%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO234+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:04 AM UTC 2025
% Result : Theorem 8.73s 8.91s
% Output : Proof 8.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO234+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:43:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 8.73/8.91 % SZS status Theorem
% 8.73/8.91 % SZS output start Proof
% 8.73/8.91 tff(unequally_directed_lines_type, type, (
% 8.73/8.91 unequally_directed_lines: ( $i * $i ) > $o)).
% 8.73/8.91 tff(tptp_fun_M_1_type, type, (
% 8.73/8.91 tptp_fun_M_1: $i)).
% 8.73/8.91 tff(tptp_fun_N_0_type, type, (
% 8.73/8.91 tptp_fun_N_0: $i)).
% 8.73/8.91 tff(reverse_line_type, type, (
% 8.73/8.91 reverse_line: $i > $i)).
% 8.73/8.91 tff(parallel_through_point_type, type, (
% 8.73/8.91 parallel_through_point: ( $i * $i ) > $i)).
% 8.73/8.91 tff(tptp_fun_L_2_type, type, (
% 8.73/8.91 tptp_fun_L_2: $i)).
% 8.73/8.91 tff(equally_directed_lines_type, type, (
% 8.73/8.91 equally_directed_lines: ( $i * $i ) > $o)).
% 8.73/8.91 tff(unequally_directed_opposite_lines_type, type, (
% 8.73/8.91 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 8.73/8.91 tff(left_convergent_lines_type, type, (
% 8.73/8.91 left_convergent_lines: ( $i * $i ) > $o)).
% 8.73/8.91 tff(1,assumption,(~unequally_directed_lines(N!0, reverse_line(reverse_line(M!1)))), introduced(assumption)).
% 8.73/8.91 tff(2,assumption,(~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))), introduced(assumption)).
% 8.73/8.91 tff(3,plain,
% 8.73/8.91 (^[X: $i, Y: $i] : refl((~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))))),
% 8.73/8.91 inference(bind,[status(th)],[])).
% 8.73/8.91 tff(4,plain,
% 8.73/8.91 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 8.73/8.91 inference(quant_intro,[status(thm)],[3])).
% 8.73/8.91 tff(5,plain,
% 8.73/8.91 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(6,plain,
% 8.73/8.91 (^[X: $i, Y: $i] : trans(rewrite((equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))), rewrite((~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))), ((equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))))),
% 8.73/8.91 inference(bind,[status(th)],[])).
% 8.73/8.91 tff(7,plain,
% 8.73/8.91 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 8.73/8.91 inference(quant_intro,[status(thm)],[6])).
% 8.73/8.91 tff(8,axiom,(![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a4_defns')).
% 8.73/8.91 tff(9,plain,
% 8.73/8.91 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[8, 7])).
% 8.73/8.91 tff(10,plain,
% 8.73/8.91 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[9, 5])).
% 8.73/8.91 tff(11,plain,(
% 8.73/8.91 ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 8.73/8.91 inference(skolemize,[status(sab)],[10])).
% 8.73/8.91 tff(12,plain,
% 8.73/8.91 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[11, 4])).
% 8.73/8.91 tff(13,plain,
% 8.73/8.91 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)) <=> equally_directed_lines(reverse_line(M!1), reverse_line(M!1))))),
% 8.73/8.91 inference(quant_inst,[status(thm)],[])).
% 8.73/8.91 tff(14,plain,
% 8.73/8.91 (~(unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)) <=> equally_directed_lines(reverse_line(M!1), reverse_line(M!1)))),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[13, 12])).
% 8.73/8.91 tff(15,assumption,(~equally_directed_lines(reverse_line(M!1), reverse_line(M!1))), introduced(assumption)).
% 8.73/8.91 tff(16,plain,
% 8.73/8.91 (^[L: $i] : refl(equally_directed_lines(L, L) <=> equally_directed_lines(L, L))),
% 8.73/8.91 inference(bind,[status(th)],[])).
% 8.73/8.91 tff(17,plain,
% 8.73/8.91 (![L: $i] : equally_directed_lines(L, L) <=> ![L: $i] : equally_directed_lines(L, L)),
% 8.73/8.91 inference(quant_intro,[status(thm)],[16])).
% 8.73/8.91 tff(18,plain,
% 8.73/8.91 (![L: $i] : equally_directed_lines(L, L) <=> ![L: $i] : equally_directed_lines(L, L)),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(19,axiom,(![L: $i] : equally_directed_lines(L, L)), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax5_basics')).
% 8.73/8.91 tff(20,plain,
% 8.73/8.91 (![L: $i] : equally_directed_lines(L, L)),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[19, 18])).
% 8.73/8.91 tff(21,plain,(
% 8.73/8.91 ![L: $i] : equally_directed_lines(L, L)),
% 8.73/8.91 inference(skolemize,[status(sab)],[20])).
% 8.73/8.91 tff(22,plain,
% 8.73/8.91 (![L: $i] : equally_directed_lines(L, L)),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[21, 17])).
% 8.73/8.91 tff(23,plain,
% 8.73/8.91 ((~![L: $i] : equally_directed_lines(L, L)) | equally_directed_lines(reverse_line(M!1), reverse_line(M!1))),
% 8.73/8.91 inference(quant_inst,[status(thm)],[])).
% 8.73/8.91 tff(24,plain,
% 8.73/8.91 ($false),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[23, 22, 15])).
% 8.73/8.91 tff(25,plain,(equally_directed_lines(reverse_line(M!1), reverse_line(M!1))), inference(lemma,lemma(discharge,[]))).
% 8.73/8.91 tff(26,plain,
% 8.73/8.91 ((unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)) <=> equally_directed_lines(reverse_line(M!1), reverse_line(M!1))) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))) | (~equally_directed_lines(reverse_line(M!1), reverse_line(M!1)))),
% 8.73/8.91 inference(tautology,[status(thm)],[])).
% 8.73/8.91 tff(27,plain,
% 8.73/8.91 ((unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)) <=> equally_directed_lines(reverse_line(M!1), reverse_line(M!1))) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)))),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[26, 25])).
% 8.73/8.91 tff(28,plain,
% 8.73/8.91 (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[27, 14])).
% 8.73/8.91 tff(29,plain,
% 8.73/8.91 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) <=> equally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1))))),
% 8.73/8.91 inference(quant_inst,[status(thm)],[])).
% 8.73/8.91 tff(30,plain,
% 8.73/8.91 (~(unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) <=> equally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)))),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[29, 12])).
