%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO266+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:06:11 AM UTC 2025
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO266+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 14:43:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 tff(unequally_directed_lines_type, type, (
% 0.19/0.45 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.45 tff(reverse_line_type, type, (
% 0.19/0.45 reverse_line: $i > $i)).
% 0.19/0.45 tff(tptp_fun_L_1_type, type, (
% 0.19/0.45 tptp_fun_L_1: $i)).
% 0.19/0.45 tff(tptp_fun_M_0_type, type, (
% 0.19/0.45 tptp_fun_M_0: $i)).
% 0.19/0.45 tff(unequally_directed_opposite_lines_type, type, (
% 0.19/0.45 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.19/0.45 tff(equally_directed_lines_type, type, (
% 0.19/0.45 equally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.45 tff(left_convergent_lines_type, type, (
% 0.19/0.45 left_convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.45 tff(1,assumption,(~unequally_directed_lines(M!0, reverse_line(L!1))), introduced(assumption)).
% 0.19/0.45 tff(2,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(3,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.45 tff(4,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(5,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')).
% 0.19/0.45 tff(6,plain,
% 0.19/0.45 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.45 tff(7,plain,(
% 0.19/0.45 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[6])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(M!0, L!1) <=> unequally_directed_lines(M!0, reverse_line(L!1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (unequally_directed_opposite_lines(M!0, L!1) <=> unequally_directed_lines(M!0, reverse_line(L!1))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 ((~(unequally_directed_opposite_lines(M!0, L!1) <=> unequally_directed_lines(M!0, reverse_line(L!1)))) | (~unequally_directed_opposite_lines(M!0, L!1)) | unequally_directed_lines(M!0, reverse_line(L!1))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 ((~unequally_directed_opposite_lines(M!0, L!1)) | unequally_directed_lines(M!0, reverse_line(L!1))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (~unequally_directed_opposite_lines(M!0, L!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 ((~(unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_opposite_lines(M!0, L!1))) <=> (~(unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_opposite_lines(M!0, L!1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 ((~![L: $i, M: $i] : (unequally_directed_opposite_lines(L, M) <=> unequally_directed_opposite_lines(M, L))) <=> (~![L: $i, M: $i] : (unequally_directed_opposite_lines(L, M) <=> unequally_directed_opposite_lines(M, L)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(16,axiom,(~![L: $i, M: $i] : (unequally_directed_opposite_lines(L, M) <=> unequally_directed_opposite_lines(M, L))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (~![L: $i, M: $i] : (unequally_directed_opposite_lines(L, M) <=> unequally_directed_opposite_lines(M, L))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (~![L: $i, M: $i] : (unequally_directed_opposite_lines(L, M) <=> unequally_directed_opposite_lines(M, L))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (~![L: $i, M: $i] : (unequally_directed_opposite_lines(L, M) <=> unequally_directed_opposite_lines(M, L))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (~![L: $i, M: $i] : (unequally_directed_opposite_lines(L, M) <=> unequally_directed_opposite_lines(M, L))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.45 tff(21,plain,(
% 0.19/0.45 ~(unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_opposite_lines(M!0, L!1))),
% 0.19/0.45 inference(skolemize,[status(sab)],[20])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (~(unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_opposite_lines(M!0, L!1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 ((unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_opposite_lines(M!0, L!1)) | unequally_directed_opposite_lines(L!1, M!0) | unequally_directed_opposite_lines(M!0, L!1)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (unequally_directed_opposite_lines(L!1, M!0) | unequally_directed_opposite_lines(M!0, L!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (unequally_directed_opposite_lines(L!1, M!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[24, 13])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1)))) | unequally_directed_lines(M!0, reverse_line(L!1))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 ((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[26, 1])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.45 tff(33,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')).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.45 tff(36,plain,(
% 0.19/0.45 ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[35])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(L!1, L!1) <=> equally_directed_lines(L!1, L!1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (~(unequally_directed_lines(L!1, L!1) <=> equally_directed_lines(L!1, L!1))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.45 tff(40,assumption,(~equally_directed_lines(L!1, L!1)), introduced(assumption)).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (^[L: $i] : refl(equally_directed_lines(L, L) <=> equally_directed_lines(L, L))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (![L: $i] : equally_directed_lines(L, L) <=> ![L: $i] : equally_directed_lines(L, L)),
% 0.19/0.45 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (![L: $i] : equally_directed_lines(L, L) <=> ![L: $i] : equally_directed_lines(L, L)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(44,axiom,(![L: $i] : equally_directed_lines(L, L)), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax5_basics')).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (![L: $i] : equally_directed_lines(L, L)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.45 tff(46,plain,(
% 0.19/0.45 ![L: $i] : equally_directed_lines(L, L)),
% 0.19/0.45 inference(skolemize,[status(sab)],[45])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (![L: $i] : equally_directed_lines(L, L)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 ((~![L: $i] : equally_directed_lines(L, L)) | equally_directed_lines(L!1, L!1)),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[48, 47, 40])).
