TSTP Solution File: GEO222+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 0.45s 0.52s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 07:02:53 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.
% 0.45/0.52 % SZS status Theorem
% 0.45/0.52 % SZS output start Proof
% 0.45/0.52 tff(convergent_lines_type, type, (
% 0.45/0.52 convergent_lines: ( $i * $i ) > $o)).
% 0.45/0.52 tff(orthogonal_through_point_type, type, (
% 0.45/0.52 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.45/0.52 tff(tptp_fun_A_1_type, type, (
% 0.45/0.52 tptp_fun_A_1: $i)).
% 0.45/0.52 tff(tptp_fun_L_0_type, type, (
% 0.45/0.52 tptp_fun_L_0: $i)).
% 0.45/0.52 tff(unorthogonal_lines_type, type, (
% 0.45/0.52 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.45/0.52 tff(apart_point_and_line_type, type, (
% 0.45/0.52 apart_point_and_line: ( $i * $i ) > $o)).
% 0.45/0.52 tff(intersection_point_type, type, (
% 0.45/0.52 intersection_point: ( $i * $i ) > $i)).
% 0.45/0.52 tff(distinct_points_type, type, (
% 0.45/0.52 distinct_points: ( $i * $i ) > $o)).
% 0.45/0.52 tff(distinct_lines_type, type, (
% 0.45/0.52 distinct_lines: ( $i * $i ) > $o)).
% 0.45/0.52 tff(1,assumption,(distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))), introduced(assumption)).
% 0.45/0.52 tff(2,plain,
% 0.45/0.52 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.45/0.52 inference(bind,[status(th)],[])).
% 0.45/0.52 tff(3,plain,
% 0.45/0.52 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.45/0.52 inference(quant_intro,[status(thm)],[2])).
% 0.45/0.52 tff(4,plain,
% 0.45/0.52 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.45/0.52 inference(rewrite,[status(thm)],[])).
% 0.45/0.52 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.45/0.52 tff(6,plain,
% 0.45/0.52 (![X: $i] : (~distinct_points(X, X))),
% 0.45/0.52 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.45/0.52 tff(7,plain,(
% 0.45/0.52 ![X: $i] : (~distinct_points(X, X))),
% 0.45/0.52 inference(skolemize,[status(sab)],[6])).
% 0.45/0.52 tff(8,plain,
% 0.45/0.52 (![X: $i] : (~distinct_points(X, X))),
% 0.45/0.52 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.45/0.52 tff(9,plain,
% 0.45/0.52 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.45/0.52 inference(quant_inst,[status(thm)],[])).
% 0.45/0.52 tff(10,plain,
% 0.45/0.52 ($false),
% 0.45/0.52 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.45/0.52 tff(11,plain,(~distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.52 tff(12,assumption,(apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0)), introduced(assumption)).
% 0.45/0.52 tff(13,plain,
% 0.45/0.52 ((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(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))),
% 0.45/0.52 inference(tautology,[status(thm)],[])).
% 0.45/0.52 tff(14,plain,
% 0.45/0.52 (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(orthogonal_through_point(L!0, A!1), A!1))),
% 0.45/0.52 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.45/0.52 tff(15,assumption,(~distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))), introduced(assumption)).
% 0.45/0.52 tff(16,plain,
% 0.45/0.52 ((~(~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))),
% 0.45/0.52 inference(rewrite,[status(thm)],[])).
% 0.45/0.52 tff(17,plain,
% 0.45/0.52 ((~![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))))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(18,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')).
% 0.45/0.53 tff(19,plain,
% 0.45/0.53 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.45/0.53 tff(20,plain,
% 0.45/0.53 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.45/0.53 tff(21,plain,
% 0.45/0.53 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.45/0.53 tff(22,plain,
% 0.45/0.53 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.45/0.53 tff(23,plain,
% 0.45/0.53 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.45/0.53 tff(24,plain,
% 0.45/0.53 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[23, 17])).
