%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO230+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:03 AM UTC 2025
% Result : Theorem 0.18s 0.45s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO230+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 14:42:48 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.45 % SZS status Theorem
% 0.18/0.45 % SZS output start Proof
% 0.18/0.45 tff(unequally_directed_lines_type, type, (
% 0.18/0.45 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.18/0.45 tff(line_connecting_type, type, (
% 0.18/0.45 line_connecting: ( $i * $i ) > $i)).
% 0.18/0.45 tff(tptp_fun_A_1_type, type, (
% 0.18/0.45 tptp_fun_A_1: $i)).
% 0.18/0.45 tff(reverse_line_type, type, (
% 0.18/0.45 reverse_line: $i > $i)).
% 0.18/0.45 tff(tptp_fun_B_0_type, type, (
% 0.18/0.45 tptp_fun_B_0: $i)).
% 0.18/0.45 tff(distinct_lines_type, type, (
% 0.18/0.45 distinct_lines: ( $i * $i ) > $o)).
% 0.18/0.45 tff(left_apart_point_type, type, (
% 0.18/0.45 left_apart_point: ( $i * $i ) > $o)).
% 0.18/0.45 tff(apart_point_and_line_type, type, (
% 0.18/0.45 apart_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.45 tff(distinct_points_type, type, (
% 0.18/0.45 distinct_points: ( $i * $i ) > $o)).
% 0.18/0.45 tff(left_convergent_lines_type, type, (
% 0.18/0.45 left_convergent_lines: ( $i * $i ) > $o)).
% 0.18/0.45 tff(1,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))), introduced(assumption)).
% 0.18/0.45 tff(2,assumption,((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0))))), introduced(assumption)).
% 0.18/0.45 tff(3,assumption,(~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))), introduced(assumption)).
% 0.18/0.45 tff(4,plain,
% 0.18/0.45 (^[A: $i, B: $i] : refl((~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(5,plain,
% 0.18/0.45 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.45 tff(6,plain,
% 0.18/0.45 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(7,axiom,(![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oagco9')).
% 0.18/0.45 tff(8,plain,
% 0.18/0.45 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.18/0.45 tff(9,plain,(
% 0.18/0.45 ![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[8])).
% 0.18/0.45 tff(10,plain,
% 0.18/0.45 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.45 tff(11,plain,
% 0.18/0.45 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(12,plain,
% 0.18/0.45 (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.18/0.45 tff(13,plain,
% 0.18/0.45 (^[L: $i, M: $i, N: $i] : refl((unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(14,plain,
% 0.18/0.45 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.45 tff(15,plain,
% 0.18/0.45 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(16,plain,
% 0.18/0.45 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(L, N) | unequally_directed_lines(M, N)) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))))), rewrite((unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(17,plain,
% 0.18/0.45 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.45 tff(18,axiom,(![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag6')).
% 0.18/0.45 tff(19,plain,
% 0.18/0.45 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.45 tff(20,plain,
% 0.18/0.45 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.45 tff(21,plain,(
% 0.18/0.45 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.45 inference(skolemize,[status(sab)],[20])).
% 0.18/0.45 tff(22,plain,
% 0.18/0.45 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.45 tff(23,plain,
% 0.18/0.45 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(24,plain,
% 0.18/0.45 ((unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)))) <=> (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(25,plain,
% 0.18/0.45 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.45 tff(26,plain,
% 0.18/0.45 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[25, 23])).
% 0.18/0.45 tff(27,plain,
% 0.18/0.45 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(28,plain,
% 0.18/0.45 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.45 tff(29,plain,
% 0.18/0.45 (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[28, 22, 12])).
% 0.18/0.45 tff(30,plain,
% 0.18/0.45 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(31,plain,
% 0.18/0.45 ((unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0)))) <=> (unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(32,plain,
% 0.18/0.45 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0)))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[31])).
% 0.18/0.45 tff(33,plain,
% 0.18/0.45 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[32, 30])).
% 0.18/0.45 tff(34,plain,
% 0.18/0.45 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(35,plain,
% 0.18/0.45 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.45 tff(36,plain,
% 0.18/0.45 (~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[35, 22, 29, 3])).
% 0.18/0.45 tff(37,plain,
% 0.18/0.45 (((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0))))) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(38,plain,
% 0.18/0.45 ((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.18/0.45 tff(39,assumption,(~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))), introduced(assumption)).
% 0.18/0.45 tff(40,assumption,(distinct_points(A!1, A!1)), introduced(assumption)).
% 0.18/0.45 tff(41,plain,
% 0.18/0.45 (^[A: $i] : refl((~distinct_points(A, A)) <=> (~distinct_points(A, A)))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(42,plain,
% 0.18/0.45 (![A: $i] : (~distinct_points(A, A)) <=> ![A: $i] : (~distinct_points(A, A))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[41])).
% 0.18/0.45 tff(43,plain,
% 0.18/0.45 (![A: $i] : (~distinct_points(A, A)) <=> ![A: $i] : (~distinct_points(A, A))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(44,axiom,(![A: $i] : (~distinct_points(A, A))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag1')).
% 0.18/0.45 tff(45,plain,
% 0.18/0.45 (![A: $i] : (~distinct_points(A, A))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.45 tff(46,plain,(
% 0.18/0.45 ![A: $i] : (~distinct_points(A, A))),
% 0.18/0.45 inference(skolemize,[status(sab)],[45])).
