0.20/0.43     unorthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.43  tff(apart_point_and_line_type, type, (
% 0.20/0.43     apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.43  tff(intersection_point_type, type, (
% 0.20/0.43     intersection_point: ( $i * $i ) > $i)).
% 0.20/0.43  tff(1,assumption,(convergent_lines(L!0, L!0)), introduced(assumption)).
% 0.20/0.43  tff(2,plain,
% 0.20/0.43      (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(3,plain,
% 0.20/0.43      (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[2])).
% 0.20/0.43  tff(4,plain,
% 0.20/0.43      (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.20/0.43  tff(6,plain,
% 0.20/0.43      (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.43  tff(7,plain,(
% 0.20/0.43      ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43      inference(skolemize,[status(sab)],[6])).
% 0.20/0.43  tff(8,plain,
% 0.20/0.43      (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.43  tff(9,plain,
% 0.20/0.43      ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(L!0, L!0))),
% 0.20/0.43      inference(quant_inst,[status(thm)],[])).
% 0.20/0.43  tff(10,plain,
% 0.20/0.43      ($false),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.43  tff(11,plain,(~convergent_lines(L!0, L!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43  tff(12,plain,
% 0.20/0.43      (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(13,plain,
% 0.20/0.43      (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[12])).
% 0.20/0.43  tff(14,plain,
% 0.20/0.43      (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(15,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.20/0.43  tff(16,plain,
% 0.20/0.43      (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.43  tff(17,plain,(
% 0.20/0.43      ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.43      inference(skolemize,[status(sab)],[16])).
% 0.20/0.43  tff(18,plain,
% 0.20/0.43      (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.43  tff(19,plain,
% 0.20/0.43      ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.20/0.43      inference(quant_inst,[status(thm)],[])).
% 0.20/0.43  tff(20,plain,
% 0.20/0.43      (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.43  tff(21,plain,
% 0.20/0.43      (((~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)),
% 0.20/0.43      inference(tautology,[status(thm)],[])).
% 0.20/0.43  tff(22,plain,
% 0.20/0.43      ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.43  tff(23,assumption,(~((~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))))), introduced(assumption)).
% 0.20/0.43  tff(24,plain,
% 0.20/0.43      (((~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)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.43      inference(tautology,[status(thm)],[])).
% 0.20/0.43  tff(25,plain,
% 0.20/0.43      (unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.43  tff(26,plain,
% 0.20/0.43      (((~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))),
% 0.20/0.43      inference(tautology,[status(thm)],[])).
% 0.20/0.43  tff(27,plain,
% 0.20/0.43      (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[26, 23])).
% 0.20/0.43  tff(28,plain,
% 0.20/0.43      (^[L: $i, M: $i, N: $i] : refl(((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(29,plain,
% 0.20/0.43      (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[28])).
% 0.20/0.43  tff(30,plain,
% 0.20/0.43      (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((convergent_lines(M, N) & unorthogonal_lines(M, N)) <=> (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N))))), rewrite((convergent_lines(L, N) & unorthogonal_lines(L, N)) <=> (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))), trans(monotonicity(rewrite((convergent_lines(L, M) & unorthogonal_lines(L, M)) <=> (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> (~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), rewrite((~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), (((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), rewrite(((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))), (((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(31,plain,
% 0.20/0.43      (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_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] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[30])).
% 0.20/0.43  tff(32,plain,
% 0.20/0.43      (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_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] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(33,plain,
% 0.20/0.43      (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite(((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (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(M, N) & unorthogonal_lines(M, N)))) <=> ((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)))))), rewrite(((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, 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(M, N) & unorthogonal_lines(M, N)))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(34,plain,
% 0.20/0.43      (![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] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[33])).
% 0.20/0.43  tff(35,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+3.ax','oac1')).
% 0.20/0.43  tff(36,plain,
% 0.20/0.43      (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.43  tff(37,plain,
% 0.20/0.43      (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.43  tff(38,plain,(
% 0.20/0.43      ![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.43      inference(skolemize,[status(sab)],[37])).
% 0.20/0.43  tff(39,plain,
% 0.20/0.43      (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.43  tff(40,plain,
% 0.20/0.43      (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[39, 29])).