% 0.45/0.53 tff(25,plain,
% 0.45/0.53 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.45/0.53 tff(26,plain,(
% 0.45/0.53 ~(~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.45/0.53 inference(skolemize,[status(sab)],[25])).
% 0.45/0.53 tff(27,plain,
% 0.45/0.53 (convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.45/0.53 tff(28,plain,
% 0.45/0.53 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))))),
% 0.45/0.53 inference(bind,[status(th)],[])).
% 0.45/0.53 tff(29,plain,
% 0.45/0.53 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.45/0.53 inference(quant_intro,[status(thm)],[28])).
% 0.45/0.53 tff(30,plain,
% 0.45/0.53 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(31,plain,
% 0.45/0.53 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) <=> (apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))))), rewrite(((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))))), rewrite((convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))))),
% 0.45/0.53 inference(bind,[status(th)],[])).
% 0.45/0.53 tff(32,plain,
% 0.45/0.53 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.45/0.53 inference(quant_intro,[status(thm)],[31])).
% 0.45/0.53 tff(33,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.45/0.53 tff(34,plain,
% 0.45/0.53 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.45/0.53 tff(35,plain,
% 0.45/0.53 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.45/0.53 tff(36,plain,(
% 0.45/0.53 ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.45/0.53 inference(skolemize,[status(sab)],[35])).
% 0.45/0.53 tff(37,plain,
% 0.45/0.53 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.45/0.53 tff(38,plain,
% 0.45/0.53 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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) | 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, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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) | 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)))))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(39,plain,
% 0.45/0.53 ((distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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))) | (~(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(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_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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) | 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)))))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(40,plain,
% 0.45/0.53 ((~(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)) | 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)), 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))))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(41,plain,
% 0.45/0.53 ((distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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))) | (~(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)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0)))) <=> (distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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))) | (~(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(orthogonal_through_point(L!0, A!1), A!1)))))),
% 0.45/0.53 inference(monotonicity,[status(thm)],[40])).
% 0.45/0.53 tff(42,plain,
% 0.45/0.53 ((distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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))) | (~(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)) | apart_point_and_line(intersection_point(L!0, 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))) | distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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) | 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)))))),
% 0.45/0.53 inference(transitivity,[status(thm)],[41, 39])).
% 0.45/0.53 tff(43,plain,
% 0.45/0.53 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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))) | (~(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)) | 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, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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) | 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))))))),
% 0.45/0.53 inference(monotonicity,[status(thm)],[42])).
% 0.45/0.53 tff(44,plain,
% 0.45/0.53 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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))) | (~(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)) | 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, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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) | 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)))))),
% 0.45/0.53 inference(transitivity,[status(thm)],[43, 38])).
% 0.45/0.53 tff(45,plain,
% 0.45/0.53 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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))) | (~(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)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0))))),
% 0.45/0.53 inference(quant_inst,[status(thm)],[])).
% 0.45/0.53 tff(46,plain,
% 0.45/0.53 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~(apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.45/0.53 tff(47,plain,
% 0.45/0.53 ($false),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[46, 37, 27, 15, 14])).
% 0.45/0.53 tff(48,plain,(distinct_points(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), intersection_point(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))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.53 tff(49,plain,
% 0.45/0.53 (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0)),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[48, 11])).
% 0.45/0.53 tff(50,plain,
% 0.45/0.53 (~(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(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[46, 37, 27, 11])).
% 0.45/0.53 tff(51,plain,
% 0.45/0.53 ((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(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)))),
% 0.45/0.53 inference(tautology,[status(thm)],[])).
% 0.45/0.53 tff(52,plain,
% 0.45/0.53 (~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))),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.45/0.53 tff(53,assumption,(~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))), introduced(assumption)).
% 0.45/0.53 tff(54,plain,
% 0.45/0.53 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.45/0.53 inference(bind,[status(th)],[])).
% 0.45/0.53 tff(55,plain,
% 0.45/0.53 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.45/0.53 inference(quant_intro,[status(thm)],[54])).
