%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO255+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 05:06:09 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO255+3 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 14:43:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(unequally_directed_lines_type, type, (
% 0.19/0.37 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.37 tff(tptp_fun_L_2_type, type, (
% 0.19/0.37 tptp_fun_L_2: $i)).
% 0.19/0.37 tff(line_connecting_type, type, (
% 0.19/0.37 line_connecting: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_A_1_type, type, (
% 0.19/0.37 tptp_fun_A_1: $i)).
% 0.19/0.37 tff(tptp_fun_B_0_type, type, (
% 0.19/0.37 tptp_fun_B_0: $i)).
% 0.19/0.37 tff(reverse_line_type, type, (
% 0.19/0.37 reverse_line: $i > $i)).
% 0.19/0.37 tff(equally_directed_lines_type, type, (
% 0.19/0.37 equally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.37 tff(distinct_points_type, type, (
% 0.19/0.37 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.37 tff(incident_point_and_line_type, type, (
% 0.19/0.37 incident_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.37 tff(before_on_line_type, type, (
% 0.19/0.37 before_on_line: ( $i * $i * $i ) > $o)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[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))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (^[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)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.37 tff(6,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')).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.37 tff(9,plain,(
% 0.19/0.37 ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[8])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) <=> equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (~(unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) <=> equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (^[L: $i, A: $i, B: $i] : refl((~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B))) <=> (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B))) <=> ![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (^[L: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))))), ((before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))))))), rewrite((before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))))) <=> (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))), ((before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B))))), rewrite((~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B))) <=> (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))), ((before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> ![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (^[L: $i, A: $i, B: $i] : rewrite((before_on_line(L, A, B) <=> (((distinct_points(A, B) & incident_point_and_line(A, L)) & incident_point_and_line(B, L)) & equally_directed_lines(L, line_connecting(A, B)))) <=> (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & incident_point_and_line(A, L)) & incident_point_and_line(B, L)) & equally_directed_lines(L, line_connecting(A, B)))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.37 tff(20,axiom,(![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & incident_point_and_line(A, L)) & incident_point_and_line(B, L)) & equally_directed_lines(L, line_connecting(A, B))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax4_defns')).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.37 tff(23,plain,(
% 0.19/0.37 ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[22])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (((~![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))) | (~(((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1)))) <=> ((~![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))) | (~(((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 ((~(((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1))) <=> (~(((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 ((((~distinct_points(B!0, A!1)) | (~incident_point_and_line(B!0, L!2)) | (~incident_point_and_line(A!1, L!2)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1)) <=> (((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 ((~(((~distinct_points(B!0, A!1)) | (~incident_point_and_line(B!0, L!2)) | (~incident_point_and_line(A!1, L!2)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1))) <=> (~(((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 ((~(((~distinct_points(B!0, A!1)) | (~incident_point_and_line(B!0, L!2)) | (~incident_point_and_line(A!1, L!2)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1))) <=> (~(((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[29, 27])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (((~![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!0, A!1)) | (~incident_point_and_line(B!0, L!2)) | (~incident_point_and_line(A!1, L!2)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1)))) <=> ((~![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))) | (~(((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (((~![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!0, A!1)) | (~incident_point_and_line(B!0, L!2)) | (~incident_point_and_line(A!1, L!2)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1)))) <=> ((~![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))) | (~(((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[31, 26])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 ((~![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!0, A!1)) | (~incident_point_and_line(B!0, L!2)) | (~incident_point_and_line(A!1, L!2)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ((~![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))) | (~(((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (~(((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[34, 25])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 ((~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))) <=> (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(37,axiom,(~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[38, 36])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.38 tff(42,plain,(
% 0.19/0.38 before_on_line(L!2, A!1, B!0) & before_on_line(L!2, B!0, A!1)),
% 0.19/0.38 inference(skolemize,[status(sab)],[41])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (before_on_line(L!2, B!0, A!1)),
% 0.19/0.38 inference(and_elim,[status(thm)],[42])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 ((((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1)) | (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))))) | (~before_on_line(L!2, B!0, A!1))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 ((((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) <=> before_on_line(L!2, B!0, A!1)) | (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[45, 35])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) | distinct_points(B!0, A!1)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (distinct_points(B!0, A!1)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl(((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (![A: $i, B: $i] : (distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.38 tff(54,axiom,(![A: $i, B: $i] : (distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax9_cons_objs')).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.38 tff(57,plain,(
% 0.19/0.38 ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[56])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(B!0, A!1)) | equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))) <=> ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(B!0, A!1)) | equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(B!0, A!1)) | equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(B!0, A!1)) | equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[61, 58, 48])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 ((unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) <=> equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))) | (~equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 ((unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) <=> equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[64, 12])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(70,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.38 tff(71,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')).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.19/0.38 tff(74,plain,(
% 0.19/0.38 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[73])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.19/0.38 tff(76,plain,