% 0.19/0.45 tff(50,plain,(equally_directed_lines(L!1, L!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 ((unequally_directed_lines(L!1, L!1) <=> equally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, L!1)) | (~equally_directed_lines(L!1, L!1))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 ((unequally_directed_lines(L!1, L!1) <=> equally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, L!1))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 (~unequally_directed_lines(L!1, L!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[52, 39])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1)))) | unequally_directed_lines(L!1, L!1)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 ((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.45 tff(56,assumption,(~unequally_directed_lines(L!1, M!0)), introduced(assumption)).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(60,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')).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.45 tff(62,plain,(
% 0.19/0.45 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[61])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 (unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[67, 56])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 (unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[69, 8])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 ((~(unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0)))) | unequally_directed_opposite_lines(L!1, M!0) | (~unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (unequally_directed_opposite_lines(L!1, M!0) | (~unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 (unequally_directed_opposite_lines(L!1, M!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[72, 68])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 ((unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_opposite_lines(M!0, L!1)) | (~unequally_directed_opposite_lines(L!1, M!0)) | (~unequally_directed_opposite_lines(M!0, L!1))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 ((~unequally_directed_opposite_lines(L!1, M!0)) | (~unequally_directed_opposite_lines(M!0, L!1))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[74, 22])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 (~unequally_directed_opposite_lines(M!0, L!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[75, 73])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 ((~(unequally_directed_opposite_lines(M!0, L!1) <=> unequally_directed_lines(M!0, reverse_line(L!1)))) | unequally_directed_opposite_lines(M!0, L!1) | (~unequally_directed_lines(M!0, reverse_line(L!1)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (unequally_directed_opposite_lines(M!0, L!1) | (~unequally_directed_lines(M!0, reverse_line(L!1)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[77, 10])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (~unequally_directed_lines(M!0, reverse_line(L!1))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[78, 76])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 (^[L: $i, M: $i, N: $i] : refl((unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(83,plain,
% 0.19/0.46 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(L, N) | unequally_directed_lines(M, N)) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))))), rewrite((unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.46 tff(85,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')).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.46 tff(88,plain,(
% 0.19/0.46 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[87])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 (((~![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!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, M!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!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, M!0)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 ((unequally_directed_lines(M!0, reverse_line(L!1)) | unequally_directed_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, M!0))) <=> (unequally_directed_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, M!0)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 (((~![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!0, reverse_line(L!1)) | unequally_directed_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, M!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!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, M!0))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[91])).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 (((~![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!0, reverse_line(L!1)) | unequally_directed_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, M!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!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, M!0)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[92, 90])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 ((~![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!0, reverse_line(L!1)) | unequally_directed_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, M!0)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 ((~![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!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, M!0))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 (unequally_directed_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, M!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[95, 89])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (~unequally_directed_lines(M!0, M!0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[96, 79])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(M!0, L!1) | unequally_directed_lines(M!0, reverse_line(L!1)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(M!0, L!1) | unequally_directed_lines(M!0, reverse_line(L!1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(M!0, L!1) | unequally_directed_lines(M!0, reverse_line(L!1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(M!0, L!1) | unequally_directed_lines(M!0, reverse_line(L!1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (unequally_directed_lines(M!0, L!1) | unequally_directed_lines(M!0, reverse_line(L!1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[100, 63])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 (unequally_directed_lines(M!0, L!1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[101, 79])).
% 0.19/0.46 tff(103,assumption,(~unequally_directed_lines(M!0, M!0)), introduced(assumption)).