% 0.18/0.45 tff(47,plain,
% 0.18/0.45 (![A: $i] : (~distinct_points(A, A))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.18/0.45 tff(48,plain,
% 0.18/0.45 ((~![A: $i] : (~distinct_points(A, A))) | (~distinct_points(A!1, A!1))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(49,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[48, 47, 40])).
% 0.18/0.45 tff(50,plain,(~distinct_points(A!1, A!1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(51,plain,
% 0.18/0.45 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~distinct_lines(line_connecting(A, B), line_connecting(B, A))) & (~unequally_directed_lines(line_connecting(B, A), line_connecting(A, B)))))) <=> (~![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~distinct_lines(line_connecting(A, B), line_connecting(B, A))) & (~unequally_directed_lines(line_connecting(B, A), line_connecting(A, B))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(52,plain,
% 0.18/0.45 ((~![A: $i, B: $i] : (distinct_points(A, B) => ((~distinct_lines(line_connecting(A, B), line_connecting(B, A))) & (~unequally_directed_lines(line_connecting(B, A), line_connecting(A, B)))))) <=> (~![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~distinct_lines(line_connecting(A, B), line_connecting(B, A))) & (~unequally_directed_lines(line_connecting(B, A), line_connecting(A, B))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(53,axiom,(~![A: $i, B: $i] : (distinct_points(A, B) => ((~distinct_lines(line_connecting(A, B), line_connecting(B, A))) & (~unequally_directed_lines(line_connecting(B, A), line_connecting(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.18/0.45 tff(54,plain,
% 0.18/0.45 (~![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~distinct_lines(line_connecting(A, B), line_connecting(B, A))) & (~unequally_directed_lines(line_connecting(B, A), line_connecting(A, B)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.18/0.45 tff(55,plain,
% 0.18/0.45 (~![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~distinct_lines(line_connecting(A, B), line_connecting(B, A))) & (~unequally_directed_lines(line_connecting(B, A), line_connecting(A, B)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.18/0.45 tff(56,plain,
% 0.18/0.45 (~![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~distinct_lines(line_connecting(A, B), line_connecting(B, A))) & (~unequally_directed_lines(line_connecting(B, A), line_connecting(A, B)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.18/0.45 tff(57,plain,
% 0.18/0.45 (~![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~distinct_lines(line_connecting(A, B), line_connecting(B, A))) & (~unequally_directed_lines(line_connecting(B, A), line_connecting(A, B)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.18/0.45 tff(58,plain,(
% 0.18/0.45 ~((~distinct_points(A!1, B!0)) | ((~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) & (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0)))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[57])).
% 0.18/0.45 tff(59,plain,
% 0.18/0.45 (distinct_points(A!1, B!0)),
% 0.18/0.45 inference(or_elim,[status(thm)],[58])).
% 0.18/0.45 tff(60,plain,
% 0.18/0.45 (^[A: $i, B: $i, C: $i] : refl((distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(61,plain,
% 0.18/0.45 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[60])).
% 0.18/0.45 tff(62,plain,
% 0.18/0.45 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(63,plain,
% 0.18/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((distinct_points(A, C) | distinct_points(B, C)) <=> (distinct_points(A, C) | distinct_points(B, C))), ((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))))), rewrite((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))), ((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(64,plain,
% 0.18/0.45 (![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[63])).
% 0.18/0.45 tff(65,axiom,(![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag2')).
% 0.18/0.45 tff(66,plain,
% 0.18/0.45 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.45 tff(67,plain,
% 0.18/0.45 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.18/0.45 tff(68,plain,(
% 0.18/0.45 ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.18/0.45 inference(skolemize,[status(sab)],[67])).
% 0.18/0.45 tff(69,plain,
% 0.18/0.45 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.18/0.45 tff(70,plain,
% 0.18/0.45 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | ((~distinct_points(A!1, B!0)) | distinct_points(B!0, A!1) | distinct_points(A!1, A!1))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!1, B!0)) | distinct_points(B!0, A!1) | distinct_points(A!1, A!1))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(71,plain,
% 0.18/0.45 ((distinct_points(A!1, A!1) | distinct_points(B!0, A!1) | (~distinct_points(A!1, B!0))) <=> ((~distinct_points(A!1, B!0)) | distinct_points(B!0, A!1) | distinct_points(A!1, A!1))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(72,plain,
% 0.18/0.45 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!1, A!1) | distinct_points(B!0, A!1) | (~distinct_points(A!1, B!0)))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | ((~distinct_points(A!1, B!0)) | distinct_points(B!0, A!1) | distinct_points(A!1, A!1)))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[71])).
% 0.18/0.45 tff(73,plain,
% 0.18/0.45 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!1, A!1) | distinct_points(B!0, A!1) | (~distinct_points(A!1, B!0)))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!1, B!0)) | distinct_points(B!0, A!1) | distinct_points(A!1, A!1))),
% 0.18/0.45 inference(transitivity,[status(thm)],[72, 70])).
% 0.18/0.45 tff(74,plain,
% 0.18/0.45 ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!1, A!1) | distinct_points(B!0, A!1) | (~distinct_points(A!1, B!0)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(75,plain,
% 0.18/0.45 ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!1, B!0)) | distinct_points(B!0, A!1) | distinct_points(A!1, A!1)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.18/0.45 tff(76,plain,
% 0.18/0.45 (distinct_points(B!0, A!1) | distinct_points(A!1, A!1)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[75, 69, 59])).
% 0.18/0.45 tff(77,plain,
% 0.18/0.45 (distinct_points(B!0, A!1)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[76, 50])).