% 0.19/0.38 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(77,plain,
% 0.19/0.38 ((unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)))) <=> (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[78, 76])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[81, 75, 65])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(L!2, line_connecting(B!0, A!1)) <=> equally_directed_lines(L!2, line_connecting(B!0, A!1))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (~(unequally_directed_lines(L!2, line_connecting(B!0, A!1)) <=> equally_directed_lines(L!2, line_connecting(B!0, A!1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[83, 10])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) | equally_directed_lines(L!2, line_connecting(B!0, A!1))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (equally_directed_lines(L!2, line_connecting(B!0, A!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[85, 46])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 ((unequally_directed_lines(L!2, line_connecting(B!0, A!1)) <=> equally_directed_lines(L!2, line_connecting(B!0, A!1))) | (~unequally_directed_lines(L!2, line_connecting(B!0, A!1))) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 ((unequally_directed_lines(L!2, line_connecting(B!0, A!1)) <=> equally_directed_lines(L!2, line_connecting(B!0, A!1))) | (~unequally_directed_lines(L!2, line_connecting(B!0, A!1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 (~unequally_directed_lines(L!2, line_connecting(B!0, A!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[88, 84])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), L!2)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), L!2)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), L!2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 (~unequally_directed_lines(line_connecting(B!0, A!1), L!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[92, 75, 89, 82])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) <=> equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (~(unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) <=> equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[94, 10])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 ((~![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))) <=> before_on_line(L!2, A!1, B!0)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (~(((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))) <=> before_on_line(L!2, A!1, B!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[96, 25])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 (before_on_line(L!2, A!1, B!0)),
% 0.19/0.39 inference(and_elim,[status(thm)],[42])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 ((((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))) <=> before_on_line(L!2, A!1, B!0)) | (~((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0))))) | (~before_on_line(L!2, A!1, B!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 ((((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))) <=> before_on_line(L!2, A!1, B!0)) | (~((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 (~((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))) | distinct_points(A!1, B!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 (distinct_points(A!1, B!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(A!1, B!0)) | equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))) <=> ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(A!1, B!0)) | equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(A!1, B!0)) | equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(A!1, B!0)) | equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.39 tff(107,plain,
% 0.19/0.39 (equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[106, 58, 103])).
% 0.19/0.39 tff(108,plain,
% 0.19/0.39 ((unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) <=> equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))) | (~equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 ((unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) <=> equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.39 tff(110,plain,
% 0.19/0.39 (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[109, 95])).
% 0.19/0.39 tff(111,plain,
% 0.19/0.39 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(112,plain,
% 0.19/0.39 ((unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)))) <=> (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(113,plain,
% 0.19/0.39 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.39 tff(114,plain,
% 0.19/0.39 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[113, 111])).
% 0.19/0.39 tff(115,plain,
% 0.19/0.39 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(116,plain,
% 0.19/0.39 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.39 tff(117,plain,
% 0.19/0.39 (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[116, 75, 110])).
% 0.19/0.39 tff(118,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(L!2, line_connecting(A!1, B!0)) <=> equally_directed_lines(L!2, line_connecting(A!1, B!0))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(119,plain,
% 0.19/0.39 (~(unequally_directed_lines(L!2, line_connecting(A!1, B!0)) <=> equally_directed_lines(L!2, line_connecting(A!1, B!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[118, 10])).
% 0.19/0.39 tff(120,plain,
% 0.19/0.39 (((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))) | equally_directed_lines(L!2, line_connecting(A!1, B!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(121,plain,
% 0.19/0.39 (equally_directed_lines(L!2, line_connecting(A!1, B!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[120, 101])).
% 0.19/0.39 tff(122,plain,
% 0.19/0.39 ((unequally_directed_lines(L!2, line_connecting(A!1, B!0)) <=> equally_directed_lines(L!2, line_connecting(A!1, B!0))) | (~unequally_directed_lines(L!2, line_connecting(A!1, B!0))) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(123,plain,
% 0.19/0.39 ((unequally_directed_lines(L!2, line_connecting(A!1, B!0)) <=> equally_directed_lines(L!2, line_connecting(A!1, B!0))) | (~unequally_directed_lines(L!2, line_connecting(A!1, B!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 (~unequally_directed_lines(L!2, line_connecting(A!1, B!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[123, 119])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)) | (~unequally_directed_lines(line_connecting(A!1, B!0), L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)) | (~unequally_directed_lines(line_connecting(A!1, B!0), L!2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)) | (~unequally_directed_lines(line_connecting(A!1, B!0), L!2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)) | (~unequally_directed_lines(line_connecting(A!1, B!0), L!2))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 (~unequally_directed_lines(line_connecting(A!1, B!0), L!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[127, 75, 124, 117])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[129])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(132,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')).
% 0.19/0.40 tff(133,plain,
% 0.19/0.40 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.40 tff(134,plain,(
% 0.19/0.40 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[133])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.19/0.40 tff(136,plain,
% 0.19/0.40 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.40 tff(139,plain,
% 0.19/0.40 (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[138, 135, 110])).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 ((unequally_directed_lines(line_connecting(B!0, A!1), L!2) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)))) <=> (unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(142,plain,
% 0.19/0.40 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), L!2) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[141])).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), L!2) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2))),
% 0.19/0.40 inference(transitivity,[status(thm)],[142, 140])).
% 0.19/0.40 tff(144,plain,
% 0.19/0.40 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), L!2) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(145,plain,
% 0.19/0.40 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.19/0.40 tff(146,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[145, 75, 139, 128, 93])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------