%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO223+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:06:02 AM UTC 2025
% Result : Theorem 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO223+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 14:42:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 % SZS output start Proof
% 0.21/0.46 tff(convergent_lines_type, type, (
% 0.21/0.46 convergent_lines: ( $i * $i ) > $o)).
% 0.21/0.46 tff(tptp_fun_L_0_type, type, (
% 0.21/0.46 tptp_fun_L_0: $i)).
% 0.21/0.46 tff(unorthogonal_lines_type, type, (
% 0.21/0.46 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.21/0.46 tff(parallel_through_point_type, type, (
% 0.21/0.46 parallel_through_point: ( $i * $i ) > $i)).
% 0.21/0.46 tff(tptp_fun_A_1_type, type, (
% 0.21/0.46 tptp_fun_A_1: $i)).
% 0.21/0.46 tff(orthogonal_through_point_type, type, (
% 0.21/0.46 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.21/0.46 tff(distinct_lines_type, type, (
% 0.21/0.46 distinct_lines: ( $i * $i ) > $o)).
% 0.21/0.46 tff(apart_point_and_line_type, type, (
% 0.21/0.46 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.46 tff(1,plain,
% 0.21/0.46 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(2,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.46 tff(3,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(4,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.21/0.46 tff(5,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.46 tff(6,plain,(
% 0.21/0.46 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.21/0.46 inference(skolemize,[status(sab)],[5])).
% 0.21/0.46 tff(7,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.46 tff(8,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(L!0, A!1), L!0))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(9,plain,
% 0.21/0.46 (~convergent_lines(parallel_through_point(L!0, A!1), L!0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.46 tff(10,plain,
% 0.21/0.46 (((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0))) | convergent_lines(parallel_through_point(L!0, A!1), L!0)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(11,plain,
% 0.21/0.46 ((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.21/0.46 tff(12,assumption,(~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)), introduced(assumption)).
% 0.21/0.46 tff(13,plain,
% 0.21/0.46 (^[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))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(14,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.46 tff(15,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(16,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')).
% 0.21/0.46 tff(17,plain,
% 0.21/0.46 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.46 tff(18,plain,(
% 0.21/0.46 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[17])).
% 0.21/0.46 tff(19,plain,
% 0.21/0.46 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.46 tff(20,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 (~apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(23,plain,
% 0.21/0.46 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(25,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.46 tff(27,plain,(
% 0.21/0.46 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.21/0.46 inference(skolemize,[status(sab)],[26])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.21/0.46 tff(31,plain,
% 0.21/0.46 (^[A: $i, L: $i, M: $i, N: $i] : refl((apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(32,plain,
% 0.21/0.46 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.46 tff(33,plain,
% 0.21/0.46 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(34,plain,
% 0.21/0.46 (^[A: $i, L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(A, L) | apart_point_and_line(A, M)) <=> (apart_point_and_line(A, M) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> ((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)))), rewrite(((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> ((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)))), rewrite(((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))))), rewrite((distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(35,plain,
% 0.21/0.46 (![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.46 tff(36,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')).
% 0.21/0.46 tff(37,plain,
% 0.21/0.46 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.46 tff(38,plain,
% 0.21/0.46 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.46 tff(39,plain,(
% 0.21/0.46 ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[38])).
% 0.21/0.46 tff(40,plain,
% 0.21/0.46 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (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))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(42,plain,
% 0.21/0.46 ((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))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 (((~![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)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[42])).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 (((~![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))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[43, 41])).
% 0.21/0.47 tff(45,plain,
% 0.21/0.47 ((~![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))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[46, 40, 30, 21])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(52,plain,
% 0.21/0.47 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.47 tff(53,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.21/0.47 tff(54,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.47 tff(55,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.21/0.47 tff(56,plain,(
% 0.21/0.47 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.47 inference(skolemize,[status(sab)],[55])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.21/0.47 tff(58,plain,
% 0.21/0.47 (((~![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(60,plain,
% 0.21/0.47 ((~![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))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.47 tff(61,plain,
% 0.21/0.47 (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[60, 57, 47])).