% 8.73/8.91 tff(31,plain,
% 8.73/8.91 (^[A: $i, L: $i] : refl(equally_directed_lines(parallel_through_point(L, A), L) <=> equally_directed_lines(parallel_through_point(L, A), L))),
% 8.73/8.91 inference(bind,[status(th)],[])).
% 8.73/8.91 tff(32,plain,
% 8.73/8.91 (![A: $i, L: $i] : equally_directed_lines(parallel_through_point(L, A), L) <=> ![A: $i, L: $i] : equally_directed_lines(parallel_through_point(L, A), L)),
% 8.73/8.91 inference(quant_intro,[status(thm)],[31])).
% 8.73/8.91 tff(33,plain,
% 8.73/8.91 (![A: $i, L: $i] : equally_directed_lines(parallel_through_point(L, A), L) <=> ![A: $i, L: $i] : equally_directed_lines(parallel_through_point(L, A), L)),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(34,axiom,(![A: $i, L: $i] : equally_directed_lines(parallel_through_point(L, A), L)), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax10_cons_objs')).
% 8.73/8.91 tff(35,plain,
% 8.73/8.91 (![A: $i, L: $i] : equally_directed_lines(parallel_through_point(L, A), L)),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[34, 33])).
% 8.73/8.91 tff(36,plain,(
% 8.73/8.91 ![A: $i, L: $i] : equally_directed_lines(parallel_through_point(L, A), L)),
% 8.73/8.91 inference(skolemize,[status(sab)],[35])).
% 8.73/8.91 tff(37,plain,
% 8.73/8.91 (![A: $i, L: $i] : equally_directed_lines(parallel_through_point(L, A), L)),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[36, 32])).
% 8.73/8.91 tff(38,plain,
% 8.73/8.91 ((~![A: $i, L: $i] : equally_directed_lines(parallel_through_point(L, A), L)) | equally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1))),
% 8.73/8.91 inference(quant_inst,[status(thm)],[])).
% 8.73/8.91 tff(39,plain,
% 8.73/8.91 (equally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1))),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[38, 37])).
% 8.73/8.91 tff(40,plain,
% 8.73/8.91 ((unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) <=> equally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1))) | (~equally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)))),
% 8.73/8.91 inference(tautology,[status(thm)],[])).
% 8.73/8.91 tff(41,plain,
% 8.73/8.91 ((unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) <=> equally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)))),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[40, 39])).
% 8.73/8.91 tff(42,plain,
% 8.73/8.91 (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1))),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[41, 30])).
% 8.73/8.91 tff(43,plain,
% 8.73/8.91 (^[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))))),
% 8.73/8.91 inference(bind,[status(th)],[])).
% 8.73/8.91 tff(44,plain,
% 8.73/8.91 (![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)))),
% 8.73/8.91 inference(quant_intro,[status(thm)],[43])).
% 8.73/8.91 tff(45,plain,
% 8.73/8.91 (![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)))),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(46,plain,
% 8.73/8.91 (^[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)))))),
% 8.73/8.91 inference(bind,[status(th)],[])).
% 8.73/8.91 tff(47,plain,
% 8.73/8.91 (![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)))),
% 8.73/8.91 inference(quant_intro,[status(thm)],[46])).
% 8.73/8.91 tff(48,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/sandbox/benchmark/Axioms/GEO009+0.ax','ax6_basics')).
% 8.73/8.91 tff(49,plain,
% 8.73/8.91 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[48, 47])).
% 8.73/8.91 tff(50,plain,
% 8.73/8.91 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[49, 45])).
% 8.73/8.91 tff(51,plain,(
% 8.73/8.91 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 8.73/8.91 inference(skolemize,[status(sab)],[50])).
% 8.73/8.91 tff(52,plain,
% 8.73/8.91 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[51, 44])).
% 8.73/8.91 tff(53,plain,
% 8.73/8.91 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))) | unequally_directed_lines(reverse_line(M!1), reverse_line(M!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(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))) | unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)))),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(54,plain,
% 8.73/8.91 ((unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))))) <=> (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))) | unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)))),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(55,plain,
% 8.73/8.91 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!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(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))) | unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))))),
% 8.73/8.91 inference(monotonicity,[status(thm)],[54])).
% 8.73/8.91 tff(56,plain,
% 8.73/8.91 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!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(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))) | unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)))),
% 8.73/8.91 inference(transitivity,[status(thm)],[55, 53])).
% 8.73/8.91 tff(57,plain,
% 8.73/8.91 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))))),
% 8.73/8.91 inference(quant_inst,[status(thm)],[])).
% 8.73/8.91 tff(58,plain,
% 8.73/8.91 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))) | unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[57, 56])).
% 8.73/8.91 tff(59,plain,
% 8.73/8.91 (~unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[58, 52, 42, 28])).
% 8.73/8.91 tff(60,assumption,(~unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))), introduced(assumption)).
% 8.73/8.91 tff(61,plain,
% 8.73/8.91 (^[X: $i, Y: $i] : refl((unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))))),
% 8.73/8.91 inference(bind,[status(th)],[])).
% 8.73/8.91 tff(62,plain,
% 8.73/8.91 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 8.73/8.91 inference(quant_intro,[status(thm)],[61])).
% 8.73/8.91 tff(63,plain,
% 8.73/8.91 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(64,axiom,(![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a1_defns')).
% 8.73/8.91 tff(65,plain,
% 8.73/8.91 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[64, 63])).
% 8.73/8.91 tff(66,plain,(
% 8.73/8.91 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 8.73/8.91 inference(skolemize,[status(sab)],[65])).
% 8.73/8.91 tff(67,plain,
% 8.73/8.91 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[66, 62])).
% 8.73/8.91 tff(68,plain,
% 8.73/8.91 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!2, M!1) <=> unequally_directed_lines(L!2, reverse_line(M!1)))),
% 8.73/8.91 inference(quant_inst,[status(thm)],[])).
% 8.73/8.91 tff(69,plain,
% 8.73/8.91 (unequally_directed_opposite_lines(L!2, M!1) <=> unequally_directed_lines(L!2, reverse_line(M!1))),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[68, 67])).