% 0.18/0.45 tff(78,plain,
% 0.18/0.45 (^[A: $i, B: $i] : refl(((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))) <=> ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(79,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[78])).
% 0.18/0.45 tff(80,plain,
% 0.18/0.45 (^[A: $i, B: $i] : rewrite(((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(81,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.18/0.45 tff(82,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(83,plain,
% 0.18/0.45 (^[A: $i, B: $i] : rewrite((distinct_points(A, B) => ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(84,plain,
% 0.18/0.45 (![A: $i, B: $i] : (distinct_points(A, B) => ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.45 tff(85,axiom,(![A: $i, B: $i] : (distinct_points(A, B) => ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oagco5')).
% 0.18/0.45 tff(86,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.45 tff(87,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.18/0.45 tff(88,plain,(
% 0.18/0.45 ![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[87])).
% 0.18/0.45 tff(89,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.18/0.45 tff(90,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.18/0.45 tff(91,plain,
% 0.18/0.45 (((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | ((~distinct_points(B!0, A!1)) | (~(apart_point_and_line(A!1, line_connecting(B!0, A!1)) | apart_point_and_line(B!0, line_connecting(B!0, A!1)))))) <=> ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | (~distinct_points(B!0, A!1)) | (~(apart_point_and_line(A!1, line_connecting(B!0, A!1)) | apart_point_and_line(B!0, line_connecting(B!0, A!1)))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(92,plain,
% 0.18/0.45 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | ((~distinct_points(B!0, A!1)) | (~(apart_point_and_line(A!1, line_connecting(B!0, A!1)) | apart_point_and_line(B!0, line_connecting(B!0, A!1)))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(93,plain,
% 0.18/0.46 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | (~distinct_points(B!0, A!1)) | (~(apart_point_and_line(A!1, line_connecting(B!0, A!1)) | apart_point_and_line(B!0, line_connecting(B!0, A!1))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.18/0.46 tff(94,plain,
% 0.18/0.46 ((~distinct_points(B!0, A!1)) | (~(apart_point_and_line(A!1, line_connecting(B!0, A!1)) | apart_point_and_line(B!0, line_connecting(B!0, A!1))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[93, 90])).
% 0.18/0.46 tff(95,plain,
% 0.18/0.46 (~(apart_point_and_line(A!1, line_connecting(B!0, A!1)) | apart_point_and_line(B!0, line_connecting(B!0, A!1)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[94, 77])).
% 0.18/0.46 tff(96,plain,
% 0.18/0.46 ((apart_point_and_line(A!1, line_connecting(B!0, A!1)) | apart_point_and_line(B!0, line_connecting(B!0, A!1))) | (~apart_point_and_line(A!1, line_connecting(B!0, A!1)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(97,plain,
% 0.18/0.46 (~apart_point_and_line(A!1, line_connecting(B!0, A!1))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.18/0.46 tff(98,assumption,(~(apart_point_and_line(A!1, line_connecting(B!0, A!1)) <=> (left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1)))))), introduced(assumption)).
% 0.18/0.46 tff(99,plain,
% 0.18/0.46 (^[A: $i, L: $i] : refl((apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(100,plain,
% 0.18/0.46 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.46 tff(101,plain,
% 0.18/0.46 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(102,axiom,(![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','apt_def')).
% 0.18/0.46 tff(103,plain,
% 0.18/0.46 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.46 tff(104,plain,(
% 0.18/0.46 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.18/0.46 inference(skolemize,[status(sab)],[103])).
% 0.18/0.46 tff(105,plain,
% 0.18/0.46 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.18/0.46 tff(106,plain,
% 0.18/0.46 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (apart_point_and_line(A!1, line_connecting(B!0, A!1)) <=> (left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1)))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(107,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[106, 105, 98])).
% 0.18/0.46 tff(108,plain,(apart_point_and_line(A!1, line_connecting(B!0, A!1)) <=> (left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(109,plain,
% 0.18/0.46 ((~(apart_point_and_line(A!1, line_connecting(B!0, A!1)) <=> (left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1)))))) | apart_point_and_line(A!1, line_connecting(B!0, A!1)) | (~(left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1)))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(110,plain,
% 0.18/0.46 (apart_point_and_line(A!1, line_connecting(B!0, A!1)) | (~(left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.18/0.46 tff(111,plain,
% 0.18/0.46 (~(left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[110, 97])).
% 0.18/0.46 tff(112,assumption,(~(left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))))), introduced(assumption)).
% 0.18/0.46 tff(113,plain,
% 0.18/0.46 ((left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1)))) | (~left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(114,plain,
% 0.18/0.46 (~left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.18/0.46 tff(115,plain,
% 0.18/0.46 ((left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1)))) | (~left_apart_point(A!1, line_connecting(B!0, A!1)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(116,plain,
% 0.18/0.46 (~left_apart_point(A!1, line_connecting(B!0, A!1))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[115, 112])).
% 0.18/0.46 tff(117,assumption,(distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))), introduced(assumption)).
% 0.18/0.46 tff(118,assumption,(~left_apart_point(A!1, line_connecting(B!0, A!1))), introduced(assumption)).
% 0.18/0.46 tff(119,assumption,(~left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1)))), introduced(assumption)).
% 0.18/0.46 tff(120,plain,
% 0.18/0.46 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (apart_point_and_line(A!1, line_connecting(A!1, B!0)) <=> (left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0)))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(121,plain,
% 0.18/0.46 (apart_point_and_line(A!1, line_connecting(A!1, B!0)) <=> (left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[120, 105])).