% 0.21/0.47 tff(62,plain,
% 0.21/0.47 (((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(63,plain,
% 0.21/0.47 ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.21/0.47 tff(64,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(65,plain,
% 0.21/0.47 (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[64, 28])).
% 0.21/0.47 tff(66,plain,
% 0.21/0.47 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(67,plain,
% 0.21/0.47 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.47 tff(68,plain,
% 0.21/0.47 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(69,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.21/0.47 tff(70,plain,
% 0.21/0.47 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.47 tff(71,plain,(
% 0.21/0.47 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.21/0.47 inference(skolemize,[status(sab)],[70])).
% 0.21/0.47 tff(72,plain,
% 0.21/0.47 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.21/0.47 tff(73,plain,
% 0.21/0.47 (((~![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(74,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(75,plain,
% 0.21/0.47 ((~![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))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.47 tff(76,plain,
% 0.21/0.47 (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[75, 72, 65])).
% 0.21/0.47 tff(77,plain,
% 0.21/0.47 (((~![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(78,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(79,plain,
% 0.21/0.47 ((~![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))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.47 tff(80,plain,
% 0.21/0.47 (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[79, 57, 76])).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(82,plain,
% 0.21/0.47 (~apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[81, 19])).
% 0.21/0.47 tff(83,plain,
% 0.21/0.47 (((~![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))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(84,plain,
% 0.21/0.47 ((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))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(85,plain,
% 0.21/0.47 (((~![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)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.47 tff(86,plain,
% 0.21/0.47 (((~![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))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[85, 83])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 ((~![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))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(88,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.47 tff(89,plain,
% 0.21/0.47 (~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))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[88, 40, 65, 82])).
% 0.21/0.47 tff(90,plain,
% 0.21/0.47 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(91,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.47 tff(92,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(93,plain,
% 0.21/0.47 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.48 tff(95,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart5')).
% 0.21/0.48 tff(96,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.21/0.48 tff(98,plain,(
% 0.21/0.48 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[97])).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 ((distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), 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)))) <=> (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[101])).
% 0.21/0.48 tff(103,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[102, 100])).
% 0.21/0.48 tff(104,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(105,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.48 tff(106,plain,
% 0.21/0.48 (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[105, 99, 89, 80])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.48 tff(109,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(110,plain,
% 0.21/0.48 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) <=> (apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> ((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)))), rewrite(((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))))), rewrite((distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(111,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[110])).
% 0.21/0.48 tff(112,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.21/0.48 tff(113,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.21/0.48 tff(115,plain,(
% 0.21/0.48 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[114])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (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)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | 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)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 ((convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | 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(orthogonal_through_point(L!0, A!1), A!1)))) <=> (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)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | 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(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (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)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.48 tff(120,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | 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(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | 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)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[119, 117])).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | 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(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(122,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | 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)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.48 tff(123,plain,
% 0.21/0.48 (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[122, 116, 21, 82, 106])).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 (((~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))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 ((~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)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[124, 65])).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 (^[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))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ![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)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (^[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)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 (^[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))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.48 tff(133,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')).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.48 tff(135,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.21/0.48 tff(136,plain,(
% 0.21/0.48 ![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))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[135])).
% 0.21/0.48 tff(137,plain,
% 0.21/0.48 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.21/0.48 tff(138,plain,
% 0.21/0.48 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[137, 127])).
% 0.21/0.49 tff(139,plain,
% 0.21/0.49 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(140,plain,
% 0.21/0.49 (((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(141,plain,
% 0.21/0.49 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.49 tff(142,plain,
% 0.21/0.49 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[141, 139])).
% 0.21/0.49 tff(143,plain,
% 0.21/0.49 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(144,plain,
% 0.21/0.49 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.21/0.49 tff(145,plain,
% 0.21/0.49 (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[144, 138, 125, 123, 63])).
% 0.21/0.49 tff(146,plain,
% 0.21/0.49 (((~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)),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(147,plain,
% 0.21/0.49 ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[146, 30])).
% 0.21/0.49 tff(148,assumption,(~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))), introduced(assumption)).