% 0.45/0.53 tff(56,plain,
% 0.45/0.53 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(57,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.45/0.53 tff(58,plain,
% 0.45/0.53 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.45/0.53 tff(59,plain,(
% 0.45/0.53 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.45/0.53 inference(skolemize,[status(sab)],[58])).
% 0.45/0.53 tff(60,plain,
% 0.45/0.53 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.45/0.53 tff(61,plain,
% 0.45/0.53 ((~![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)))),
% 0.45/0.53 inference(quant_inst,[status(thm)],[])).
% 0.45/0.53 tff(62,plain,
% 0.45/0.53 (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.45/0.53 tff(63,plain,
% 0.45/0.53 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.45/0.53 inference(bind,[status(th)],[])).
% 0.45/0.53 tff(64,plain,
% 0.45/0.53 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.45/0.53 inference(quant_intro,[status(thm)],[63])).
% 0.45/0.53 tff(65,plain,
% 0.45/0.53 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(66,plain,
% 0.45/0.53 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.45/0.53 inference(bind,[status(th)],[])).
% 0.45/0.53 tff(67,plain,
% 0.45/0.53 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.45/0.53 inference(quant_intro,[status(thm)],[66])).
% 0.45/0.53 tff(68,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.45/0.53 tff(69,plain,
% 0.45/0.53 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.45/0.53 tff(70,plain,
% 0.45/0.53 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.45/0.53 tff(71,plain,(
% 0.45/0.53 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.45/0.53 inference(skolemize,[status(sab)],[70])).
% 0.45/0.53 tff(72,plain,
% 0.45/0.53 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.45/0.53 tff(73,plain,
% 0.45/0.53 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(74,plain,
% 0.45/0.53 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.45/0.53 inference(quant_inst,[status(thm)],[])).
% 0.45/0.53 tff(75,plain,
% 0.45/0.53 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.45/0.53 tff(76,plain,
% 0.45/0.53 (distinct_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[75, 72, 27])).
% 0.45/0.53 tff(77,plain,
% 0.45/0.53 (^[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))))),
% 0.45/0.53 inference(bind,[status(th)],[])).
% 0.45/0.53 tff(78,plain,
% 0.45/0.53 (![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)))),
% 0.45/0.53 inference(quant_intro,[status(thm)],[77])).
% 0.45/0.53 tff(79,plain,
% 0.45/0.53 (![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)))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(80,plain,
% 0.45/0.53 (^[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)))))),
% 0.45/0.53 inference(bind,[status(th)],[])).
% 0.45/0.53 tff(81,plain,
% 0.45/0.53 (![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)))),
% 0.45/0.53 inference(quant_intro,[status(thm)],[80])).
% 0.45/0.53 tff(82,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')).
% 0.45/0.53 tff(83,plain,
% 0.45/0.53 (![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)))),
% 0.47/0.53 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.47/0.53 tff(84,plain,
% 0.47/0.53 (![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)))),
% 0.47/0.53 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.47/0.53 tff(85,plain,(
% 0.47/0.53 ![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)))),
% 0.47/0.53 inference(skolemize,[status(sab)],[84])).
% 0.47/0.53 tff(86,plain,
% 0.47/0.53 (![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)))),
% 0.47/0.53 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.47/0.53 tff(87,plain,
% 0.47/0.53 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, 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(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)))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, 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(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)))),
% 0.47/0.53 inference(rewrite,[status(thm)],[])).
% 0.47/0.53 tff(88,plain,
% 0.47/0.53 ((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(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | (~distinct_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, 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(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)))),
% 0.47/0.53 inference(rewrite,[status(thm)],[])).
% 0.47/0.53 tff(89,plain,
% 0.47/0.53 (((~![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(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | (~distinct_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, 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(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))))),
% 0.47/0.54 inference(monotonicity,[status(thm)],[88])).
% 0.47/0.54 tff(90,plain,
% 0.47/0.54 (((~![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(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | (~distinct_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, 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(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)))),
% 0.47/0.54 inference(transitivity,[status(thm)],[89, 87])).