% 0.19/0.46 tff(104,assumption,(unequally_directed_lines(M!0, L!1)), introduced(assumption)).
% 0.19/0.46 tff(105,plain,
% 0.19/0.46 (((~![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!1, M!0) | (~unequally_directed_lines(M!0, L!1)) | unequally_directed_lines(M!0, M!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!1, M!0) | (~unequally_directed_lines(M!0, L!1)) | unequally_directed_lines(M!0, M!0))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(106,plain,
% 0.19/0.46 ((unequally_directed_lines(L!1, M!0) | unequally_directed_lines(M!0, M!0) | (~unequally_directed_lines(M!0, L!1))) <=> (unequally_directed_lines(L!1, M!0) | (~unequally_directed_lines(M!0, L!1)) | unequally_directed_lines(M!0, M!0))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(107,plain,
% 0.19/0.46 (((~![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!1, M!0) | unequally_directed_lines(M!0, M!0) | (~unequally_directed_lines(M!0, L!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!1, M!0) | (~unequally_directed_lines(M!0, L!1)) | unequally_directed_lines(M!0, M!0)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.46 tff(108,plain,
% 0.19/0.46 (((~![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!1, M!0) | unequally_directed_lines(M!0, M!0) | (~unequally_directed_lines(M!0, L!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!1, M!0) | (~unequally_directed_lines(M!0, L!1)) | unequally_directed_lines(M!0, M!0))),
% 0.19/0.46 inference(transitivity,[status(thm)],[107, 105])).
% 0.19/0.46 tff(109,plain,
% 0.19/0.46 ((~![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!1, M!0) | unequally_directed_lines(M!0, M!0) | (~unequally_directed_lines(M!0, L!1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(110,plain,
% 0.19/0.46 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!1, M!0) | (~unequally_directed_lines(M!0, L!1)) | unequally_directed_lines(M!0, M!0)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[110, 89, 56, 104, 103])).
% 0.19/0.46 tff(112,plain,(unequally_directed_lines(L!1, M!0) | (~unequally_directed_lines(M!0, L!1)) | unequally_directed_lines(M!0, M!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(113,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[112, 102, 97, 56])).
% 0.19/0.46 tff(114,plain,(unequally_directed_lines(L!1, M!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(115,plain,
% 0.19/0.46 (^[L: $i, M: $i, N: $i] : refl(((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(116,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.46 tff(117,plain,
% 0.19/0.46 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) <=> (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N)))))), rewrite((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) <=> (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))), trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite(((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(118,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[117])).
% 0.19/0.46 tff(119,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(120,plain,
% 0.19/0.46 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite(((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))))), rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(121,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[120])).
% 0.19/0.46 tff(122,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')).
% 0.19/0.46 tff(123,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.46 tff(124,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.19/0.46 tff(125,plain,(
% 0.19/0.46 ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[124])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 (((~![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(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))))) | (~((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!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(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))))) | (~((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (((~unequally_directed_lines(L!1, M!0)) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))))) | (~((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1))))) | (~unequally_directed_lines(L!1, reverse_line(M!0)))) <=> ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))))) | (~((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 (((~![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(L!1, M!0)) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))))) | (~((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1))))) | (~unequally_directed_lines(L!1, reverse_line(M!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))))) | (~((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[129])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 (((~![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(L!1, M!0)) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))))) | (~((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1))))) | (~unequally_directed_lines(L!1, reverse_line(M!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))))) | (~((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[130, 128])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 ((~![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(L!1, M!0)) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))))) | (~((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1))))) | (~unequally_directed_lines(L!1, reverse_line(M!0))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))))) | (~((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))))) | (~((~unequally_directed_lines(L!1, L!1)) | (~unequally_directed_lines(L!1, reverse_line(L!1)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[133, 127])).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 ((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[134, 114, 55])).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 (~unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[135, 27])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 ((~(unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0)))) | (~unequally_directed_opposite_lines(L!1, M!0)) | unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(138,plain,
% 0.19/0.47 ((~unequally_directed_opposite_lines(L!1, M!0)) | unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[137, 70])).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[138, 136, 25])).
% 0.19/0.47 tff(140,plain,(unequally_directed_lines(M!0, reverse_line(L!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(141,assumption,(unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))), introduced(assumption)).