% 0.21/0.49 tff(149,plain,
% 0.21/0.49 (((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(150,plain,
% 0.21/0.49 (unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.21/0.49 tff(151,plain,
% 0.21/0.49 (((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(152,plain,
% 0.21/0.49 (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[151, 148])).
% 0.21/0.49 tff(153,plain,
% 0.21/0.49 (((~![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(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(154,plain,
% 0.21/0.49 (((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(155,plain,
% 0.21/0.49 (((~![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(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[154])).
% 0.21/0.49 tff(156,plain,
% 0.21/0.49 (((~![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(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[155, 153])).
% 0.21/0.49 tff(157,plain,
% 0.21/0.49 ((~![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(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(158,plain,
% 0.21/0.49 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.49 tff(159,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[158, 138, 152, 150, 11, 147])).
% 0.21/0.49 tff(160,plain,((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(161,plain,
% 0.21/0.49 (^[X: $i, Y: $i] : refl((~apart_point_and_line(X, parallel_through_point(Y, X))) <=> (~apart_point_and_line(X, parallel_through_point(Y, X))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(162,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[161])).
% 0.21/0.49 tff(163,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(164,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.21/0.49 tff(165,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.21/0.49 tff(166,plain,(
% 0.21/0.49 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[165])).
% 0.21/0.49 tff(167,plain,
% 0.21/0.49 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.21/0.49 tff(168,plain,
% 0.21/0.49 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(A!1, parallel_through_point(L!0, A!1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(169,plain,
% 0.21/0.49 (~apart_point_and_line(A!1, parallel_through_point(L!0, A!1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.21/0.49 tff(170,plain,
% 0.21/0.49 ((~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))) <=> (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(171,axiom,(~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.49 tff(172,plain,
% 0.21/0.49 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.21/0.49 tff(173,plain,
% 0.21/0.49 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[172, 170])).
% 0.21/0.49 tff(174,plain,
% 0.21/0.49 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[173, 170])).
% 0.21/0.49 tff(175,plain,
% 0.21/0.49 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.21/0.49 tff(176,plain,(
% 0.21/0.49 distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.21/0.49 inference(skolemize,[status(sab)],[175])).
% 0.21/0.49 tff(177,plain,
% 0.21/0.49 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (apart_point_and_line(A!1, parallel_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(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(A!1, parallel_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(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(178,plain,
% 0.21/0.49 ((convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> (apart_point_and_line(A!1, parallel_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(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(179,plain,
% 0.21/0.49 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (apart_point_and_line(A!1, parallel_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(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[178])).
% 0.21/0.49 tff(180,plain,
% 0.21/0.50 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(A!1, parallel_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(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[179, 177])).
% 0.21/0.50 tff(181,plain,
% 0.21/0.50 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(182,plain,
% 0.21/0.50 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(A!1, parallel_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(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.21/0.50 tff(183,plain,
% 0.21/0.50 (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[182, 116, 176, 169, 82])).
% 0.21/0.50 tff(184,plain,
% 0.21/0.50 (((~![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(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(185,plain,
% 0.21/0.50 (((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(186,plain,
% 0.21/0.50 (((~![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(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[185])).
% 0.21/0.50 tff(187,plain,
% 0.21/0.50 (((~![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(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[186, 184])).
% 0.21/0.50 tff(188,plain,
% 0.21/0.50 ((~![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(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(189,plain,
% 0.21/0.50 ((~![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(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.21/0.50 tff(190,plain,
% 0.21/0.50 ((~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[189, 138, 183, 125])).
% 0.21/0.50 tff(191,plain,
% 0.21/0.50 (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[190, 160])).
% 0.21/0.50 tff(192,plain,
% 0.21/0.50 (((~![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, parallel_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~![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, parallel_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(193,plain,
% 0.21/0.50 ((apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> (apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(194,plain,
% 0.21/0.50 (((~![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), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_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)))) | (apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[193])).
% 0.21/0.50 tff(195,plain,
% 0.21/0.50 (((~![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), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_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)))) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[194, 192])).