% 8.73/8.91 tff(70,plain,
% 8.73/8.91 ((~(unequally_directed_opposite_lines(M!1, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_opposite_lines(L!2, M!1)))) <=> (~(unequally_directed_opposite_lines(M!1, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_opposite_lines(L!2, M!1))))),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(71,plain,
% 8.73/8.91 ((~![L: $i, M: $i, N: $i] : (unequally_directed_opposite_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_opposite_lines(L, M)))) <=> (~![L: $i, M: $i, N: $i] : (unequally_directed_opposite_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_opposite_lines(L, M))))),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(72,plain,
% 8.73/8.91 ((~![L: $i, M: $i, N: $i] : (unequally_directed_opposite_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_opposite_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : (unequally_directed_opposite_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_opposite_lines(L, M))))),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(73,axiom,(~![L: $i, M: $i, N: $i] : (unequally_directed_opposite_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_opposite_lines(M, N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 8.73/8.91 tff(74,plain,
% 8.73/8.91 (~![L: $i, M: $i, N: $i] : (unequally_directed_opposite_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_opposite_lines(L, M)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[73, 72])).
% 8.73/8.91 tff(75,plain,
% 8.73/8.91 (~![L: $i, M: $i, N: $i] : (unequally_directed_opposite_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_opposite_lines(L, M)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[74, 71])).
% 8.73/8.91 tff(76,plain,
% 8.73/8.91 (~![L: $i, M: $i, N: $i] : (unequally_directed_opposite_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_opposite_lines(L, M)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[75, 71])).
% 8.73/8.91 tff(77,plain,
% 8.73/8.91 (~![L: $i, M: $i, N: $i] : (unequally_directed_opposite_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_opposite_lines(L, M)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[76, 71])).
% 8.73/8.91 tff(78,plain,(
% 8.73/8.91 ~(unequally_directed_opposite_lines(M!1, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_opposite_lines(L!2, M!1)))),
% 8.73/8.91 inference(skolemize,[status(sab)],[77])).
% 8.73/8.91 tff(79,plain,
% 8.73/8.91 (~(unequally_directed_opposite_lines(M!1, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_opposite_lines(L!2, M!1)))),
% 8.73/8.91 inference(modus_ponens,[status(thm)],[78, 70])).
% 8.73/8.91 tff(80,plain,
% 8.73/8.91 (unequally_directed_opposite_lines(L!2, M!1)),
% 8.73/8.91 inference(or_elim,[status(thm)],[79])).
% 8.73/8.91 tff(81,plain,
% 8.73/8.91 ((~(unequally_directed_opposite_lines(L!2, M!1) <=> unequally_directed_lines(L!2, reverse_line(M!1)))) | (~unequally_directed_opposite_lines(L!2, M!1)) | unequally_directed_lines(L!2, reverse_line(M!1))),
% 8.73/8.91 inference(tautology,[status(thm)],[])).
% 8.73/8.91 tff(82,plain,
% 8.73/8.91 ((~(unequally_directed_opposite_lines(L!2, M!1) <=> unequally_directed_lines(L!2, reverse_line(M!1)))) | unequally_directed_lines(L!2, reverse_line(M!1))),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[81, 80])).
% 8.73/8.91 tff(83,plain,
% 8.73/8.91 (unequally_directed_lines(L!2, reverse_line(M!1))),
% 8.73/8.91 inference(unit_resolution,[status(thm)],[82, 69])).
% 8.73/8.91 tff(84,plain,
% 8.73/8.91 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!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(L!2, reverse_line(M!1))) | unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))))),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(85,plain,
% 8.73/8.91 ((unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | (~unequally_directed_lines(L!2, reverse_line(M!1)))) <=> ((~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))))),
% 8.73/8.91 inference(rewrite,[status(thm)],[])).
% 8.73/8.91 tff(86,plain,
% 8.73/8.91 (((~![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(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | (~unequally_directed_lines(L!2, reverse_line(M!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(L!2, reverse_line(M!1))) | unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))))),
% 8.73/8.92 inference(monotonicity,[status(thm)],[85])).
% 8.73/8.92 tff(87,plain,
% 8.73/8.92 (((~![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(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | (~unequally_directed_lines(L!2, reverse_line(M!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(L!2, reverse_line(M!1))) | unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(transitivity,[status(thm)],[86, 84])).
% 8.73/8.92 tff(88,plain,
% 8.73/8.92 ((~![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(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | (~unequally_directed_lines(L!2, reverse_line(M!1))))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(89,plain,
% 8.73/8.92 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))) | unequally_directed_lines(reverse_line(M!1), parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[88, 87])).
% 8.73/8.92 tff(90,plain,
% 8.73/8.92 ($false),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[89, 52, 83, 60, 59])).
% 8.73/8.92 tff(91,plain,(unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))), inference(lemma,lemma(discharge,[]))).
% 8.73/8.92 tff(92,assumption,(~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)), introduced(assumption)).
% 8.73/8.92 tff(93,plain,
% 8.73/8.92 (~unequally_directed_lines(L!2, N!0)),
% 8.73/8.92 inference(or_elim,[status(thm)],[79])).
% 8.73/8.92 tff(94,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, L!2)))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(95,plain,
% 8.73/8.92 ((unequally_directed_lines(L!2, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, L!2))) <=> (unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, L!2)))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(96,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, L!2))))),
% 8.73/8.92 inference(monotonicity,[status(thm)],[95])).
% 8.73/8.92 tff(97,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, L!2)))),
% 8.73/8.92 inference(transitivity,[status(thm)],[96, 94])).
% 8.73/8.92 tff(98,plain,
% 8.73/8.92 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, L!2)))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(99,plain,
% 8.73/8.92 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, L!2))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[98, 97])).
% 8.73/8.92 tff(100,plain,
% 8.73/8.92 (~unequally_directed_lines(L!2, L!2)),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[99, 52, 93])).
% 8.73/8.92 tff(101,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, L!2) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2) | (~unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!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(L!2, L!2) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2) | (~unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(102,plain,
% 8.73/8.92 ((unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2) | unequally_directed_lines(L!2, L!2) | (~unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))))) <=> (unequally_directed_lines(L!2, L!2) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2) | (~unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(103,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2) | unequally_directed_lines(L!2, L!2) | (~unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!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(L!2, L!2) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2) | (~unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))))))),
% 8.73/8.92 inference(monotonicity,[status(thm)],[102])).
% 8.73/8.92 tff(104,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2) | unequally_directed_lines(L!2, L!2) | (~unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!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(L!2, L!2) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2) | (~unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))))),
% 8.73/8.92 inference(transitivity,[status(thm)],[103, 101])).