% 0.18/0.46 tff(122,plain,
% 0.18/0.46 (((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | ((~distinct_points(A!1, B!0)) | (~(apart_point_and_line(B!0, line_connecting(A!1, B!0)) | apart_point_and_line(A!1, line_connecting(A!1, B!0)))))) <=> ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | (~distinct_points(A!1, B!0)) | (~(apart_point_and_line(B!0, line_connecting(A!1, B!0)) | apart_point_and_line(A!1, line_connecting(A!1, B!0)))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(123,plain,
% 0.18/0.46 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | ((~distinct_points(A!1, B!0)) | (~(apart_point_and_line(B!0, line_connecting(A!1, B!0)) | apart_point_and_line(A!1, line_connecting(A!1, B!0)))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(124,plain,
% 0.18/0.46 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | (~distinct_points(A!1, B!0)) | (~(apart_point_and_line(B!0, line_connecting(A!1, B!0)) | apart_point_and_line(A!1, line_connecting(A!1, B!0))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.18/0.46 tff(125,plain,
% 0.18/0.46 (~(apart_point_and_line(B!0, line_connecting(A!1, B!0)) | apart_point_and_line(A!1, line_connecting(A!1, B!0)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[124, 90, 59])).
% 0.18/0.46 tff(126,plain,
% 0.18/0.46 ((apart_point_and_line(B!0, line_connecting(A!1, B!0)) | apart_point_and_line(A!1, line_connecting(A!1, B!0))) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(127,plain,
% 0.18/0.46 (~apart_point_and_line(A!1, line_connecting(A!1, B!0))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.18/0.46 tff(128,plain,
% 0.18/0.46 ((~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) <=> (left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0)))))) | apart_point_and_line(A!1, line_connecting(A!1, B!0)) | (~(left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0)))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(129,plain,
% 0.18/0.46 ((~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) <=> (left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0)))))) | (~(left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.18/0.46 tff(130,plain,
% 0.18/0.46 (~(left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[129, 121])).
% 0.18/0.46 tff(131,plain,
% 0.18/0.46 ((left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0)))) | (~left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(132,plain,
% 0.18/0.46 (~left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.18/0.46 tff(133,plain,
% 0.18/0.46 ((left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0)))) | (~left_apart_point(A!1, line_connecting(A!1, B!0)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(134,plain,
% 0.18/0.46 (~left_apart_point(A!1, line_connecting(A!1, B!0))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[133, 130])).
% 0.18/0.46 tff(135,plain,
% 0.18/0.46 (^[A: $i, B: $i, L: $i, M: $i] : refl((left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(136,plain,
% 0.18/0.46 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[135])).
% 0.18/0.46 tff(137,plain,
% 0.18/0.46 (^[A: $i, B: $i, L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(A, B) & distinct_lines(L, M)) <=> (~((~distinct_points(A, B)) | (~distinct_lines(L, M))))), ((~(distinct_points(A, B) & distinct_lines(L, M))) <=> (~(~((~distinct_points(A, B)) | (~distinct_lines(L, M))))))), rewrite((~(~((~distinct_points(A, B)) | (~distinct_lines(L, M))))) <=> ((~distinct_points(A, B)) | (~distinct_lines(L, M)))), ((~(distinct_points(A, B) & distinct_lines(L, M))) <=> ((~distinct_points(A, B)) | (~distinct_lines(L, M))))), ((left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | ((~distinct_points(A, B)) | (~distinct_lines(L, M)))))), rewrite((left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | ((~distinct_points(A, B)) | (~distinct_lines(L, M)))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))), ((left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(138,plain,
% 0.18/0.46 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[137])).
% 0.18/0.46 tff(139,plain,
% 0.18/0.46 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(140,plain,
% 0.18/0.46 (^[A: $i, B: $i, L: $i, M: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((left_apart_point(A, L) | left_apart_point(B, L)) <=> (left_apart_point(B, L) | left_apart_point(A, L))), (((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) <=> ((left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, M)))), rewrite(((left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, M)) <=> (left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), (((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) <=> (left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), ((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) <=> ((left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, M)))), rewrite(((left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, M)) <=> (left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), ((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) <=> (left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), (((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) <=> ((left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(L))))), rewrite(((left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), (((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), ((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) <=> ((left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(L))))), rewrite(((left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), ((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) <=> ((left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(M))))), rewrite(((left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(M))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), ((((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M))) <=> ((left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(M))))), rewrite(((left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(M))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), ((((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), (((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M)))) <=> ((distinct_points(A, B) & distinct_lines(L, M)) => (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))))), rewrite(((distinct_points(A, B) & distinct_lines(L, M)) => (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))), (((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M)))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(141,plain,
% 0.18/0.46 (![A: $i, B: $i, L: $i, M: $i] : ((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M)))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[140])).
% 0.18/0.46 tff(142,axiom,(![A: $i, B: $i, L: $i, M: $i] : ((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oaguc1')).
% 0.18/0.46 tff(143,plain,
% 0.18/0.46 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.18/0.46 tff(144,plain,
% 0.18/0.46 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.18/0.46 tff(145,plain,(
% 0.18/0.46 ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.18/0.46 inference(skolemize,[status(sab)],[144])).
% 0.18/0.46 tff(146,plain,
% 0.18/0.46 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.18/0.46 tff(147,plain,
% 0.18/0.46 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[146, 136])).