% 0.19/0.47 tff(142,assumption,(left_convergent_lines(M!0, reverse_line(L!1)) | left_convergent_lines(M!0, reverse_line(reverse_line(L!1)))), introduced(assumption)).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 (^[L: $i, M: $i] : refl((~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[143])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(146,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')).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.47 tff(148,plain,(
% 0.19/0.47 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[147])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(M!0, reverse_line(L!1)) | left_convergent_lines(M!0, reverse_line(reverse_line(L!1)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(151,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[150, 149, 142])).
% 0.19/0.47 tff(152,plain,(~(left_convergent_lines(M!0, reverse_line(L!1)) | left_convergent_lines(M!0, reverse_line(reverse_line(L!1))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(153,plain,
% 0.19/0.47 ((left_convergent_lines(M!0, reverse_line(L!1)) | left_convergent_lines(M!0, reverse_line(reverse_line(L!1)))) | (~left_convergent_lines(M!0, reverse_line(reverse_line(L!1))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(154,plain,
% 0.19/0.47 (~left_convergent_lines(M!0, reverse_line(reverse_line(L!1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.19/0.47 tff(155,plain,
% 0.19/0.47 ((left_convergent_lines(M!0, reverse_line(L!1)) | left_convergent_lines(M!0, reverse_line(reverse_line(L!1)))) | (~left_convergent_lines(M!0, reverse_line(L!1)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(156,plain,
% 0.19/0.47 (~left_convergent_lines(M!0, reverse_line(L!1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[155, 152])).
% 0.19/0.47 tff(157,assumption,(unequally_directed_lines(M!0, reverse_line(L!1))), introduced(assumption)).
% 0.19/0.47 tff(158,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(159,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[158])).
% 0.19/0.47 tff(160,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(161,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[160])).
% 0.19/0.47 tff(162,plain,
% 0.19/0.47 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(163,plain,
% 0.19/0.47 (^[L: $i, M: $i] : rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(164,plain,
% 0.19/0.47 (![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[163])).
% 0.19/0.47 tff(165,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')).
% 0.19/0.47 tff(166,plain,
% 0.19/0.47 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.47 tff(167,plain,
% 0.19/0.47 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.19/0.47 tff(168,plain,(
% 0.19/0.47 ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[167])).
% 0.19/0.47 tff(169,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.19/0.47 tff(170,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[169, 159])).
% 0.19/0.47 tff(171,plain,
% 0.19/0.47 (((~![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(M!0, reverse_line(L!1))) | left_convergent_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))) | left_convergent_lines(M!0, reverse_line(reverse_line(L!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(M!0, reverse_line(L!1))) | left_convergent_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))) | left_convergent_lines(M!0, reverse_line(reverse_line(L!1))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(172,plain,
% 0.19/0.47 ((left_convergent_lines(M!0, reverse_line(reverse_line(L!1))) | (~unequally_directed_lines(M!0, reverse_line(L!1))) | left_convergent_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))))) <=> ((~unequally_directed_lines(M!0, reverse_line(L!1))) | left_convergent_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))) | left_convergent_lines(M!0, reverse_line(reverse_line(L!1))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(173,plain,
% 0.19/0.47 (((~![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(M!0, reverse_line(reverse_line(L!1))) | (~unequally_directed_lines(M!0, reverse_line(L!1))) | left_convergent_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(L!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(M!0, reverse_line(L!1))) | left_convergent_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))) | left_convergent_lines(M!0, reverse_line(reverse_line(L!1)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[172])).
% 0.19/0.47 tff(174,plain,
% 0.19/0.47 (((~![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(M!0, reverse_line(reverse_line(L!1))) | (~unequally_directed_lines(M!0, reverse_line(L!1))) | left_convergent_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(L!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(M!0, reverse_line(L!1))) | left_convergent_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))) | left_convergent_lines(M!0, reverse_line(reverse_line(L!1))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[173, 171])).
% 0.19/0.47 tff(175,plain,
% 0.19/0.47 ((~![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(M!0, reverse_line(reverse_line(L!1))) | (~unequally_directed_lines(M!0, reverse_line(L!1))) | left_convergent_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(176,plain,
% 0.19/0.47 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(M!0, reverse_line(L!1))) | left_convergent_lines(M!0, reverse_line(L!1)) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))) | left_convergent_lines(M!0, reverse_line(reverse_line(L!1)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.19/0.47 tff(177,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[176, 170, 157, 156, 154, 141])).