% 8.73/8.92 tff(105,plain,
% 8.73/8.92 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2) | unequally_directed_lines(L!2, L!2) | (~unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))))))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(106,plain,
% 8.73/8.92 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, L!2) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2) | (~unequally_directed_lines(L!2, parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[105, 104])).
% 8.73/8.92 tff(107,plain,
% 8.73/8.92 ($false),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[106, 52, 100, 92, 91])).
% 8.73/8.92 tff(108,plain,(unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)), inference(lemma,lemma(discharge,[]))).
% 8.73/8.92 tff(109,assumption,(~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1)))), introduced(assumption)).
% 8.73/8.92 tff(110,assumption,(unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)), introduced(assumption)).
% 8.73/8.92 tff(111,assumption,(left_convergent_lines(L!2, reverse_line(M!1)) | left_convergent_lines(L!2, reverse_line(reverse_line(M!1)))), introduced(assumption)).
% 8.73/8.92 tff(112,plain,
% 8.73/8.92 (^[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)))))),
% 8.73/8.92 inference(bind,[status(th)],[])).
% 8.73/8.92 tff(113,plain,
% 8.73/8.92 (![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))))),
% 8.73/8.92 inference(quant_intro,[status(thm)],[112])).
% 8.73/8.92 tff(114,plain,
% 8.73/8.92 (![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))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(115,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax11_basics')).
% 8.73/8.92 tff(116,plain,
% 8.73/8.92 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[115, 114])).
% 8.73/8.92 tff(117,plain,(
% 8.73/8.92 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 8.73/8.92 inference(skolemize,[status(sab)],[116])).
% 8.73/8.92 tff(118,plain,
% 8.73/8.92 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[117, 113])).
% 8.73/8.92 tff(119,plain,
% 8.73/8.92 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!2, reverse_line(M!1)) | left_convergent_lines(L!2, reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(120,plain,
% 8.73/8.92 ($false),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[119, 118, 111])).
% 8.73/8.92 tff(121,plain,(~(left_convergent_lines(L!2, reverse_line(M!1)) | left_convergent_lines(L!2, reverse_line(reverse_line(M!1))))), inference(lemma,lemma(discharge,[]))).
% 8.73/8.92 tff(122,plain,
% 8.73/8.92 ((left_convergent_lines(L!2, reverse_line(M!1)) | left_convergent_lines(L!2, reverse_line(reverse_line(M!1)))) | (~left_convergent_lines(L!2, reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(tautology,[status(thm)],[])).
% 8.73/8.92 tff(123,plain,
% 8.73/8.92 (~left_convergent_lines(L!2, reverse_line(reverse_line(M!1)))),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[122, 121])).
% 8.73/8.92 tff(124,assumption,(unequally_directed_lines(L!2, reverse_line(reverse_line(M!1)))), introduced(assumption)).
% 8.73/8.92 tff(125,plain,
% 8.73/8.92 ((left_convergent_lines(L!2, reverse_line(M!1)) | left_convergent_lines(L!2, reverse_line(reverse_line(M!1)))) | (~left_convergent_lines(L!2, reverse_line(M!1)))),
% 8.73/8.92 inference(tautology,[status(thm)],[])).
% 8.73/8.92 tff(126,plain,
% 8.73/8.92 (~left_convergent_lines(L!2, reverse_line(M!1))),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[125, 121])).
% 8.73/8.92 tff(127,plain,
% 8.73/8.92 (^[L: $i, M: $i] : refl((left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 8.73/8.92 inference(bind,[status(th)],[])).
% 8.73/8.92 tff(128,plain,
% 8.73/8.92 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 8.73/8.92 inference(quant_intro,[status(thm)],[127])).
% 8.73/8.92 tff(129,plain,
% 8.73/8.92 (^[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)) | (~unequally_directed_lines(L, M)) | left_convergent_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)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 8.73/8.92 inference(bind,[status(th)],[])).
% 8.73/8.92 tff(130,plain,
% 8.73/8.92 (![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)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 8.73/8.92 inference(quant_intro,[status(thm)],[129])).
% 8.73/8.92 tff(131,plain,
% 8.73/8.92 (![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)))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(132,plain,
% 8.73/8.92 (^[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))))))),
% 8.73/8.92 inference(bind,[status(th)],[])).
% 8.73/8.92 tff(133,plain,
% 8.73/8.92 (![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)))))),
% 8.73/8.92 inference(quant_intro,[status(thm)],[132])).
% 8.73/8.92 tff(134,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/sandbox/benchmark/Axioms/GEO009+0.ax','ax9_basics')).
% 8.73/8.92 tff(135,plain,
% 8.73/8.92 (![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)))))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[134, 133])).
% 8.73/8.92 tff(136,plain,
% 8.73/8.92 (![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)))))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[135, 131])).
% 8.73/8.92 tff(137,plain,(
% 8.73/8.92 ![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)))))),
% 8.73/8.92 inference(skolemize,[status(sab)],[136])).
% 8.73/8.92 tff(138,plain,
% 8.73/8.92 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[137, 130])).
% 8.73/8.92 tff(139,plain,
% 8.73/8.92 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[138, 128])).
% 8.73/8.92 tff(140,plain,
% 8.73/8.92 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!2, reverse_line(M!1))) | left_convergent_lines(L!2, reverse_line(M!1)) | (~unequally_directed_lines(L!2, reverse_line(reverse_line(M!1)))) | left_convergent_lines(L!2, reverse_line(reverse_line(M!1))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | left_convergent_lines(L!2, reverse_line(M!1)) | (~unequally_directed_lines(L!2, reverse_line(reverse_line(M!1)))) | left_convergent_lines(L!2, reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(141,plain,
% 8.73/8.92 ((left_convergent_lines(L!2, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | left_convergent_lines(L!2, reverse_line(M!1)) | (~unequally_directed_lines(L!2, reverse_line(reverse_line(M!1))))) <=> ((~unequally_directed_lines(L!2, reverse_line(M!1))) | left_convergent_lines(L!2, reverse_line(M!1)) | (~unequally_directed_lines(L!2, reverse_line(reverse_line(M!1)))) | left_convergent_lines(L!2, reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(142,plain,
% 8.73/8.92 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!2, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | left_convergent_lines(L!2, reverse_line(M!1)) | (~unequally_directed_lines(L!2, reverse_line(reverse_line(M!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!2, reverse_line(M!1))) | left_convergent_lines(L!2, reverse_line(M!1)) | (~unequally_directed_lines(L!2, reverse_line(reverse_line(M!1)))) | left_convergent_lines(L!2, reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(monotonicity,[status(thm)],[141])).