% 0.18/0.46 tff(148,plain,
% 0.18/0.46 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | ((~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~distinct_points(A!1, A!1)))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~distinct_points(A!1, A!1)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(149,plain,
% 0.18/0.46 ((left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | (~distinct_points(A!1, A!1)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)))) <=> ((~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~distinct_points(A!1, A!1)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(150,plain,
% 0.18/0.46 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | (~distinct_points(A!1, A!1)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | ((~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~distinct_points(A!1, A!1))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[149])).
% 0.18/0.46 tff(151,plain,
% 0.18/0.46 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | (~distinct_points(A!1, A!1)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~distinct_points(A!1, A!1)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[150, 148])).
% 0.18/0.46 tff(152,plain,
% 0.18/0.46 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | (~distinct_points(A!1, A!1)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(153,plain,
% 0.18/0.46 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~distinct_points(A!1, A!1))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.18/0.46 tff(154,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[153, 147, 117, 134, 132, 119, 118, 40])).
% 0.18/0.46 tff(155,plain,((~distinct_points(A!1, A!1)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(156,plain,
% 0.18/0.46 (~distinct_points(A!1, A!1)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[155, 114, 117, 116])).
% 0.18/0.46 tff(157,plain,
% 0.18/0.46 (distinct_points(B!0, A!1)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[76, 156])).
% 0.18/0.46 tff(158,plain,
% 0.18/0.46 (^[L: $i, M: $i] : refl((~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(159,plain,
% 0.18/0.46 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[158])).
% 0.18/0.46 tff(160,plain,
% 0.18/0.46 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(161,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag11')).
% 0.18/0.46 tff(162,plain,
% 0.18/0.46 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.18/0.46 tff(163,plain,(
% 0.18/0.46 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.18/0.46 inference(skolemize,[status(sab)],[162])).
% 0.18/0.46 tff(164,plain,
% 0.18/0.46 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.18/0.47 tff(165,plain,
% 0.18/0.47 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(reverse_line(line_connecting(B!0, A!1))))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(166,plain,
% 0.18/0.47 (~(left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(reverse_line(line_connecting(B!0, A!1)))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.18/0.47 tff(167,plain,
% 0.18/0.47 ((left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(reverse_line(line_connecting(B!0, A!1))))) | (~left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(168,plain,
% 0.18/0.47 (~left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.18/0.47 tff(169,plain,
% 0.18/0.47 (^[A: $i, B: $i, L: $i] : refl((left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L))) <=> (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(170,plain,
% 0.18/0.47 (![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L))) <=> ![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[169])).
% 0.18/0.47 tff(171,plain,
% 0.18/0.47 (^[A: $i, B: $i, L: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(A, B) & left_apart_point(A, L)) <=> (~((~distinct_points(A, B)) | (~left_apart_point(A, L))))), ((~(distinct_points(A, B) & left_apart_point(A, L))) <=> (~(~((~distinct_points(A, B)) | (~left_apart_point(A, L))))))), rewrite((~(~((~distinct_points(A, B)) | (~left_apart_point(A, L))))) <=> ((~distinct_points(A, B)) | (~left_apart_point(A, L)))), ((~(distinct_points(A, B) & left_apart_point(A, L))) <=> ((~distinct_points(A, B)) | (~left_apart_point(A, L))))), ((left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~(distinct_points(A, B) & left_apart_point(A, L)))) <=> (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | ((~distinct_points(A, B)) | (~left_apart_point(A, L)))))), rewrite((left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | ((~distinct_points(A, B)) | (~left_apart_point(A, L)))) <=> (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))), ((left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~(distinct_points(A, B) & left_apart_point(A, L)))) <=> (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(172,plain,
% 0.18/0.47 (![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~(distinct_points(A, B) & left_apart_point(A, L)))) <=> ![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[171])).
% 0.18/0.47 tff(173,plain,
% 0.18/0.47 (![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~(distinct_points(A, B) & left_apart_point(A, L)))) <=> ![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~(distinct_points(A, B) & left_apart_point(A, L))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(174,plain,
% 0.18/0.47 (^[A: $i, B: $i, L: $i] : rewrite(((distinct_points(A, B) & left_apart_point(A, L)) => (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L))) <=> (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~(distinct_points(A, B) & left_apart_point(A, L)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(175,plain,
% 0.18/0.47 (![A: $i, B: $i, L: $i] : ((distinct_points(A, B) & left_apart_point(A, L)) => (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L))) <=> ![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~(distinct_points(A, B) & left_apart_point(A, L))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[174])).
% 0.18/0.47 tff(176,axiom,(![A: $i, B: $i, L: $i] : ((distinct_points(A, B) & left_apart_point(A, L)) => (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oaguc2')).
% 0.18/0.47 tff(177,plain,
% 0.18/0.47 (![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~(distinct_points(A, B) & left_apart_point(A, L))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.18/0.47 tff(178,plain,
% 0.18/0.47 (![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~(distinct_points(A, B) & left_apart_point(A, L))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.18/0.47 tff(179,plain,(
% 0.18/0.47 ![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~(distinct_points(A, B) & left_apart_point(A, L))))),
% 0.18/0.47 inference(skolemize,[status(sab)],[178])).
% 0.18/0.47 tff(180,plain,
% 0.18/0.47 (![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.18/0.47 tff(181,plain,
% 0.18/0.47 (![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[180, 170])).