% 0.20/0.43  tff(41,plain,
% 0.20/0.43      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~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))) | (~((~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] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~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))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(42,plain,
% 0.20/0.43      (((~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), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~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), 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))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(43,plain,
% 0.20/0.43      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~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), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~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), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~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))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))))))),
% 0.20/0.43      inference(monotonicity,[status(thm)],[42])).
% 0.20/0.43  tff(44,plain,
% 0.20/0.43      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~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), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~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), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~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))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.20/0.44      inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.44  tff(45,plain,
% 0.20/0.44      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~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), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~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), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(46,plain,
% 0.20/0.44      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.44  tff(47,plain,
% 0.20/0.44      ($false),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[46, 40, 27, 25, 22])).
% 0.20/0.44  tff(48,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44  tff(49,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)).
% 0.20/0.44  tff(50,plain,
% 0.20/0.44      ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(51,plain,
% 0.20/0.44      ($false),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[50, 8, 49])).
% 0.20/0.44  tff(52,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,[]))).
% 0.20/0.44  tff(53,plain,
% 0.20/0.44      ((~![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)))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(54,plain,
% 0.20/0.44      (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[53, 18])).
% 0.20/0.44  tff(55,plain,
% 0.20/0.44      (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(56,plain,
% 0.20/0.44      (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[55])).
% 0.20/0.44  tff(57,plain,
% 0.20/0.44      (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(58,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.20/0.44  tff(59,plain,
% 0.20/0.44      (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.44  tff(60,plain,(
% 0.20/0.44      ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.44      inference(skolemize,[status(sab)],[59])).
% 0.20/0.44  tff(61,plain,
% 0.20/0.44      (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.44  tff(62,plain,
% 0.20/0.44      (((~![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)))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(63,plain,
% 0.20/0.44      ((~![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)))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(64,plain,
% 0.20/0.44      ((~![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))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.44  tff(65,plain,
% 0.20/0.44      (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[64, 61, 54])).
% 0.20/0.44  tff(66,plain,
% 0.20/0.44      (^[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))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(67,plain,
% 0.20/0.44      (![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)))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[66])).
% 0.20/0.44  tff(68,plain,
% 0.20/0.44      (![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)))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(69,plain,
% 0.20/0.44      (^[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)))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(70,plain,
% 0.20/0.44      (![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)))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[69])).
% 0.20/0.44  tff(71,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')).
% 0.20/0.44  tff(72,plain,
% 0.20/0.44      (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.44  tff(73,plain,
% 0.20/0.44      (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.44  tff(74,plain,(
% 0.20/0.44      ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44      inference(skolemize,[status(sab)],[73])).
% 0.20/0.44  tff(75,plain,
% 0.20/0.44      (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[74, 67])).
% 0.20/0.44  tff(76,plain,
% 0.20/0.44      (((~![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)))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(77,plain,
% 0.20/0.44      ((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)))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(78,plain,
% 0.20/0.44      (((~![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))))),
% 0.20/0.44      inference(monotonicity,[status(thm)],[77])).
% 0.20/0.44  tff(79,plain,
% 0.20/0.44      (((~![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)))),
% 0.20/0.44      inference(transitivity,[status(thm)],[78, 76])).
% 0.20/0.44  tff(80,plain,
% 0.20/0.44      ((~![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))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(81,plain,
% 0.20/0.44      ((~![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))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.44  tff(82,plain,
% 0.20/0.44      (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))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[81, 75, 65])).
% 0.20/0.44  tff(83,plain,
% 0.20/0.44      (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[82, 52])).
% 0.20/0.44  tff(84,plain,
% 0.20/0.44      (((~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))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(85,plain,
% 0.20/0.44      ((~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)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[84, 54])).
% 0.20/0.44  tff(86,plain,
% 0.20/0.44      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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))))) | (~unorthogonal_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), orthogonal_through_point(orthogonal_through_point(L!0, A!1), 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] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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))))) | (~unorthogonal_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), orthogonal_through_point(orthogonal_through_point(L!0, A!1), 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))))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(87,plain,
% 0.20/0.45      (((~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(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(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_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(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(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), orthogonal_through_point(orthogonal_through_point(L!0, A!1), 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))))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(88,plain,
% 0.20/0.45      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~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(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(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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))))) | (~unorthogonal_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), orthogonal_through_point(orthogonal_through_point(L!0, A!1), 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)))))))),
% 0.20/0.45      inference(monotonicity,[status(thm)],[87])).