% 8.73/8.92 tff(143,plain,
% 8.73/8.92 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!2, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | left_convergent_lines(L!2, reverse_line(M!1)) | (~unequally_directed_lines(L!2, reverse_line(reverse_line(M!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | left_convergent_lines(L!2, reverse_line(M!1)) | (~unequally_directed_lines(L!2, reverse_line(reverse_line(M!1)))) | left_convergent_lines(L!2, reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(transitivity,[status(thm)],[142, 140])).
% 8.73/8.92 tff(144,plain,
% 8.73/8.92 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!2, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | left_convergent_lines(L!2, reverse_line(M!1)) | (~unequally_directed_lines(L!2, reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(145,plain,
% 8.73/8.92 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | left_convergent_lines(L!2, reverse_line(M!1)) | (~unequally_directed_lines(L!2, reverse_line(reverse_line(M!1)))) | left_convergent_lines(L!2, reverse_line(reverse_line(M!1)))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[144, 143])).
% 8.73/8.92 tff(146,plain,
% 8.73/8.92 ($false),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[145, 139, 83, 126, 124, 123])).
% 8.73/8.92 tff(147,plain,(~unequally_directed_lines(L!2, reverse_line(reverse_line(M!1)))), inference(lemma,lemma(discharge,[]))).
% 8.73/8.92 tff(148,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!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(L!2, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(149,plain,
% 8.73/8.92 ((unequally_directed_lines(L!2, reverse_line(reverse_line(M!1))) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2))) <=> (unequally_directed_lines(L!2, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(150,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, reverse_line(reverse_line(M!1))) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(monotonicity,[status(thm)],[149])).
% 8.73/8.92 tff(151,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, reverse_line(reverse_line(M!1))) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(transitivity,[status(thm)],[150, 148])).
% 8.73/8.92 tff(152,plain,
% 8.73/8.92 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, reverse_line(reverse_line(M!1))) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(153,plain,
% 8.73/8.92 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1)))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[152, 151])).
% 8.73/8.92 tff(154,plain,
% 8.73/8.92 ($false),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[153, 52, 147, 110, 109])).
% 8.73/8.92 tff(155,plain,(unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2))), inference(lemma,lemma(discharge,[]))).
% 8.73/8.92 tff(156,plain,
% 8.73/8.92 (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1)))),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[155, 108])).
% 8.73/8.92 tff(157,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!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(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(158,plain,
% 8.73/8.92 ((unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1))))) <=> (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(159,plain,
% 8.73/8.92 (((~![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(reverse_line(M!1)), reverse_line(M!1)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!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(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1))))))),
% 8.73/8.92 inference(monotonicity,[status(thm)],[158])).
% 8.73/8.92 tff(160,plain,
% 8.73/8.92 (((~![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(reverse_line(M!1)), reverse_line(M!1)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!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(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(transitivity,[status(thm)],[159, 157])).
% 8.73/8.92 tff(161,plain,
% 8.73/8.92 ((~![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(reverse_line(M!1)), reverse_line(M!1)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(162,plain,
% 8.73/8.92 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[161, 160])).
% 8.73/8.92 tff(163,plain,
% 8.73/8.92 ($false),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[162, 52, 42, 156, 2])).
% 8.73/8.92 tff(164,plain,(unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))), inference(lemma,lemma(discharge,[]))).
% 8.73/8.92 tff(165,plain,
% 8.73/8.92 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(166,plain,
% 8.73/8.92 (~(left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)))),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[165, 118])).
% 8.73/8.92 tff(167,plain,
% 8.73/8.92 ((left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))) | (~left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)))),
% 8.73/8.92 inference(tautology,[status(thm)],[])).
% 8.73/8.92 tff(168,plain,
% 8.73/8.92 (~left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[167, 166])).
% 8.73/8.92 tff(169,plain,
% 8.73/8.92 ((left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))) | (~left_convergent_lines(reverse_line(reverse_line(M!1)), M!1))),
% 8.73/8.92 inference(tautology,[status(thm)],[])).
% 8.73/8.92 tff(170,plain,
% 8.73/8.92 (~left_convergent_lines(reverse_line(reverse_line(M!1)), M!1)),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[169, 166])).
% 8.73/8.92 tff(171,plain,
% 8.73/8.92 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(172,plain,
% 8.73/8.92 ((left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)) | left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)))) <=> (left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(173,plain,
% 8.73/8.92 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)) | left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)))))),
% 8.73/8.92 inference(monotonicity,[status(thm)],[172])).
% 8.73/8.92 tff(174,plain,
% 8.73/8.92 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)) | left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))))),
% 8.73/8.92 inference(transitivity,[status(thm)],[173, 171])).
% 8.73/8.92 tff(175,plain,
% 8.73/8.92 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)) | left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1))))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(176,plain,
% 8.73/8.92 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(reverse_line(reverse_line(M!1)), M!1) | left_convergent_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[175, 174])).
% 8.73/8.92 tff(177,plain,
% 8.73/8.92 ((~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)) | (~unequally_directed_lines(reverse_line(reverse_line(M!1)), reverse_line(M!1)))),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[176, 139, 170, 168])).
% 8.73/8.92 tff(178,plain,
% 8.73/8.92 (~unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1)),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[177, 164])).
% 8.73/8.92 tff(179,plain,
% 8.73/8.92 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(M!1, N!0) <=> unequally_directed_lines(M!1, reverse_line(N!0)))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(180,plain,
% 8.73/8.92 (unequally_directed_opposite_lines(M!1, N!0) <=> unequally_directed_lines(M!1, reverse_line(N!0))),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[179, 67])).
% 8.73/8.92 tff(181,plain,
% 8.73/8.92 (~unequally_directed_opposite_lines(M!1, N!0)),
% 8.73/8.92 inference(or_elim,[status(thm)],[79])).
% 8.73/8.92 tff(182,plain,
% 8.73/8.92 ((~(unequally_directed_opposite_lines(M!1, N!0) <=> unequally_directed_lines(M!1, reverse_line(N!0)))) | unequally_directed_opposite_lines(M!1, N!0) | (~unequally_directed_lines(M!1, reverse_line(N!0)))),
% 8.73/8.92 inference(tautology,[status(thm)],[])).
% 8.73/8.92 tff(183,plain,
% 8.73/8.92 ((~(unequally_directed_opposite_lines(M!1, N!0) <=> unequally_directed_lines(M!1, reverse_line(N!0)))) | (~unequally_directed_lines(M!1, reverse_line(N!0)))),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[182, 181])).