% 0.19/0.47 tff(178,plain,((~unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))) | (~unequally_directed_lines(M!0, reverse_line(L!1)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(179,plain,
% 0.19/0.47 (~unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[178, 140])).
% 0.19/0.47 tff(180,assumption,(~unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))), introduced(assumption)).
% 0.19/0.47 tff(181,assumption,(~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))), introduced(assumption)).
% 0.19/0.47 tff(182,plain,
% 0.19/0.47 (unequally_directed_opposite_lines(M!0, L!1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[78, 140])).
% 0.19/0.47 tff(183,plain,
% 0.19/0.47 (~unequally_directed_opposite_lines(L!1, M!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[75, 182])).
% 0.19/0.47 tff(184,plain,
% 0.19/0.47 (~unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[72, 183])).
% 0.19/0.47 tff(185,plain,
% 0.19/0.47 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(186,plain,
% 0.19/0.47 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(187,plain,
% 0.19/0.47 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.47 tff(188,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[187, 63, 184, 181])).
% 0.19/0.47 tff(189,plain,(unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(190,assumption,(~unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1)), introduced(assumption)).
% 0.19/0.47 tff(191,plain,
% 0.19/0.47 (((~![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!1, L!1) | unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!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!1, L!1) | unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(192,plain,
% 0.19/0.47 ((unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1) | unequally_directed_lines(L!1, L!1) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))) <=> (unequally_directed_lines(L!1, L!1) | unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(193,plain,
% 0.19/0.47 (((~![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!0)), L!1) | unequally_directed_lines(L!1, L!1) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!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!1, L!1) | unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[192])).
% 0.19/0.47 tff(194,plain,
% 0.19/0.47 (((~![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!0)), L!1) | unequally_directed_lines(L!1, L!1) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!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!1, L!1) | unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[193, 191])).
% 0.19/0.48 tff(195,plain,
% 0.19/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1) | unequally_directed_lines(L!1, L!1) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(196,plain,
% 0.19/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!1, L!1) | unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.19/0.48 tff(197,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[196, 89, 53, 190, 189])).
% 0.19/0.48 tff(198,plain,(unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(199,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1)) | unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!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!1, reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1)) | unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(200,plain,
% 0.19/0.48 ((unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1))) <=> (unequally_directed_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1)) | unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(201,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), L!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!1, reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1)) | unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[200])).
% 0.19/0.48 tff(202,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), L!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!1, reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1)) | unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[201, 199])).
% 0.19/0.48 tff(203,plain,
% 0.19/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(204,plain,
% 0.19/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), L!1)) | unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.19/0.48 tff(205,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[204, 89, 184, 198, 180])).
% 0.19/0.48 tff(206,plain,(unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(207,assumption,(left_convergent_lines(reverse_line(reverse_line(M!0)), M!0) | left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))), introduced(assumption)).
% 0.19/0.48 tff(208,plain,
% 0.19/0.48 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(M!0)), M!0) | left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(209,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[208, 149, 207])).
% 0.19/0.48 tff(210,plain,(~(left_convergent_lines(reverse_line(reverse_line(M!0)), M!0) | left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(211,plain,
% 0.19/0.48 ((left_convergent_lines(reverse_line(reverse_line(M!0)), M!0) | left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))) | (~left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(212,plain,
% 0.19/0.48 (~left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.19/0.48 tff(213,plain,
% 0.19/0.48 ((left_convergent_lines(reverse_line(reverse_line(M!0)), M!0) | left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))) | (~left_convergent_lines(reverse_line(reverse_line(M!0)), M!0))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(214,plain,
% 0.19/0.48 (~left_convergent_lines(reverse_line(reverse_line(M!0)), M!0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[213, 210])).
% 0.19/0.48 tff(215,assumption,(unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)), introduced(assumption)).
% 0.19/0.48 tff(216,assumption,(unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))), introduced(assumption)).