% 0.18/0.47 tff(182,plain,
% 0.18/0.47 (((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | ((~distinct_points(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1)))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))))) <=> ((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (~distinct_points(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1)))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(183,plain,
% 0.18/0.47 ((left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))) | (~distinct_points(B!0, A!1)) | (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))))) <=> ((~distinct_points(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1)))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(184,plain,
% 0.18/0.47 (((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))) | (~distinct_points(B!0, A!1)) | (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1)))))) <=> ((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | ((~distinct_points(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1)))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[183])).
% 0.18/0.47 tff(185,plain,
% 0.18/0.47 (((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))) | (~distinct_points(B!0, A!1)) | (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1)))))) <=> ((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (~distinct_points(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1)))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[184, 182])).
% 0.18/0.47 tff(186,plain,
% 0.18/0.47 ((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))) | (~distinct_points(B!0, A!1)) | (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(187,plain,
% 0.18/0.47 ((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (~distinct_points(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1)))) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.18/0.47 tff(188,plain,
% 0.18/0.47 ((~distinct_points(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[187, 181, 168])).
% 0.18/0.47 tff(189,plain,
% 0.18/0.47 (~left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[188, 157, 114])).
% 0.18/0.47 tff(190,plain,
% 0.18/0.47 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(191,plain,
% 0.18/0.47 (~(left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[190, 164])).
% 0.18/0.47 tff(192,plain,
% 0.18/0.47 ((left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | left_convergent_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(B!0, A!1)))) | (~left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(193,plain,
% 0.18/0.47 (~left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.18/0.47 tff(194,plain,
% 0.18/0.47 (((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | ((~distinct_points(B!0, A!1)) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~left_apart_point(B!0, line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)))) <=> ((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (~distinct_points(B!0, A!1)) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~left_apart_point(B!0, line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(195,plain,
% 0.18/0.47 ((left_apart_point(A!1, line_connecting(B!0, A!1)) | left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~distinct_points(B!0, A!1)) | (~left_apart_point(B!0, line_connecting(B!0, A!1)))) <=> ((~distinct_points(B!0, A!1)) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~left_apart_point(B!0, line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(196,plain,
% 0.18/0.47 (((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (left_apart_point(A!1, line_connecting(B!0, A!1)) | left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~distinct_points(B!0, A!1)) | (~left_apart_point(B!0, line_connecting(B!0, A!1))))) <=> ((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | ((~distinct_points(B!0, A!1)) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~left_apart_point(B!0, line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[195])).
% 0.18/0.47 tff(197,plain,
% 0.18/0.47 (((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (left_apart_point(A!1, line_connecting(B!0, A!1)) | left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~distinct_points(B!0, A!1)) | (~left_apart_point(B!0, line_connecting(B!0, A!1))))) <=> ((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (~distinct_points(B!0, A!1)) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~left_apart_point(B!0, line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[196, 194])).
% 0.18/0.47 tff(198,plain,
% 0.18/0.47 ((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (left_apart_point(A!1, line_connecting(B!0, A!1)) | left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~distinct_points(B!0, A!1)) | (~left_apart_point(B!0, line_connecting(B!0, A!1))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(199,plain,
% 0.18/0.47 ((~![A: $i, B: $i, L: $i] : (left_apart_point(B, L) | left_convergent_lines(line_connecting(A, B), L) | (~distinct_points(A, B)) | (~left_apart_point(A, L)))) | (~distinct_points(B!0, A!1)) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~left_apart_point(B!0, line_connecting(B!0, A!1))) | left_convergent_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.18/0.47 tff(200,plain,
% 0.18/0.47 ((~distinct_points(B!0, A!1)) | left_apart_point(A!1, line_connecting(B!0, A!1)) | (~left_apart_point(B!0, line_connecting(B!0, A!1)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[199, 181, 193])).
% 0.18/0.47 tff(201,plain,
% 0.18/0.47 (~left_apart_point(B!0, line_connecting(B!0, A!1))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[200, 157, 116])).
% 0.18/0.47 tff(202,plain,
% 0.18/0.47 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (apart_point_and_line(B!0, line_connecting(A!1, B!0)) <=> (left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(203,plain,
% 0.18/0.47 (apart_point_and_line(B!0, line_connecting(A!1, B!0)) <=> (left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[202, 105])).
% 0.18/0.47 tff(204,plain,
% 0.18/0.47 ((apart_point_and_line(B!0, line_connecting(A!1, B!0)) | apart_point_and_line(A!1, line_connecting(A!1, B!0))) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(205,plain,
% 0.18/0.47 (~apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[204, 125])).
% 0.18/0.47 tff(206,plain,
% 0.18/0.47 ((~(apart_point_and_line(B!0, line_connecting(A!1, B!0)) <=> (left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0)))))) | apart_point_and_line(B!0, line_connecting(A!1, B!0)) | (~(left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0)))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(207,plain,
% 0.18/0.47 ((~(apart_point_and_line(B!0, line_connecting(A!1, B!0)) <=> (left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0)))))) | (~(left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0)))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.18/0.47 tff(208,plain,
% 0.18/0.47 (~(left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[207, 203])).
% 0.18/0.47 tff(209,plain,
% 0.18/0.47 ((left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0)))) | (~left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(210,plain,
% 0.18/0.47 (~left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.18/0.47 tff(211,plain,
% 0.18/0.47 ((left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0)))) | (~left_apart_point(B!0, line_connecting(A!1, B!0)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(212,plain,
% 0.18/0.47 (~left_apart_point(B!0, line_connecting(A!1, B!0))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[211, 208])).