% 0.47/0.54 tff(91,plain,
% 0.47/0.54 ((~![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(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | (~distinct_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.47/0.54 inference(quant_inst,[status(thm)],[])).
% 0.47/0.54 tff(92,plain,
% 0.47/0.54 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | (~distinct_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.47/0.54 tff(93,plain,
% 0.47/0.54 ($false),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[92, 86, 76, 62, 53, 52, 49])).
% 0.47/0.54 tff(94,plain,(unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.54 tff(95,assumption,(convergent_lines(L!0, L!0)), introduced(assumption)).
% 0.47/0.54 tff(96,plain,
% 0.47/0.54 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.47/0.54 inference(bind,[status(th)],[])).
% 0.47/0.54 tff(97,plain,
% 0.47/0.54 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.47/0.54 inference(quant_intro,[status(thm)],[96])).
% 0.47/0.54 tff(98,plain,
% 0.47/0.54 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.47/0.54 inference(rewrite,[status(thm)],[])).
% 0.47/0.54 tff(99,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart3')).
% 0.47/0.54 tff(100,plain,
% 0.47/0.54 (![X: $i] : (~convergent_lines(X, X))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.47/0.54 tff(101,plain,(
% 0.47/0.54 ![X: $i] : (~convergent_lines(X, X))),
% 0.47/0.54 inference(skolemize,[status(sab)],[100])).
% 0.47/0.54 tff(102,plain,
% 0.47/0.54 (![X: $i] : (~convergent_lines(X, X))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.47/0.54 tff(103,plain,
% 0.47/0.54 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(L!0, L!0))),
% 0.47/0.54 inference(quant_inst,[status(thm)],[])).
% 0.47/0.54 tff(104,plain,
% 0.47/0.54 ($false),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[103, 102, 95])).
% 0.47/0.54 tff(105,plain,(~convergent_lines(L!0, L!0)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.54 tff(106,plain,
% 0.47/0.54 (((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))) | convergent_lines(L!0, L!0)),
% 0.47/0.54 inference(tautology,[status(thm)],[])).
% 0.47/0.54 tff(107,plain,
% 0.47/0.54 ((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.47/0.54 tff(108,plain,
% 0.47/0.54 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.47/0.54 inference(quant_inst,[status(thm)],[])).
% 0.47/0.54 tff(109,plain,
% 0.47/0.54 (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[108, 60])).
% 0.47/0.54 tff(110,plain,
% 0.47/0.54 (((~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)),
% 0.47/0.54 inference(tautology,[status(thm)],[])).
% 0.47/0.54 tff(111,plain,
% 0.47/0.54 ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.47/0.54 tff(112,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)).
% 0.47/0.54 tff(113,plain,
% 0.47/0.54 (((~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))),
% 0.47/0.54 inference(tautology,[status(thm)],[])).
% 0.47/0.54 tff(114,plain,
% 0.47/0.54 (unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.47/0.54 tff(115,plain,
% 0.47/0.54 (((~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))),
% 0.47/0.54 inference(tautology,[status(thm)],[])).
% 0.47/0.54 tff(116,plain,
% 0.47/0.54 (convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[115, 112])).
% 0.47/0.54 tff(117,plain,
% 0.47/0.54 (^[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))))),
% 0.47/0.54 inference(bind,[status(th)],[])).
% 0.47/0.54 tff(118,plain,
% 0.47/0.54 (![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)))),
% 0.47/0.54 inference(quant_intro,[status(thm)],[117])).
% 0.47/0.54 tff(119,plain,
% 0.47/0.54 (^[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)))))),
% 0.47/0.54 inference(bind,[status(th)],[])).
% 0.47/0.54 tff(120,plain,
% 0.47/0.54 (![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)))),
% 0.47/0.54 inference(quant_intro,[status(thm)],[119])).
% 0.47/0.54 tff(121,plain,
% 0.47/0.54 (![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))))),
% 0.47/0.54 inference(rewrite,[status(thm)],[])).
% 0.47/0.54 tff(122,plain,
% 0.47/0.54 (^[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))))))),
% 0.47/0.54 inference(bind,[status(th)],[])).