% 8.73/8.92 tff(184,plain,
% 8.73/8.92 (~unequally_directed_lines(M!1, reverse_line(N!0))),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[183, 180])).
% 8.73/8.92 tff(185,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, M!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(M!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, M!1)))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(186,plain,
% 8.73/8.92 ((unequally_directed_lines(M!1, reverse_line(N!0)) | unequally_directed_lines(M!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, M!1))) <=> (unequally_directed_lines(M!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, M!1)))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(187,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, reverse_line(N!0)) | unequally_directed_lines(M!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, M!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(M!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, M!1))))),
% 8.73/8.92 inference(monotonicity,[status(thm)],[186])).
% 8.73/8.92 tff(188,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, reverse_line(N!0)) | unequally_directed_lines(M!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, M!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(M!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, M!1)))),
% 8.73/8.92 inference(transitivity,[status(thm)],[187, 185])).
% 8.73/8.92 tff(189,plain,
% 8.73/8.92 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, reverse_line(N!0)) | unequally_directed_lines(M!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, M!1)))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(190,plain,
% 8.73/8.92 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(M!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, M!1))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[189, 188])).
% 8.73/8.92 tff(191,plain,
% 8.73/8.92 (~unequally_directed_lines(M!1, M!1)),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[190, 52, 184])).
% 8.73/8.92 tff(192,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1) | (~unequally_directed_lines(M!1, reverse_line(reverse_line(M!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(M!1, M!1) | unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1) | (~unequally_directed_lines(M!1, reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(193,plain,
% 8.73/8.92 ((unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))))) <=> (unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1) | (~unequally_directed_lines(M!1, reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(194,plain,
% 8.73/8.92 (((~![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(reverse_line(M!1)), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(reverse_line(M!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(M!1, M!1) | unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1) | (~unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))))))),
% 8.73/8.92 inference(monotonicity,[status(thm)],[193])).
% 8.73/8.92 tff(195,plain,
% 8.73/8.92 (((~![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(reverse_line(M!1)), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(reverse_line(M!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(M!1, M!1) | unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1) | (~unequally_directed_lines(M!1, reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(transitivity,[status(thm)],[194, 192])).
% 8.73/8.92 tff(196,plain,
% 8.73/8.92 ((~![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(reverse_line(M!1)), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(reverse_line(M!1)))))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(197,plain,
% 8.73/8.92 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(reverse_line(M!1)), M!1) | (~unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[196, 195])).
% 8.73/8.92 tff(198,plain,
% 8.73/8.92 (~unequally_directed_lines(M!1, reverse_line(reverse_line(M!1)))),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[197, 52, 191, 178])).
% 8.73/8.92 tff(199,plain,
% 8.73/8.92 (^[L: $i, M: $i] : refl((unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))),
% 8.73/8.92 inference(bind,[status(th)],[])).
% 8.73/8.92 tff(200,plain,
% 8.73/8.92 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 8.73/8.92 inference(quant_intro,[status(thm)],[199])).
% 8.73/8.92 tff(201,plain,
% 8.73/8.92 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(202,axiom,(![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax8_basics')).
% 8.73/8.92 tff(203,plain,
% 8.73/8.92 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[202, 201])).
% 8.73/8.92 tff(204,plain,(
% 8.73/8.92 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 8.73/8.92 inference(skolemize,[status(sab)],[203])).
% 8.73/8.92 tff(205,plain,
% 8.73/8.92 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[204, 200])).
% 8.73/8.92 tff(206,plain,
% 8.73/8.92 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(M!1, N!0) | unequally_directed_lines(M!1, reverse_line(N!0)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(M!1, N!0) | unequally_directed_lines(M!1, reverse_line(N!0)))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(207,plain,
% 8.73/8.92 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(M!1, N!0) | unequally_directed_lines(M!1, reverse_line(N!0)))),
% 8.73/8.92 inference(quant_inst,[status(thm)],[])).
% 8.73/8.92 tff(208,plain,
% 8.73/8.92 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(M!1, N!0) | unequally_directed_lines(M!1, reverse_line(N!0))),
% 8.73/8.92 inference(modus_ponens,[status(thm)],[207, 206])).
% 8.73/8.92 tff(209,plain,
% 8.73/8.92 (unequally_directed_lines(M!1, N!0)),
% 8.73/8.92 inference(unit_resolution,[status(thm)],[208, 205, 184])).
% 8.73/8.92 tff(210,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(M!1, N!0)) | unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))) | unequally_directed_lines(N!0, reverse_line(reverse_line(M!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(M!1, N!0)) | unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))) | unequally_directed_lines(N!0, reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(211,plain,
% 8.73/8.92 ((unequally_directed_lines(N!0, reverse_line(reverse_line(M!1))) | unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(M!1, N!0))) <=> ((~unequally_directed_lines(M!1, N!0)) | unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))) | unequally_directed_lines(N!0, reverse_line(reverse_line(M!1))))),
% 8.73/8.92 inference(rewrite,[status(thm)],[])).
% 8.73/8.92 tff(212,plain,
% 8.73/8.92 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(N!0, reverse_line(reverse_line(M!1))) | unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(M!1, N!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(M!1, N!0)) | unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))) | unequally_directed_lines(N!0, reverse_line(reverse_line(M!1)))))),
% 8.73/8.93 inference(monotonicity,[status(thm)],[211])).
% 8.73/8.93 tff(213,plain,
% 8.73/8.93 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(N!0, reverse_line(reverse_line(M!1))) | unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(M!1, N!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(M!1, N!0)) | unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))) | unequally_directed_lines(N!0, reverse_line(reverse_line(M!1))))),
% 8.73/8.93 inference(transitivity,[status(thm)],[212, 210])).
% 8.73/8.93 tff(214,plain,
% 8.73/8.93 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(N!0, reverse_line(reverse_line(M!1))) | unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))) | (~unequally_directed_lines(M!1, N!0)))),
% 8.73/8.93 inference(quant_inst,[status(thm)],[])).
% 8.73/8.93 tff(215,plain,
% 8.73/8.93 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, N!0)) | unequally_directed_lines(M!1, reverse_line(reverse_line(M!1))) | unequally_directed_lines(N!0, reverse_line(reverse_line(M!1)))),
% 8.73/8.93 inference(modus_ponens,[status(thm)],[214, 213])).
% 8.73/8.93 tff(216,plain,
% 8.73/8.93 ($false),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[215, 52, 209, 198, 1])).