% 0.18/0.47 tff(213,plain,
% 0.18/0.47 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | ((~distinct_points(A!1, B!0)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, line_connecting(B!0, A!1)))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(A!1, B!0)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, line_connecting(B!0, A!1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(214,plain,
% 0.18/0.47 ((left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | (~distinct_points(A!1, B!0)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)))) <=> ((~distinct_points(A!1, B!0)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, line_connecting(B!0, A!1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(215,plain,
% 0.18/0.47 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | (~distinct_points(A!1, B!0)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | ((~distinct_points(A!1, B!0)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, line_connecting(B!0, A!1))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[214])).
% 0.18/0.47 tff(216,plain,
% 0.18/0.47 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | (~distinct_points(A!1, B!0)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(A!1, B!0)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, line_connecting(B!0, A!1)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[215, 213])).
% 0.18/0.47 tff(217,plain,
% 0.18/0.47 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(A!1, line_connecting(A!1, B!0)) | (~distinct_points(A!1, B!0)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(218,plain,
% 0.18/0.47 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(A!1, B!0)) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(A!1, B!0)) | left_apart_point(A!1, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(B!0, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(line_connecting(A!1, B!0))) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, line_connecting(B!0, A!1))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.18/0.47 tff(219,plain,
% 0.18/0.47 (left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(B!0, reverse_line(line_connecting(B!0, A!1))) | left_apart_point(B!0, line_connecting(B!0, A!1))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[218, 147, 59, 117, 134, 132, 212, 210])).
% 0.18/0.47 tff(220,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[219, 201, 189, 116, 114])).
% 0.18/0.47 tff(221,plain,((left_apart_point(A!1, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(line_connecting(B!0, A!1)))) | (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(222,plain,
% 0.18/0.47 (~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[221, 111])).
% 0.18/0.48 tff(223,plain,
% 0.18/0.48 ((~(~(distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))))) <=> (distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(224,plain,
% 0.18/0.48 (((~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) & (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0)))) <=> (~(distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(225,plain,
% 0.18/0.48 ((~((~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) & (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))))) <=> (~(~(distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0)))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[224])).
% 0.18/0.48 tff(226,plain,
% 0.18/0.48 ((~((~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) & (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))))) <=> (distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[225, 223])).
% 0.18/0.48 tff(227,plain,
% 0.18/0.48 (~((~distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) & (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))))),
% 0.18/0.48 inference(or_elim,[status(thm)],[58])).
% 0.18/0.48 tff(228,plain,
% 0.18/0.48 (distinct_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.18/0.48 tff(229,plain,
% 0.18/0.48 (unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[228, 222])).
% 0.18/0.48 tff(230,plain,
% 0.18/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(231,plain,
% 0.18/0.48 ((unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0)))) <=> ((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(232,plain,
% 0.18/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[231])).
% 0.18/0.48 tff(233,plain,
% 0.18/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[232, 230])).
% 0.18/0.48 tff(234,plain,
% 0.18/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(235,plain,
% 0.18/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.18/0.48 tff(236,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[235, 22, 229, 3, 39])).
% 0.18/0.48 tff(237,plain,(unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(238,plain,
% 0.18/0.48 (unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[237, 3])).
% 0.18/0.48 tff(239,plain,
% 0.18/0.48 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(240,plain,
% 0.18/0.48 (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[239, 10])).
% 0.18/0.48 tff(241,plain,
% 0.18/0.48 (((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(242,plain,
% 0.18/0.48 ((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.18/0.48 tff(243,plain,
% 0.18/0.48 (^[L: $i, M: $i, N: $i] : refl(((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(244,plain,
% 0.18/0.48 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[243])).
% 0.18/0.48 tff(245,plain,
% 0.18/0.48 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) <=> (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N)))))), rewrite((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) <=> (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))), trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite(((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(246,plain,
% 0.18/0.48 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[245])).
% 0.18/0.48 tff(247,plain,
% 0.18/0.48 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(248,plain,
% 0.18/0.48 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite(((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))))), rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(249,plain,
% 0.18/0.48 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[248])).
% 0.18/0.48 tff(250,axiom,(![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag7')).
% 0.18/0.48 tff(251,plain,
% 0.18/0.48 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.18/0.48 tff(252,plain,
% 0.18/0.48 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.18/0.48 tff(253,plain,(
% 0.18/0.48 ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.48 inference(skolemize,[status(sab)],[252])).
% 0.18/0.48 tff(254,plain,
% 0.18/0.48 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.18/0.48 tff(255,plain,
% 0.18/0.48 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[254, 244])).
% 0.18/0.48 tff(256,plain,
% 0.18/0.48 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(257,plain,
% 0.18/0.48 (((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1))))) <=> ((~((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(258,plain,
% 0.18/0.48 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[257])).
% 0.18/0.48 tff(259,plain,
% 0.18/0.48 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[258, 256])).
% 0.18/0.48 tff(260,plain,
% 0.18/0.48 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1)))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(261,plain,
% 0.18/0.48 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.18/0.48 tff(262,plain,
% 0.18/0.48 (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[261, 255, 242, 238, 38])).
% 0.18/0.48 tff(263,plain,
% 0.18/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(264,plain,
% 0.18/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(265,plain,
% 0.18/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(A!1, A!1)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.18/0.48 tff(266,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[265, 22, 12, 238, 262])).
% 0.18/0.48 tff(267,plain,(unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(268,assumption,(~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1)))), introduced(assumption)).