% 0.21/0.50 tff(196,plain,
% 0.21/0.50 ((~![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), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(197,plain,
% 0.21/0.50 ((~![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, parallel_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.21/0.50 tff(198,plain,
% 0.21/0.50 (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[197, 40, 169, 21, 191, 145])).
% 0.21/0.50 tff(199,plain,
% 0.21/0.50 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(parallel_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(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(200,plain,
% 0.21/0.50 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(201,plain,
% 0.21/0.50 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.21/0.50 tff(202,plain,
% 0.21/0.50 (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[201, 57, 198])).
% 0.21/0.50 tff(203,plain,
% 0.21/0.50 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(204,plain,
% 0.21/0.50 (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[203, 28])).
% 0.21/0.50 tff(205,plain,
% 0.21/0.50 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(206,plain,
% 0.21/0.50 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(207,plain,
% 0.21/0.50 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.21/0.50 tff(208,plain,
% 0.21/0.50 (convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[207, 72, 204])).
% 0.21/0.50 tff(209,plain,
% 0.21/0.50 (^[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))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(210,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[209])).
% 0.21/0.50 tff(211,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(212,plain,
% 0.21/0.50 (^[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)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(213,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[212])).
% 0.21/0.50 tff(214,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')).
% 0.21/0.50 tff(215,plain,
% 0.21/0.50 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.50 tff(216,plain,
% 0.21/0.50 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.21/0.50 tff(217,plain,(
% 0.21/0.50 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[216])).
% 0.21/0.50 tff(218,plain,
% 0.21/0.50 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[217, 210])).
% 0.21/0.50 tff(219,plain,
% 0.21/0.50 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(220,plain,
% 0.21/0.50 ((convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)))) <=> ((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(221,plain,
% 0.21/0.50 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_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(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[220])).
% 0.21/0.50 tff(222,plain,
% 0.21/0.50 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_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(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[221, 219])).
% 0.21/0.51 tff(223,plain,
% 0.21/0.51 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(224,plain,
% 0.21/0.51 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.21/0.51 tff(225,plain,
% 0.21/0.51 (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[224, 218, 208])).
% 0.21/0.51 tff(226,plain,
% 0.21/0.51 (convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[225, 202])).
% 0.21/0.51 tff(227,plain,
% 0.21/0.51 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(parallel_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(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(228,plain,
% 0.21/0.51 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(229,plain,
% 0.21/0.51 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.21/0.51 tff(230,plain,
% 0.21/0.51 (distinct_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[229, 57, 226])).
% 0.21/0.51 tff(231,plain,
% 0.21/0.51 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(A!1, orthogonal_through_point(parallel_through_point(L!0, A!1), A!1)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(232,plain,
% 0.21/0.51 (~apart_point_and_line(A!1, orthogonal_through_point(parallel_through_point(L!0, A!1), A!1))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[231, 19])).
% 0.21/0.51 tff(233,plain,
% 0.21/0.51 (((~![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(parallel_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0) | (~distinct_lines(orthogonal_through_point(parallel_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(parallel_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0) | (~distinct_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(234,plain,
% 0.21/0.51 ((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(parallel_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(parallel_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(parallel_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(parallel_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0) | (~distinct_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(235,plain,
% 0.21/0.51 (((~![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(parallel_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(parallel_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(parallel_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(parallel_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0) | (~distinct_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[234])).
% 0.21/0.51 tff(236,plain,
% 0.21/0.51 (((~![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(parallel_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(parallel_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(parallel_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(parallel_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0) | (~distinct_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[235, 233])).
% 0.21/0.51 tff(237,plain,
% 0.21/0.51 ((~![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(parallel_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(parallel_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(238,plain,
% 0.21/0.51 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(parallel_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0) | (~distinct_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.21/0.51 tff(239,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[238, 40, 30, 21, 232, 230, 12])).
% 0.21/0.51 tff(240,plain,(unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(241,plain,
% 0.21/0.51 (((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)))) | unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(242,plain,
% 0.21/0.51 ((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[241, 204])).