% 0.19/0.48 tff(217,plain,
% 0.19/0.48 (((~![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(reverse_line(reverse_line(M!0)), reverse_line(M!0))) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), M!0))) <=> ((~![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(reverse_line(reverse_line(M!0)), reverse_line(M!0))) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), M!0))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(218,plain,
% 0.19/0.48 ((left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), M!0) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)))) <=> ((~unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), M!0))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(219,plain,
% 0.19/0.48 (((~![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!0)), reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), M!0) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))))) <=> ((~![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(reverse_line(reverse_line(M!0)), reverse_line(M!0))) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), M!0)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[218])).
% 0.19/0.48 tff(220,plain,
% 0.19/0.48 (((~![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!0)), reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), M!0) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))))) <=> ((~![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(reverse_line(reverse_line(M!0)), reverse_line(M!0))) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), M!0))),
% 0.19/0.48 inference(transitivity,[status(thm)],[219, 217])).
% 0.19/0.48 tff(221,plain,
% 0.19/0.48 ((~![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!0)), reverse_line(M!0)) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), M!0) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(222,plain,
% 0.19/0.48 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0)) | left_convergent_lines(reverse_line(reverse_line(M!0)), M!0)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.19/0.48 tff(223,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[222, 170, 216, 215, 214, 212])).
% 0.19/0.48 tff(224,plain,((~unequally_directed_lines(reverse_line(reverse_line(M!0)), reverse_line(M!0))) | (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(225,plain,
% 0.19/0.48 (~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[224, 206])).
% 0.19/0.48 tff(226,assumption,(~unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0)), introduced(assumption)).
% 0.19/0.48 tff(227,assumption,((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0))))), introduced(assumption)).
% 0.19/0.48 tff(228,plain,
% 0.19/0.48 (((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))) | unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(229,plain,
% 0.19/0.48 ((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[228, 184])).
% 0.19/0.48 tff(230,assumption,(~unequally_directed_lines(M!0, L!1)), introduced(assumption)).
% 0.19/0.48 tff(231,plain,
% 0.19/0.48 (unequally_directed_lines(M!0, reverse_line(L!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[101, 230])).
% 0.19/0.48 tff(232,plain,
% 0.19/0.48 (unequally_directed_opposite_lines(M!0, L!1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[78, 231])).
% 0.19/0.48 tff(233,plain,
% 0.19/0.48 (~unequally_directed_opposite_lines(L!1, M!0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[75, 232])).
% 0.19/0.48 tff(234,plain,
% 0.19/0.48 (~unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[72, 233])).
% 0.19/0.48 tff(235,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, L!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!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, L!1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 ((unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, L!1))) <=> (unequally_directed_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, L!1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(237,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, L!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!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, L!1))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[236])).
% 0.19/0.48 tff(238,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, L!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!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, L!1)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[237, 235])).
% 0.19/0.48 tff(239,plain,
% 0.19/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, L!1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, L!1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 (unequally_directed_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, L!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[240, 89])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 (~unequally_directed_lines(L!1, L!1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[241, 234])).
% 0.19/0.48 tff(243,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(L!1, M!0)) | unequally_directed_lines(M!0, L!1) | unequally_directed_lines(L!1, L!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!1, M!0)) | unequally_directed_lines(M!0, L!1) | unequally_directed_lines(L!1, L!1))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(244,plain,
% 0.19/0.48 ((unequally_directed_lines(M!0, L!1) | unequally_directed_lines(L!1, L!1) | (~unequally_directed_lines(L!1, M!0))) <=> ((~unequally_directed_lines(L!1, M!0)) | unequally_directed_lines(M!0, L!1) | unequally_directed_lines(L!1, L!1))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(245,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!0, L!1) | unequally_directed_lines(L!1, L!1) | (~unequally_directed_lines(L!1, M!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!1, M!0)) | unequally_directed_lines(M!0, L!1) | unequally_directed_lines(L!1, L!1)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[244])).
% 0.19/0.48 tff(246,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!0, L!1) | unequally_directed_lines(L!1, L!1) | (~unequally_directed_lines(L!1, M!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!1, M!0)) | unequally_directed_lines(M!0, L!1) | unequally_directed_lines(L!1, L!1))),
% 0.19/0.48 inference(transitivity,[status(thm)],[245, 243])).