% 0.47/0.54 tff(123,plain,
% 0.47/0.54 (![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))))),
% 0.47/0.54 inference(quant_intro,[status(thm)],[122])).
% 0.47/0.54 tff(124,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')).
% 0.47/0.54 tff(125,plain,
% 0.47/0.54 (![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))))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.47/0.54 tff(126,plain,
% 0.47/0.54 (![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))))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.47/0.54 tff(127,plain,(
% 0.47/0.54 ![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))))),
% 0.47/0.54 inference(skolemize,[status(sab)],[126])).
% 0.47/0.54 tff(128,plain,
% 0.47/0.54 (![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)))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.47/0.54 tff(129,plain,
% 0.47/0.54 (![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)))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[128, 118])).
% 0.47/0.54 tff(130,plain,
% 0.47/0.54 (((~![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(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)))))) <=> ((~![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(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)))))),
% 0.47/0.54 inference(rewrite,[status(thm)],[])).
% 0.47/0.54 tff(131,plain,
% 0.47/0.54 (((~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(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)))))),
% 0.47/0.54 inference(rewrite,[status(thm)],[])).
% 0.47/0.54 tff(132,plain,
% 0.47/0.54 (((~![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(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))))))),
% 0.47/0.54 inference(monotonicity,[status(thm)],[131])).
% 0.47/0.54 tff(133,plain,
% 0.47/0.54 (((~![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(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)))))),
% 0.47/0.54 inference(transitivity,[status(thm)],[132, 130])).
% 0.47/0.54 tff(134,plain,
% 0.47/0.54 ((~![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))))),
% 0.47/0.54 inference(quant_inst,[status(thm)],[])).
% 0.47/0.54 tff(135,plain,
% 0.47/0.54 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.47/0.54 tff(136,plain,
% 0.47/0.54 ($false),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[135, 129, 116, 114, 111, 107])).
% 0.47/0.54 tff(137,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,[]))).
% 0.47/0.54 tff(138,plain,
% 0.47/0.54 ((~((~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))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.47/0.54 inference(tautology,[status(thm)],[])).
% 0.47/0.54 tff(139,plain,
% 0.47/0.54 ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.47/0.54 tff(140,plain,
% 0.47/0.54 (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[139, 94])).
% 0.47/0.54 tff(141,plain,
% 0.47/0.54 (^[A: $i, L: $i] : refl((~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> (~apart_point_and_line(A, orthogonal_through_point(L, A))))),
% 0.47/0.54 inference(bind,[status(th)],[])).
% 0.47/0.54 tff(142,plain,
% 0.47/0.54 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.47/0.54 inference(quant_intro,[status(thm)],[141])).
% 0.47/0.54 tff(143,plain,
% 0.47/0.54 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.47/0.54 inference(rewrite,[status(thm)],[])).
% 0.47/0.54 tff(144,axiom,(![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ooc2')).
% 0.47/0.54 tff(145,plain,
% 0.47/0.54 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.47/0.54 tff(146,plain,(
% 0.47/0.54 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.47/0.54 inference(skolemize,[status(sab)],[145])).
% 0.47/0.54 tff(147,plain,
% 0.47/0.54 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.47/0.54 tff(148,plain,
% 0.47/0.54 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)))),
% 0.47/0.54 inference(quant_inst,[status(thm)],[])).
% 0.47/0.54 tff(149,plain,
% 0.47/0.54 (~apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.47/0.54 tff(150,plain,
% 0.47/0.54 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.47/0.54 inference(rewrite,[status(thm)],[])).
% 0.47/0.54 tff(151,plain,
% 0.47/0.54 ((apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.47/0.54 inference(rewrite,[status(thm)],[])).
% 0.47/0.54 tff(152,plain,
% 0.47/0.54 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.47/0.54 inference(monotonicity,[status(thm)],[151])).
% 0.47/0.54 tff(153,plain,
% 0.47/0.54 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.47/0.54 inference(transitivity,[status(thm)],[152, 150])).