% 0.20/0.45  tff(89,plain,
% 0.20/0.45      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~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(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(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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))))) | (~unorthogonal_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), orthogonal_through_point(orthogonal_through_point(L!0, A!1), 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))))))),
% 0.20/0.45      inference(transitivity,[status(thm)],[88, 86])).
% 0.20/0.45  tff(90,plain,
% 0.20/0.45      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~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(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(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.45      inference(quant_inst,[status(thm)],[])).
% 0.20/0.45  tff(91,plain,
% 0.20/0.45      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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))))) | (~unorthogonal_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), orthogonal_through_point(orthogonal_through_point(L!0, A!1), 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)))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.45  tff(92,plain,
% 0.20/0.45      ((~unorthogonal_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), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[91, 40, 85, 83])).
% 0.20/0.45  tff(93,plain,
% 0.20/0.45      (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[92, 48])).
% 0.20/0.45  tff(94,plain,
% 0.20/0.45      (((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))) | convergent_lines(L!0, L!0)),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(95,plain,
% 0.20/0.45      ((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[94, 11])).
% 0.20/0.45  tff(96,assumption,(~((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))), introduced(assumption)).
% 0.20/0.45  tff(97,plain,
% 0.20/0.45      (((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(98,plain,
% 0.20/0.45      (unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[97, 96])).
% 0.20/0.45  tff(99,plain,
% 0.20/0.45      (((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(100,plain,
% 0.20/0.45      (convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[99, 96])).
% 0.20/0.45  tff(101,plain,
% 0.20/0.45      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~((~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] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(102,plain,
% 0.20/0.45      (((~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)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))) <=> ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(103,plain,
% 0.20/0.45      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))))))),
% 0.20/0.45      inference(monotonicity,[status(thm)],[102])).
% 0.20/0.45  tff(104,plain,
% 0.20/0.45      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))))),
% 0.20/0.45      inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.45  tff(105,plain,
% 0.20/0.45      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))),
% 0.20/0.45      inference(quant_inst,[status(thm)],[])).
% 0.20/0.45  tff(106,plain,
% 0.20/0.45      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.45  tff(107,plain,
% 0.20/0.45      ($false),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[106, 40, 100, 98, 95, 22])).
% 0.20/0.45  tff(108,plain,((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45  tff(109,plain,
% 0.20/0.45      ((~(~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))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(110,plain,
% 0.20/0.46      ((~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))) <=> (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(111,axiom,(~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.46  tff(112,plain,
% 0.20/0.46      (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.46  tff(113,plain,
% 0.20/0.46      (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[112, 110])).
% 0.20/0.46  tff(114,plain,
% 0.20/0.46      (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[113, 110])).
% 0.20/0.46  tff(115,plain,
% 0.20/0.46      (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.46  tff(116,plain,
% 0.20/0.46      (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[115, 110])).
% 0.20/0.46  tff(117,plain,
% 0.20/0.46      (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[116, 110])).
% 0.20/0.46  tff(118,plain,
% 0.20/0.46      (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[117, 110])).
% 0.20/0.46  tff(119,plain,(
% 0.20/0.46      ~(~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.46      inference(skolemize,[status(sab)],[118])).
% 0.20/0.46  tff(120,plain,
% 0.20/0.46      (convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[119, 109])).
% 0.20/0.46  tff(121,plain,
% 0.20/0.46      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(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(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(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(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(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(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(122,plain,
% 0.20/0.46      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(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(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(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(123,plain,
% 0.20/0.46      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(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(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(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.46  tff(124,plain,
% 0.20/0.46      ((~((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[123, 40, 120, 85])).
% 0.20/0.46  tff(125,plain,
% 0.20/0.46      (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[124, 108])).