% 8.73/8.93 tff(217,plain,(unequally_directed_lines(N!0, reverse_line(reverse_line(M!1)))), inference(lemma,lemma(discharge,[]))).
% 8.73/8.93 tff(218,assumption,(~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0)), introduced(assumption)).
% 8.73/8.93 tff(219,plain,
% 8.73/8.93 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!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(L!2, N!0) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0))),
% 8.73/8.93 inference(rewrite,[status(thm)],[])).
% 8.73/8.93 tff(220,plain,
% 8.73/8.93 ((unequally_directed_lines(L!2, N!0) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2))) <=> (unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0))),
% 8.73/8.93 inference(rewrite,[status(thm)],[])).
% 8.73/8.93 tff(221,plain,
% 8.73/8.93 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0)))),
% 8.73/8.93 inference(monotonicity,[status(thm)],[220])).
% 8.73/8.93 tff(222,plain,
% 8.73/8.93 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0))),
% 8.73/8.93 inference(transitivity,[status(thm)],[221, 219])).
% 8.73/8.93 tff(223,plain,
% 8.73/8.93 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)))),
% 8.73/8.93 inference(quant_inst,[status(thm)],[])).
% 8.73/8.93 tff(224,plain,
% 8.73/8.93 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), L!2)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0)),
% 8.73/8.93 inference(modus_ponens,[status(thm)],[223, 222])).
% 8.73/8.93 tff(225,plain,
% 8.73/8.93 ($false),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[224, 52, 93, 108, 218])).
% 8.73/8.93 tff(226,plain,(unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0)), inference(lemma,lemma(discharge,[]))).
% 8.73/8.93 tff(227,assumption,(~unequally_directed_lines(N!0, reverse_line(M!1))), introduced(assumption)).
% 8.73/8.93 tff(228,plain,
% 8.73/8.93 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!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(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0)))),
% 8.73/8.93 inference(rewrite,[status(thm)],[])).
% 8.73/8.93 tff(229,plain,
% 8.73/8.93 ((unequally_directed_lines(N!0, reverse_line(M!1)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0))) <=> (unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0)))),
% 8.73/8.93 inference(rewrite,[status(thm)],[])).
% 8.73/8.93 tff(230,plain,
% 8.73/8.93 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(N!0, reverse_line(M!1)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!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(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0))))),
% 8.73/8.93 inference(monotonicity,[status(thm)],[229])).
% 8.73/8.93 tff(231,plain,
% 8.73/8.93 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(N!0, reverse_line(M!1)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!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(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0)))),
% 8.73/8.93 inference(transitivity,[status(thm)],[230, 228])).
% 8.73/8.93 tff(232,plain,
% 8.73/8.93 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(N!0, reverse_line(M!1)) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0)))),
% 8.73/8.93 inference(quant_inst,[status(thm)],[])).
% 8.73/8.93 tff(233,plain,
% 8.73/8.93 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), reverse_line(M!1)) | unequally_directed_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(M!1), reverse_line(reverse_line(M!1))), N!0))),
% 8.73/8.93 inference(modus_ponens,[status(thm)],[232, 231])).
% 8.73/8.93 tff(234,plain,
% 8.73/8.93 ($false),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[233, 52, 42, 227, 226])).
% 8.73/8.93 tff(235,plain,(unequally_directed_lines(N!0, reverse_line(M!1))), inference(lemma,lemma(discharge,[]))).
% 8.73/8.93 tff(236,plain,
% 8.73/8.93 (((~unequally_directed_lines(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)))) | unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))),
% 8.73/8.93 inference(tautology,[status(thm)],[])).
% 8.73/8.93 tff(237,plain,
% 8.73/8.93 ((~unequally_directed_lines(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1)))),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[236, 28])).
% 8.73/8.93 tff(238,plain,
% 8.73/8.93 (^[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)))))),
% 8.73/8.93 inference(bind,[status(th)],[])).
% 8.73/8.93 tff(239,plain,
% 8.73/8.93 (![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))))),
% 8.73/8.93 inference(quant_intro,[status(thm)],[238])).
% 8.73/8.93 tff(240,plain,
% 8.73/8.93 (^[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))))))),
% 8.73/8.93 inference(bind,[status(th)],[])).
% 8.73/8.93 tff(241,plain,
% 8.73/8.93 (![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))))),
% 8.73/8.93 inference(quant_intro,[status(thm)],[240])).
% 8.73/8.93 tff(242,plain,
% 8.73/8.93 (![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)))))),
% 8.73/8.93 inference(rewrite,[status(thm)],[])).
% 8.73/8.93 tff(243,plain,
% 8.73/8.93 (^[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)))))))),
% 8.73/8.93 inference(bind,[status(th)],[])).
% 8.73/8.93 tff(244,plain,
% 8.73/8.93 (![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)))))),
% 8.73/8.93 inference(quant_intro,[status(thm)],[243])).
% 8.73/8.93 tff(245,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/sandbox/benchmark/Axioms/GEO009+0.ax','ax7_basics')).
% 8.73/8.93 tff(246,plain,
% 8.73/8.93 (![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)))))),
% 8.73/8.93 inference(modus_ponens,[status(thm)],[245, 244])).
% 8.73/8.93 tff(247,plain,
% 8.73/8.93 (![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)))))),
% 8.73/8.93 inference(modus_ponens,[status(thm)],[246, 242])).
% 8.73/8.93 tff(248,plain,(
% 8.73/8.93 ![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)))))),
% 8.73/8.93 inference(skolemize,[status(sab)],[247])).
% 8.73/8.93 tff(249,plain,
% 8.73/8.93 (![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))))),
% 8.73/8.93 inference(modus_ponens,[status(thm)],[248, 241])).
% 8.73/8.93 tff(250,plain,
% 8.73/8.93 (![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))))),
% 8.73/8.93 inference(modus_ponens,[status(thm)],[249, 239])).
% 8.73/8.93 tff(251,plain,
% 8.73/8.93 (((~![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(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))))) | (~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) | (~unequally_directed_lines(N!0, reverse_line(M!1))) | (~unequally_directed_lines(N!0, reverse_line(reverse_line(M!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(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))))) | (~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) | (~unequally_directed_lines(N!0, reverse_line(M!1))) | (~unequally_directed_lines(N!0, reverse_line(reverse_line(M!1)))))),
% 8.73/8.93 inference(rewrite,[status(thm)],[])).