% 0.47/0.54 tff(154,plain,
% 0.47/0.54 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.47/0.54 inference(quant_inst,[status(thm)],[])).
% 0.47/0.54 tff(155,plain,
% 0.47/0.54 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.47/0.54 tff(156,plain,
% 0.47/0.54 (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[155, 86, 109, 149])).
% 0.47/0.54 tff(157,plain,
% 0.47/0.54 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.47/0.54 inference(rewrite,[status(thm)],[])).
% 0.47/0.54 tff(158,plain,
% 0.47/0.54 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.47/0.54 inference(quant_inst,[status(thm)],[])).
% 0.47/0.54 tff(159,plain,
% 0.47/0.54 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.47/0.54 tff(160,plain,
% 0.47/0.54 (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[159, 72, 156])).
% 0.47/0.54 tff(161,plain,
% 0.47/0.54 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.47/0.54 inference(bind,[status(th)],[])).
% 0.47/0.54 tff(162,plain,
% 0.47/0.54 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.47/0.54 inference(quant_intro,[status(thm)],[161])).
% 0.47/0.54 tff(163,plain,
% 0.47/0.54 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.47/0.54 inference(rewrite,[status(thm)],[])).
% 0.47/0.54 tff(164,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.47/0.54 tff(165,plain,
% 0.47/0.54 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.47/0.54 tff(166,plain,(
% 0.47/0.54 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.47/0.54 inference(skolemize,[status(sab)],[165])).
% 0.47/0.54 tff(167,plain,
% 0.47/0.54 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.47/0.54 tff(168,plain,
% 0.47/0.54 (((~![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))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(169,plain,
% 0.47/0.55 ((~![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))),
% 0.47/0.55 inference(quant_inst,[status(thm)],[])).
% 0.47/0.55 tff(170,plain,
% 0.47/0.55 ((~![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)),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.47/0.55 tff(171,plain,
% 0.47/0.55 (convergent_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[170, 167, 109])).
% 0.47/0.55 tff(172,plain,
% 0.47/0.55 (^[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))))),
% 0.47/0.55 inference(bind,[status(th)],[])).
% 0.47/0.55 tff(173,plain,
% 0.47/0.55 (![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)))),
% 0.47/0.55 inference(quant_intro,[status(thm)],[172])).
% 0.47/0.55 tff(174,plain,
% 0.47/0.55 (![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)))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(175,plain,
% 0.47/0.55 (^[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)))))),
% 0.47/0.55 inference(bind,[status(th)],[])).
% 0.47/0.55 tff(176,plain,
% 0.47/0.55 (![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)))),
% 0.47/0.55 inference(quant_intro,[status(thm)],[175])).
% 0.47/0.55 tff(177,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/GEO008+0.ax','apart6')).
% 0.47/0.55 tff(178,plain,
% 0.47/0.55 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.47/0.55 tff(179,plain,
% 0.47/0.55 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.47/0.55 tff(180,plain,(
% 0.47/0.55 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.47/0.55 inference(skolemize,[status(sab)],[179])).
% 0.47/0.55 tff(181,plain,
% 0.47/0.55 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.47/0.55 tff(182,plain,
% 0.47/0.55 (((~![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(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(183,plain,
% 0.47/0.55 ((convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0))) <=> (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(184,plain,
% 0.47/0.55 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1))))),
% 0.47/0.55 inference(monotonicity,[status(thm)],[183])).
% 0.47/0.55 tff(185,plain,
% 0.47/0.55 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.47/0.55 inference(transitivity,[status(thm)],[184, 182])).
% 0.47/0.55 tff(186,plain,
% 0.47/0.55 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.47/0.55 inference(quant_inst,[status(thm)],[])).
% 0.47/0.55 tff(187,plain,
% 0.47/0.55 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.47/0.55 tff(188,plain,
% 0.47/0.55 ($false),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[187, 181, 171, 160, 140])).
% 0.47/0.55 % SZS output end Proof
%------------------------------------------------------------------------------