% 0.20/0.46  tff(126,plain,
% 0.20/0.46      (((~![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))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(127,plain,
% 0.20/0.46      ((~![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))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(128,plain,
% 0.20/0.46      ((~![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)),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.46  tff(129,plain,
% 0.20/0.46      (convergent_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[128, 61, 20])).
% 0.20/0.46  tff(130,plain,
% 0.20/0.46      (^[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))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(131,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[130])).
% 0.20/0.46  tff(132,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(133,plain,
% 0.20/0.46      (^[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))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(134,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[133])).
% 0.20/0.46  tff(135,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')).
% 0.20/0.46  tff(136,plain,
% 0.20/0.46      (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.46  tff(137,plain,
% 0.20/0.46      (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[136, 132])).
% 0.20/0.46  tff(138,plain,(
% 0.20/0.46      ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.46      inference(skolemize,[status(sab)],[137])).
% 0.20/0.46  tff(139,plain,
% 0.20/0.46      (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[138, 131])).
% 0.20/0.46  tff(140,plain,
% 0.20/0.46      (((~![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))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(141,plain,
% 0.20/0.46      ((~![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))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(142,plain,
% 0.20/0.46      ((~![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)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.46  tff(143,plain,
% 0.20/0.46      (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[142, 139, 129])).
% 0.20/0.46  tff(144,plain,
% 0.20/0.46      (^[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))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(145,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[144])).
% 0.20/0.46  tff(146,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(147,plain,
% 0.20/0.46      (^[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))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(148,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[147])).
% 0.20/0.46  tff(149,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')).
% 0.20/0.46  tff(150,plain,
% 0.20/0.46      (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.46  tff(151,plain,
% 0.20/0.46      (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[150, 146])).
% 0.20/0.46  tff(152,plain,(
% 0.20/0.46      ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.46      inference(skolemize,[status(sab)],[151])).
% 0.20/0.46  tff(153,plain,
% 0.20/0.46      (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[152, 145])).
% 0.20/0.46  tff(154,plain,
% 0.20/0.46      (((~![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)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(155,plain,
% 0.20/0.46      ((~![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)))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(156,plain,
% 0.20/0.46      ((~![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))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.46  tff(157,plain,
% 0.20/0.46      (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0)),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[156, 153, 129])).
% 0.20/0.46  tff(158,plain,
% 0.20/0.46      (^[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))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(159,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[158])).
% 0.20/0.46  tff(160,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(161,plain,
% 0.20/0.46      (^[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)))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(162,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[161])).
% 0.20/0.46  tff(163,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')).
% 0.20/0.46  tff(164,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.46  tff(165,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[164, 160])).
% 0.20/0.46  tff(166,plain,(
% 0.20/0.46      ![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)))),
% 0.20/0.46      inference(skolemize,[status(sab)],[165])).
% 0.20/0.46  tff(167,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[166, 159])).
% 0.20/0.46  tff(168,plain,
% 0.20/0.46      (((~![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(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, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, 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)))) | 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, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(169,plain,
% 0.20/0.46      ((apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(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, A!1), L!0), orthogonal_through_point(L!0, A!1)) | (~distinct_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) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(170,plain,
% 0.20/0.46      (((~![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(L!0, A!1), L!0), L!0) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(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, A!1), L!0), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![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(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, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.46      inference(monotonicity,[status(thm)],[169])).
% 0.20/0.46  tff(171,plain,
% 0.20/0.46      (((~![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(L!0, A!1), L!0), L!0) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(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, A!1), L!0), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![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(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, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.46      inference(transitivity,[status(thm)],[170, 168])).
% 0.20/0.46  tff(172,plain,
% 0.20/0.46      ((~![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(L!0, A!1), L!0), L!0) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(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, A!1), L!0), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(173,plain,
% 0.20/0.46      ((~![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(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, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[172, 171])).
% 0.20/0.46  tff(174,plain,
% 0.20/0.46      (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[173, 167, 157, 143, 125, 93])).
% 0.20/0.46  tff(175,plain,
% 0.20/0.46      (^[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))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(176,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[175])).
% 0.20/0.46  tff(177,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(178,plain,
% 0.20/0.46      (^[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)))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(179,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[178])).
% 0.20/0.46  tff(180,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')).