% 8.73/8.93 tff(252,plain,
% 8.73/8.93 (((~unequally_directed_lines(N!0, reverse_line(M!1))) | (~((~unequally_directed_lines(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))))) | (~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) | (~unequally_directed_lines(N!0, reverse_line(reverse_line(M!1))))) <=> ((~((~unequally_directed_lines(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))))) | (~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) | (~unequally_directed_lines(N!0, reverse_line(M!1))) | (~unequally_directed_lines(N!0, reverse_line(reverse_line(M!1)))))),
% 8.73/8.93 inference(rewrite,[status(thm)],[])).
% 8.73/8.93 tff(253,plain,
% 8.73/8.93 (((~![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(N!0, reverse_line(M!1))) | (~((~unequally_directed_lines(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))))) | (~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) | (~unequally_directed_lines(N!0, reverse_line(reverse_line(M!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(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))))) | (~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) | (~unequally_directed_lines(N!0, reverse_line(M!1))) | (~unequally_directed_lines(N!0, reverse_line(reverse_line(M!1))))))),
% 8.73/8.93 inference(monotonicity,[status(thm)],[252])).
% 8.73/8.93 tff(254,plain,
% 8.73/8.93 (((~![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(N!0, reverse_line(M!1))) | (~((~unequally_directed_lines(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))))) | (~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) | (~unequally_directed_lines(N!0, reverse_line(reverse_line(M!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(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))))) | (~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) | (~unequally_directed_lines(N!0, reverse_line(M!1))) | (~unequally_directed_lines(N!0, reverse_line(reverse_line(M!1)))))),
% 8.73/8.93 inference(transitivity,[status(thm)],[253, 251])).
% 8.73/8.93 tff(255,plain,
% 8.73/8.93 ((~![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(N!0, reverse_line(M!1))) | (~((~unequally_directed_lines(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))))) | (~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) | (~unequally_directed_lines(N!0, reverse_line(reverse_line(M!1)))))),
% 8.73/8.93 inference(quant_inst,[status(thm)],[])).
% 8.73/8.93 tff(256,plain,
% 8.73/8.93 ((~![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(reverse_line(M!1), M!1)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(M!1))))) | (~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) | (~unequally_directed_lines(N!0, reverse_line(M!1))) | (~unequally_directed_lines(N!0, reverse_line(reverse_line(M!1))))),
% 8.73/8.93 inference(modus_ponens,[status(thm)],[255, 254])).
% 8.73/8.93 tff(257,plain,
% 8.73/8.93 ((~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) | (~unequally_directed_lines(N!0, reverse_line(reverse_line(M!1))))),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[256, 250, 237, 235])).
% 8.73/8.93 tff(258,plain,
% 8.73/8.93 (~((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[257, 217])).
% 8.73/8.93 tff(259,plain,
% 8.73/8.93 (((~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1)))) | unequally_directed_lines(N!0, M!1)),
% 8.73/8.93 inference(tautology,[status(thm)],[])).
% 8.73/8.93 tff(260,plain,
% 8.73/8.93 (unequally_directed_lines(N!0, M!1)),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[259, 258])).
% 8.73/8.93 tff(261,assumption,(left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1))), introduced(assumption)).
% 8.73/8.93 tff(262,plain,
% 8.73/8.93 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1))))),
% 8.73/8.93 inference(quant_inst,[status(thm)],[])).
% 8.73/8.93 tff(263,plain,
% 8.73/8.93 ($false),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[262, 118, 261])).
% 8.73/8.93 tff(264,plain,(~(left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1)))), inference(lemma,lemma(discharge,[]))).
% 8.73/8.93 tff(265,plain,
% 8.73/8.93 ((left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1))) | (~left_convergent_lines(N!0, M!1))),
% 8.73/8.93 inference(tautology,[status(thm)],[])).
% 8.73/8.93 tff(266,plain,
% 8.73/8.93 (~left_convergent_lines(N!0, M!1)),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[265, 264])).
% 8.73/8.93 tff(267,plain,
% 8.73/8.93 ((left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1))) | (~left_convergent_lines(N!0, reverse_line(M!1)))),
% 8.73/8.93 inference(tautology,[status(thm)],[])).
% 8.73/8.93 tff(268,plain,
% 8.73/8.93 (~left_convergent_lines(N!0, reverse_line(M!1))),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[267, 264])).
% 8.73/8.93 tff(269,plain,
% 8.73/8.93 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))),
% 8.73/8.93 inference(rewrite,[status(thm)],[])).
% 8.73/8.93 tff(270,plain,
% 8.73/8.93 ((left_convergent_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(N!0, M!1)) | left_convergent_lines(N!0, M!1) | (~unequally_directed_lines(N!0, reverse_line(M!1)))) <=> (left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))),
% 8.73/8.93 inference(rewrite,[status(thm)],[])).
% 8.73/8.93 tff(271,plain,
% 8.73/8.93 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(N!0, M!1)) | left_convergent_lines(N!0, M!1) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1)))))),
% 8.73/8.93 inference(monotonicity,[status(thm)],[270])).
% 8.73/8.93 tff(272,plain,
% 8.73/8.93 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(N!0, M!1)) | left_convergent_lines(N!0, M!1) | (~unequally_directed_lines(N!0, reverse_line(M!1))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1))))),
% 8.73/8.93 inference(transitivity,[status(thm)],[271, 269])).
% 8.73/8.93 tff(273,plain,
% 8.73/8.93 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(N!0, M!1)) | left_convergent_lines(N!0, M!1) | (~unequally_directed_lines(N!0, reverse_line(M!1))))),
% 8.73/8.93 inference(quant_inst,[status(thm)],[])).
% 8.73/8.93 tff(274,plain,
% 8.73/8.93 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(N!0, M!1)) | (~unequally_directed_lines(N!0, reverse_line(M!1)))),
% 8.73/8.93 inference(modus_ponens,[status(thm)],[273, 272])).
% 8.73/8.93 tff(275,plain,
% 8.73/8.93 (left_convergent_lines(N!0, M!1) | left_convergent_lines(N!0, reverse_line(M!1)) | (~unequally_directed_lines(N!0, M!1))),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[274, 139, 235])).
% 8.73/8.93 tff(276,plain,
% 8.73/8.93 ($false),
% 8.73/8.93 inference(unit_resolution,[status(thm)],[275, 268, 266, 260])).
% 8.73/8.93 % SZS output end Proof
% 8.77/8.94 % E exiting
%------------------------------------------------------------------------------