% 0.21/0.51 tff(243,plain,
% 0.21/0.51 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), L!0) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(parallel_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(parallel_through_point(L!0, A!1), L!0) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(244,plain,
% 0.21/0.51 ((convergent_lines(parallel_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1)))) <=> (convergent_lines(parallel_through_point(L!0, A!1), L!0) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(245,plain,
% 0.21/0.51 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_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(parallel_through_point(L!0, A!1), L!0) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[244])).
% 0.21/0.51 tff(246,plain,
% 0.21/0.51 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_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(parallel_through_point(L!0, A!1), L!0) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0))),
% 0.21/0.51 inference(transitivity,[status(thm)],[245, 243])).
% 0.21/0.51 tff(247,plain,
% 0.21/0.51 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(248,plain,
% 0.21/0.51 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(parallel_through_point(L!0, A!1), L!0) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.21/0.51 tff(249,plain,
% 0.21/0.51 (convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[248, 218, 9, 208])).
% 0.21/0.51 tff(250,plain,
% 0.21/0.51 (((~![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(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(251,plain,
% 0.21/0.51 (((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0))) <=> ((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(252,plain,
% 0.21/0.51 (((~![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(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(parallel_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(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1)))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[251])).
% 0.21/0.51 tff(253,plain,
% 0.21/0.51 (((~![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(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(parallel_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(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[252, 250])).
% 0.21/0.51 tff(254,plain,
% 0.21/0.51 ((~![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(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))))) | (~((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(255,plain,
% 0.21/0.51 ((~![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(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), parallel_through_point(L!0, A!1))))) | (~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.21/0.51 tff(256,plain,
% 0.21/0.51 ((~unorthogonal_lines(orthogonal_through_point(parallel_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[255, 138, 249, 242])).
% 0.21/0.51 tff(257,plain,
% 0.21/0.51 (~((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[256, 240])).
% 0.21/0.51 tff(258,plain,
% 0.21/0.51 (((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1)))) | unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(259,plain,
% 0.21/0.51 (unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.21/0.51 tff(260,plain,
% 0.21/0.51 (((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1)))) | convergent_lines(L!0, parallel_through_point(L!0, A!1))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(261,plain,
% 0.21/0.51 (convergent_lines(L!0, parallel_through_point(L!0, A!1))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[260, 257])).
% 0.21/0.51 tff(262,plain,
% 0.21/0.51 (((~![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(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))) | (~((~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(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(263,plain,
% 0.21/0.51 (((~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1)))) <=> ((~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(264,plain,
% 0.21/0.51 (((~![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, parallel_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, parallel_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(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[263])).
% 0.21/0.51 tff(265,plain,
% 0.21/0.51 (((~![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, parallel_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, parallel_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(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[264, 262])).
% 0.21/0.51 tff(266,plain,
% 0.21/0.51 ((~![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, parallel_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(267,plain,
% 0.21/0.52 ((~![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(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, parallel_through_point(L!0, A!1))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.21/0.52 tff(268,plain,
% 0.21/0.52 (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[267, 138, 261, 259, 11])).
% 0.21/0.52 tff(269,plain,
% 0.21/0.52 (((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))) | convergent_lines(L!0, L!0)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(270,plain,
% 0.21/0.52 (convergent_lines(L!0, L!0)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[269, 268])).
% 0.21/0.52 tff(271,plain,
% 0.21/0.52 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(272,plain,
% 0.21/0.52 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[271])).
% 0.21/0.52 tff(273,plain,
% 0.21/0.52 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(274,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart3')).
% 0.21/0.52 tff(275,plain,
% 0.21/0.52 (![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.21/0.52 tff(276,plain,(
% 0.21/0.52 ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.52 inference(skolemize,[status(sab)],[275])).
% 0.21/0.52 tff(277,plain,
% 0.21/0.52 (![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[276, 272])).
% 0.21/0.52 tff(278,plain,
% 0.21/0.52 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(L!0, L!0))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(279,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[278, 277, 270])).
% 0.21/0.52 % SZS output end Proof
% 0.21/0.52 % E exiting
%------------------------------------------------------------------------------