% 0.20/0.46  tff(181,plain,
% 0.20/0.47      (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[180, 179])).
% 0.20/0.47  tff(182,plain,
% 0.20/0.47      (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[181, 177])).
% 0.20/0.47  tff(183,plain,(
% 0.20/0.47      ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.47      inference(skolemize,[status(sab)],[182])).
% 0.20/0.47  tff(184,plain,
% 0.20/0.47      (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[183, 176])).
% 0.20/0.47  tff(185,plain,
% 0.20/0.47      (((~![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, A!1), L!0) | convergent_lines(L!0, 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(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(L!0, L!0))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(186,plain,
% 0.20/0.47      ((distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, 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, A!1), L!0) | convergent_lines(L!0, L!0))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(187,plain,
% 0.20/0.47      (((~![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), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, 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, A!1), L!0) | convergent_lines(L!0, L!0)))),
% 0.20/0.47      inference(monotonicity,[status(thm)],[186])).
% 0.20/0.47  tff(188,plain,
% 0.20/0.47      (((~![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), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, 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, A!1), L!0) | convergent_lines(L!0, L!0))),
% 0.20/0.47      inference(transitivity,[status(thm)],[187, 185])).
% 0.20/0.47  tff(189,plain,
% 0.20/0.47      ((~![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), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))))),
% 0.20/0.47      inference(quant_inst,[status(thm)],[])).
% 0.20/0.47  tff(190,plain,
% 0.20/0.47      ((~![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, A!1), L!0) | convergent_lines(L!0, L!0)),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.47  tff(191,plain,
% 0.20/0.47      (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[190, 184, 174, 11])).
% 0.20/0.47  tff(192,plain,
% 0.20/0.47      (((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(193,plain,
% 0.20/0.47      ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[192, 125])).
% 0.20/0.47  tff(194,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))) | (~unorthogonal_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)).
% 0.20/0.47  tff(195,plain,
% 0.20/0.47      (((~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))) | (~unorthogonal_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(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(196,plain,
% 0.20/0.47      (unorthogonal_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))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[195, 194])).
% 0.20/0.47  tff(197,plain,
% 0.20/0.47      (((~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))) | (~unorthogonal_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(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(198,plain,
% 0.20/0.47      (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))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[197, 194])).
% 0.20/0.47  tff(199,plain,
% 0.20/0.47      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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))))) | (~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))) | (~unorthogonal_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))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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))))) | (~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))) | (~unorthogonal_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))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(200,plain,
% 0.20/0.47      (((~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))) | (~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), 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(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))) | (~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), 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(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(201,plain,
% 0.20/0.47      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~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))) | (~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), 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(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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))))) | (~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))) | (~unorthogonal_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)))))),
% 0.20/0.47      inference(monotonicity,[status(thm)],[200])).
% 0.20/0.47  tff(202,plain,
% 0.20/0.47      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~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))) | (~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), 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(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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))))) | (~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))) | (~unorthogonal_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))))),
% 0.20/0.47      inference(transitivity,[status(thm)],[201, 199])).
% 0.20/0.47  tff(203,plain,
% 0.20/0.47      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~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))) | (~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), 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(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.47      inference(quant_inst,[status(thm)],[])).
% 0.20/0.47  tff(204,plain,
% 0.20/0.47      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.47  tff(205,plain,
% 0.20/0.47      ($false),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[204, 40, 85, 198, 196])).
% 0.20/0.47  tff(206,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))) | (~unorthogonal_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,[]))).
% 0.20/0.47  tff(207,plain,
% 0.20/0.47      (((~![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(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | 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)))) | (~convergent_lines(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), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(208,plain,
% 0.20/0.47      ((distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | 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), 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))) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(209,plain,
% 0.20/0.47      (((~![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), L!0) | 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), 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(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), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.20/0.47      inference(monotonicity,[status(thm)],[208])).
% 0.20/0.47  tff(210,plain,
% 0.20/0.47      (((~![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), L!0) | 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), 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(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), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.20/0.47      inference(transitivity,[status(thm)],[209, 207])).