% 0.19/0.48 tff(247,plain,
% 0.19/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!0, L!1) | unequally_directed_lines(L!1, L!1) | (~unequally_directed_lines(L!1, M!0)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(248,plain,
% 0.19/0.48 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!1, M!0)) | unequally_directed_lines(M!0, L!1) | unequally_directed_lines(L!1, L!1)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.19/0.48 tff(249,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[248, 89, 114, 230, 242])).
% 0.19/0.48 tff(250,plain,(unequally_directed_lines(M!0, L!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(251,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))) | (~((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))) | (~((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))) | (~((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))) | (~((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(252,plain,
% 0.19/0.48 (((~unequally_directed_lines(M!0, L!1)) | (~((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))) | (~((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))) | (~unequally_directed_lines(M!0, reverse_line(L!1)))) <=> ((~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))) | (~((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))) | (~((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(253,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(M!0, L!1)) | (~((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))) | (~((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))) | (~unequally_directed_lines(M!0, reverse_line(L!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(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))) | (~((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))) | (~((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[252])).
% 0.19/0.48 tff(254,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(M!0, L!1)) | (~((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))) | (~((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))) | (~unequally_directed_lines(M!0, reverse_line(L!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(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))) | (~((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))) | (~((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[253, 251])).
% 0.19/0.48 tff(255,plain,
% 0.19/0.48 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(M!0, L!1)) | (~((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))) | (~((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))) | (~unequally_directed_lines(M!0, reverse_line(L!1))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(256,plain,
% 0.19/0.48 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(M!0, L!1)) | (~unequally_directed_lines(M!0, reverse_line(L!1))) | (~((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))) | (~((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.19/0.48 tff(257,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[256, 127, 250, 140, 229, 227])).
% 0.19/0.48 tff(258,plain,(~((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(259,plain,
% 0.19/0.48 (((~unequally_directed_lines(M!0, reverse_line(M!0))) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0))))) | unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(260,plain,
% 0.19/0.48 (unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[259, 258])).
% 0.19/0.48 tff(261,plain,
% 0.19/0.48 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!0, M!0) | unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!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!0, M!0) | unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(262,plain,
% 0.19/0.49 ((unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0) | unequally_directed_lines(M!0, M!0) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0))))) <=> (unequally_directed_lines(M!0, M!0) | unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(263,plain,
% 0.19/0.49 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0) | unequally_directed_lines(M!0, M!0) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!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!0, M!0) | unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[262])).
% 0.19/0.49 tff(264,plain,
% 0.19/0.49 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0) | unequally_directed_lines(M!0, M!0) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!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!0, M!0) | unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[263, 261])).
% 0.19/0.49 tff(265,plain,
% 0.19/0.49 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0) | unequally_directed_lines(M!0, M!0) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(266,plain,
% 0.19/0.49 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(M!0, M!0) | unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0) | (~unequally_directed_lines(M!0, reverse_line(reverse_line(M!0))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.19/0.49 tff(267,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[266, 89, 103, 260, 226])).
% 0.19/0.49 tff(268,plain,(unequally_directed_lines(reverse_line(reverse_line(M!0)), M!0) | unequally_directed_lines(M!0, M!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(269,plain,
% 0.19/0.49 (unequally_directed_lines(M!0, M!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[268, 225])).
% 0.19/0.49 tff(270,plain,
% 0.19/0.49 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(M!0, M!0)) | unequally_directed_lines(M!0, reverse_line(reverse_line(L!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!0, M!0)) | unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(271,plain,
% 0.19/0.49 ((unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))) | unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))) | (~unequally_directed_lines(M!0, M!0))) <=> ((~unequally_directed_lines(M!0, M!0)) | unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(272,plain,
% 0.19/0.49 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))) | unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))) | (~unequally_directed_lines(M!0, M!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!0, M!0)) | unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[271])).
% 0.19/0.49 tff(273,plain,
% 0.19/0.49 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))) | unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))) | (~unequally_directed_lines(M!0, M!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!0, M!0)) | unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[272, 270])).
% 0.19/0.49 tff(274,plain,
% 0.19/0.49 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))) | unequally_directed_lines(M!0, reverse_line(reverse_line(L!1))) | (~unequally_directed_lines(M!0, M!0)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(275,plain,
% 0.19/0.49 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!0, M!0)) | unequally_directed_lines(M!0, reverse_line(reverse_line(L!1)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.19/0.49 tff(276,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[275, 89, 269, 179])).
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------