%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO222+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 : Sat Jun 21 05:06:01 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO222+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:42:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(unorthogonal_lines_type, type, (
% 0.19/0.39 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_L_0_type, type, (
% 0.19/0.39 tptp_fun_L_0: $i)).
% 0.19/0.39 tff(orthogonal_through_point_type, type, (
% 0.19/0.39 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_A_1_type, type, (
% 0.19/0.39 tptp_fun_A_1: $i)).
% 0.19/0.39 tff(convergent_lines_type, type, (
% 0.19/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.39 tff(distinct_lines_type, type, (
% 0.19/0.39 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.39 tff(apart_point_and_line_type, type, (
% 0.19/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (((~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)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(15,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart3')).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.39 tff(17,plain,(
% 0.19/0.39 ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.39 inference(skolemize,[status(sab)],[16])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(L!0, L!0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (~convergent_lines(L!0, L!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))) | convergent_lines(L!0, L!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,assumption,(~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)), introduced(assumption)).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 ((~![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)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[24, 7])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(29,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.40 tff(31,plain,(
% 0.19/0.40 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.40 inference(skolemize,[status(sab)],[30])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (((~![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 ((~![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)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((~![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))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[35, 32, 25])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.40 tff(42,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.40 tff(45,plain,(
% 0.19/0.40 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.40 inference(skolemize,[status(sab)],[44])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_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(orthogonal_through_point(L!0, A!1), 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(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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_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(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_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(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(54,axiom,(![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc2')).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.40 tff(56,plain,(
% 0.19/0.40 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[55])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (~apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((~![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)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (~apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.40 tff(67,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/sandbox/benchmark/Axioms/GEO006+3.ax','ouo1')).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.40 tff(70,plain,(
% 0.19/0.40 ![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)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[69])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (((~![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)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(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)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((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(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(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)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~![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(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(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)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[73])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (((~![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(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(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)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.19/0.40 inference(transitivity,[status(thm)],[74, 72])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~![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(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[77, 71, 9, 61, 59, 50, 23])).
% 0.19/0.40 tff(79,plain,(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 ((~![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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(81,axiom,(~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[82, 80])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.19/0.41 tff(86,plain,(
% 0.19/0.41 convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.19/0.41 inference(skolemize,[status(sab)],[85])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.41 tff(92,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.19/0.41 tff(95,plain,(
% 0.19/0.41 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[94])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (((~![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(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))) <=> ((~![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(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ((convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (((~![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), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[98])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (((~![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), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.19/0.41 inference(transitivity,[status(thm)],[99, 97])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 ((~![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), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 ((~![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(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(L!0, L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[102, 96, 86, 20])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[105])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[106, 104])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[109, 71, 25, 59])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(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)) | distinct_lines(X, Y))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (~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))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[113, 46, 110])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (((~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))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 ((~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)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[117])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[119])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (^[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))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[122])).
% 0.19/0.42 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/sandbox/benchmark/Axioms/GEO006+3.ax','oac1')).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.19/0.42 tff(127,plain,(
% 0.19/0.42 ![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))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[126])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 118])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (((~![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))) | (~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(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), L!0)) | (~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)))) | (~((~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(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), L!0)) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 (((~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))) <=> ((~((~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(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), L!0)) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (((~![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)))) | ((~((~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(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), L!0)) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[131])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (((~![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)))) | (~((~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(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), L!0)) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[132, 130])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((~![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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((~![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))) | (~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(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), L!0)) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 ((~((~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(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[135, 129, 116, 103])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (~((~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))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[136, 79])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (((~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))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (((~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))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 ((~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)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[140, 25])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (((~![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 ((~![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(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))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(144,plain,
% 0.19/0.43 ((~![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(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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 ((~((~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)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[144, 129, 86, 141])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 (~((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[145, 139])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 (((~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))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 (unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 (((~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))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(150,plain,
% 0.19/0.43 (convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[149, 146])).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 (((~![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(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)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 (((~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)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 (((~![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(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))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[152])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (((~![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(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)))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[153, 151])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 ((~![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(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))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[156, 129, 150, 148, 22, 11])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------