% 0.20/0.47  tff(211,plain,
% 0.20/0.47      ((~![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), L!0) | 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), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.47      inference(quant_inst,[status(thm)],[])).
% 0.20/0.47  tff(212,plain,
% 0.20/0.47      ((~![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(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[211, 210])).
% 0.20/0.47  tff(213,plain,
% 0.20/0.47      (distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[212, 184, 65])).
% 0.20/0.47  tff(214,plain,
% 0.20/0.47      (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[213, 174])).
% 0.20/0.47  tff(215,plain,
% 0.20/0.47      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~unorthogonal_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)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(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))) | (~unorthogonal_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))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_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)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(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))) | (~unorthogonal_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))))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(216,plain,
% 0.20/0.47      (((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(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))) | (~unorthogonal_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), L!0))) <=> ((~unorthogonal_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)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(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))) | (~unorthogonal_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))))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(217,plain,
% 0.20/0.47      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(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))) | (~unorthogonal_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), L!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~unorthogonal_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)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(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))) | (~unorthogonal_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)))))))),
% 0.20/0.48      inference(monotonicity,[status(thm)],[216])).
% 0.20/0.48  tff(218,plain,
% 0.20/0.48      (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(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))) | (~unorthogonal_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), L!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_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)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(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))) | (~unorthogonal_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))))))),
% 0.20/0.48      inference(transitivity,[status(thm)],[217, 215])).
% 0.20/0.48  tff(219,plain,
% 0.20/0.48      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(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))) | (~unorthogonal_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), L!0)))),
% 0.20/0.48      inference(quant_inst,[status(thm)],[])).
% 0.20/0.48  tff(220,plain,
% 0.20/0.48      ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~unorthogonal_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)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(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))) | (~unorthogonal_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)))))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[219, 218])).
% 0.20/0.48  tff(221,plain,
% 0.20/0.48      (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[220, 40, 214, 206, 193])).
% 0.20/0.48  tff(222,plain,
% 0.20/0.48      (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0)))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(223,plain,
% 0.20/0.48      ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0)))),
% 0.20/0.48      inference(quant_inst,[status(thm)],[])).
% 0.20/0.48  tff(224,plain,
% 0.20/0.48      ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[223, 222])).
% 0.20/0.48  tff(225,plain,
% 0.20/0.48      (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0)),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[224, 139, 120])).
% 0.20/0.48  tff(226,plain,
% 0.20/0.48      (^[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))))),
% 0.20/0.48      inference(bind,[status(th)],[])).
% 0.20/0.48  tff(227,plain,
% 0.20/0.48      (![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)))),
% 0.20/0.48      inference(quant_intro,[status(thm)],[226])).
% 0.20/0.48  tff(228,plain,
% 0.20/0.48      (![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)))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(229,plain,
% 0.20/0.48      (^[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)))))),
% 0.20/0.48      inference(bind,[status(th)],[])).
% 0.20/0.48  tff(230,plain,
% 0.20/0.48      (![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)))),
% 0.20/0.48      inference(quant_intro,[status(thm)],[229])).
% 0.20/0.48  tff(231,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')).
% 0.20/0.48  tff(232,plain,
% 0.20/0.48      (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[231, 230])).
% 0.20/0.48  tff(233,plain,
% 0.20/0.48      (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[232, 228])).
% 0.20/0.48  tff(234,plain,(
% 0.20/0.48      ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.48      inference(skolemize,[status(sab)],[233])).
% 0.20/0.48  tff(235,plain,
% 0.20/0.48      (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[234, 227])).
% 0.20/0.48  tff(236,plain,
% 0.20/0.48      (((~![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(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | (~apart_point_and_line(intersection_point(L!0, 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(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(237,plain,
% 0.20/0.48      ((distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | (~apart_point_and_line(intersection_point(L!0, 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(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(238,plain,
% 0.20/0.48      (((~![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, A!1), L!0) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | (~apart_point_and_line(intersection_point(L!0, 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(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)))))),
% 0.20/0.48      inference(monotonicity,[status(thm)],[237])).
% 0.20/0.48  tff(239,plain,
% 0.20/0.48      (((~![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, A!1), L!0) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | (~apart_point_and_line(intersection_point(L!0, 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(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.48      inference(transitivity,[status(thm)],[238, 236])).