% 0.18/0.48 tff(269,plain,
% 0.18/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(270,plain,
% 0.18/0.49 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(271,plain,
% 0.18/0.49 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.18/0.49 tff(272,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[271, 22, 12, 268, 267])).
% 0.18/0.49 tff(273,plain,(unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(274,plain,
% 0.18/0.49 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(275,plain,
% 0.18/0.49 (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[274, 10])).
% 0.18/0.49 tff(276,plain,
% 0.18/0.49 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(277,plain,
% 0.18/0.49 ((unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)))) <=> (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(278,plain,
% 0.18/0.49 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[277])).
% 0.18/0.49 tff(279,plain,
% 0.18/0.49 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[278, 276])).
% 0.18/0.49 tff(280,plain,
% 0.18/0.49 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(281,plain,
% 0.18/0.49 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.18/0.49 tff(282,plain,
% 0.18/0.49 (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[281, 22, 275])).
% 0.18/0.49 tff(283,plain,
% 0.18/0.49 (((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0))))) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(284,plain,
% 0.18/0.49 ((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.18/0.49 tff(285,plain,
% 0.18/0.49 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(286,plain,
% 0.18/0.49 (((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1))))) <=> ((~((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(287,plain,
% 0.18/0.49 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0))))))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[286])).
% 0.18/0.49 tff(288,plain,
% 0.18/0.49 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[287, 285])).
% 0.18/0.49 tff(289,plain,
% 0.18/0.49 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1)))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(290,plain,
% 0.18/0.49 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, A!1))) | (~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0))))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.18/0.49 tff(291,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[290, 255, 284, 273, 267, 2])).
% 0.18/0.49 tff(292,plain,(~((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(293,plain,
% 0.18/0.49 (((~unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0))))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(294,plain,
% 0.18/0.49 (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[293, 292])).
% 0.18/0.49 tff(295,plain,
% 0.18/0.49 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(296,plain,
% 0.18/0.49 ((unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0))))) <=> (unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(297,plain,
% 0.18/0.49 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0))))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[296])).
% 0.18/0.49 tff(298,plain,
% 0.18/0.49 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[297, 295])).
% 0.18/0.49 tff(299,plain,
% 0.18/0.49 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0)))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(300,plain,
% 0.18/0.49 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), line_connecting(A!1, A!1)) | unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.18/0.49 tff(301,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[300, 22, 29, 294, 1])).
% 0.18/0.49 tff(302,plain,(unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(303,plain,
% 0.18/0.49 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(304,plain,
% 0.18/0.49 ((~(left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))))) <=> (~(left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(305,plain,
% 0.18/0.49 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[304])).
% 0.18/0.49 tff(306,plain,
% 0.18/0.49 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[305, 303])).
% 0.18/0.49 tff(307,plain,
% 0.18/0.49 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(308,plain,
% 0.18/0.49 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.18/0.49 tff(309,plain,
% 0.18/0.49 (~(left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[308, 164])).
% 0.18/0.49 tff(310,plain,
% 0.18/0.49 ((left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))) | (~left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(311,plain,
% 0.18/0.49 (~left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[310, 309])).
% 0.18/0.49 tff(312,plain,
% 0.18/0.49 ((left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))) | (~left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(313,plain,
% 0.18/0.49 (~left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[312, 309])).
% 0.18/0.49 tff(314,plain,
% 0.18/0.49 (^[L: $i, M: $i] : refl((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(315,plain,
% 0.18/0.49 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[314])).
% 0.18/0.49 tff(316,plain,
% 0.18/0.49 (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(317,plain,
% 0.18/0.49 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[316])).
% 0.18/0.49 tff(318,plain,
% 0.18/0.49 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(319,plain,
% 0.18/0.49 (^[L: $i, M: $i] : rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(320,plain,
% 0.18/0.49 (![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[319])).
% 0.18/0.49 tff(321,axiom,(![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag9')).
% 0.18/0.49 tff(322,plain,
% 0.18/0.49 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.18/0.49 tff(323,plain,
% 0.18/0.49 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[322, 318])).
% 0.18/0.49 tff(324,plain,(
% 0.18/0.49 ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.18/0.49 inference(skolemize,[status(sab)],[323])).
% 0.18/0.49 tff(325,plain,
% 0.18/0.49 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[324, 317])).
% 0.18/0.49 tff(326,plain,
% 0.18/0.49 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[325, 315])).
% 0.18/0.49 tff(327,plain,
% 0.18/0.49 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(328,plain,
% 0.18/0.49 ((left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(329,plain,
% 0.18/0.50 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[328])).
% 0.18/0.50 tff(330,plain,
% 0.18/0.50 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[329, 327])).
% 0.18/0.50 tff(331,plain,
% 0.18/0.50 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(332,plain,
% 0.18/0.50 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | left_convergent_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.18/0.50 tff(333,plain,
% 0.18/0.50 ((~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[332, 326, 313, 311])).
% 0.18/0.50 tff(334,plain,
% 0.18/0.50 (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[333, 302])).
% 0.18/0.50 tff(335,plain,
% 0.18/0.50 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(336,plain,
% 0.18/0.50 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(337,plain,
% 0.18/0.50 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, A!1), reverse_line(line_connecting(A!1, A!1))) | unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), reverse_line(line_connecting(A!1, A!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!1, B!0)), line_connecting(A!1, A!1)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.18/0.50 tff(338,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[337, 22, 12, 334, 302])).
% 0.18/0.50 % SZS output end Proof
% 0.18/0.50 % E exiting
%------------------------------------------------------------------------------