% 0.20/0.48  tff(240,plain,
% 0.20/0.48      ((~![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, A!1), L!0) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.48      inference(quant_inst,[status(thm)],[])).
% 0.20/0.48  tff(241,plain,
% 0.20/0.48      ((~![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(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[240, 239])).
% 0.20/0.48  tff(242,plain,
% 0.20/0.48      (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1))),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[241, 235, 225, 174])).
% 0.20/0.48  tff(243,plain,
% 0.20/0.48      (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, 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] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(244,plain,
% 0.20/0.48      ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.48      inference(quant_inst,[status(thm)],[])).
% 0.20/0.48  tff(245,plain,
% 0.20/0.48      ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[244, 243])).
% 0.20/0.48  tff(246,plain,
% 0.20/0.48      (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[245, 153, 120])).
% 0.20/0.48  tff(247,plain,
% 0.20/0.48      (((~![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(L!0, 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(L!0, A!1), L!0) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)) | (~distinct_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), L!0))) <=> ((~![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(L!0, 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(L!0, A!1), L!0) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)) | (~distinct_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), L!0))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(248,plain,
% 0.20/0.48      ((apart_point_and_line(intersection_point(L!0, 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), L!0) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(intersection_point(L!0, 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), orthogonal_through_point(L!0, A!1)))) <=> (apart_point_and_line(intersection_point(L!0, 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(L!0, A!1), L!0) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)) | (~distinct_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), L!0))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(249,plain,
% 0.20/0.48      (((~![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(L!0, 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), L!0) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(intersection_point(L!0, 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), 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)))) | (apart_point_and_line(intersection_point(L!0, 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(L!0, A!1), L!0) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)) | (~distinct_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), L!0)))),
% 0.20/0.48      inference(monotonicity,[status(thm)],[248])).
% 0.20/0.48  tff(250,plain,
% 0.20/0.48      (((~![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(L!0, 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), L!0) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(intersection_point(L!0, 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), 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)))) | apart_point_and_line(intersection_point(L!0, 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(L!0, A!1), L!0) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)) | (~distinct_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), L!0))),
% 0.20/0.48      inference(transitivity,[status(thm)],[249, 247])).
% 0.20/0.48  tff(251,plain,
% 0.20/0.48      ((~![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(L!0, 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), L!0) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(intersection_point(L!0, 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), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.48      inference(quant_inst,[status(thm)],[])).
% 0.20/0.48  tff(252,plain,
% 0.20/0.48      ((~![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(L!0, 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(L!0, A!1), L!0) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)) | (~distinct_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), L!0)),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.48  tff(253,plain,
% 0.20/0.48      (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[252, 167, 246, 20, 242, 221])).
% 0.20/0.48  tff(254,plain,
% 0.20/0.48      (((~![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))) | distinct_lines(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)))) <=> ((~![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))) | distinct_lines(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)))),
% 0.20/0.49      inference(rewrite,[status(thm)],[])).
% 0.20/0.49  tff(255,plain,
% 0.20/0.49      ((distinct_lines(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)) | (~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))) | distinct_lines(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)))),
% 0.20/0.49      inference(rewrite,[status(thm)],[])).
% 0.20/0.49  tff(256,plain,
% 0.20/0.49      (((~![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), 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(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))) | distinct_lines(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))))),
% 0.20/0.49      inference(monotonicity,[status(thm)],[255])).
% 0.20/0.49  tff(257,plain,
% 0.20/0.49      (((~![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), 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(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))) | distinct_lines(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)))),
% 0.20/0.49      inference(transitivity,[status(thm)],[256, 254])).
% 0.20/0.49  tff(258,plain,
% 0.20/0.49      ((~![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), 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(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.49      inference(quant_inst,[status(thm)],[])).
% 0.20/0.49  tff(259,plain,
% 0.20/0.49      ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.49  tff(260,plain,
% 0.20/0.49      ($false),
% 0.20/0.49      inference(unit_resolution,[status(thm)],[259, 184, 120, 253, 191])).
% 0.20/0.49  % SZS output end Proof
%------------------------------------------------------------------------------