%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO188+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:50 AM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO188+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 14:40:47 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(distinct_points_type, type, (
% 0.21/0.43 distinct_points: ( $i * $i ) > $o)).
% 0.21/0.43 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.43 tptp_fun_Y_1: $i)).
% 0.21/0.43 tff(tptp_fun_Z_0_type, type, (
% 0.21/0.43 tptp_fun_Z_0: $i)).
% 0.21/0.43 tff(intersection_point_type, type, (
% 0.21/0.43 intersection_point: ( $i * $i ) > $i)).
% 0.21/0.43 tff(line_connecting_type, type, (
% 0.21/0.43 line_connecting: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_X_2_type, type, (
% 0.21/0.43 tptp_fun_X_2: $i)).
% 0.21/0.43 tff(apart_point_and_line_type, type, (
% 0.21/0.43 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.43 tff(convergent_lines_type, type, (
% 0.21/0.43 convergent_lines: ( $i * $i ) > $o)).
% 0.21/0.43 tff(distinct_lines_type, type, (
% 0.21/0.43 distinct_lines: ( $i * $i ) > $o)).
% 0.21/0.43 tff(incident_point_and_line_type, type, (
% 0.21/0.43 incident_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.43 tff(1,assumption,(distinct_points(Z!0, Y!1)), introduced(assumption)).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.43 tff(7,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.43 tff(10,plain,(
% 0.21/0.43 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[9])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.21/0.43 tff(17,assumption,(~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))), introduced(assumption)).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (^[X: $i, Y: $i] : refl((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (^[X: $i, Y: $i] : trans(rewrite((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), rewrite((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), ((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.43 tff(23,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.43 tff(26,plain,(
% 0.21/0.43 ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[25])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(X!2, line_connecting(Z!0, Y!1)) <=> incident_point_and_line(X!2, line_connecting(Z!0, Y!1))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (~(apart_point_and_line(X!2, line_connecting(Z!0, Y!1)) <=> incident_point_and_line(X!2, line_connecting(Z!0, Y!1)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(X, line_connecting(Z, Y)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(X, line_connecting(Z, Y))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & incident_point_and_line(Z, line_connecting(X, Y))) => incident_point_and_line(X, line_connecting(Z, Y)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(X, line_connecting(Z, Y))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(32,axiom,(~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & incident_point_and_line(Z, line_connecting(X, Y))) => incident_point_and_line(X, line_connecting(Z, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(X, line_connecting(Z, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(X, line_connecting(Z, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(X, line_connecting(Z, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(X, line_connecting(Z, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.21/0.43 tff(37,plain,(
% 0.21/0.43 ~((~(distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & incident_point_and_line(Z!0, line_connecting(X!2, Y!1)))) | incident_point_and_line(X!2, line_connecting(Z!0, Y!1)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[36])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 (~incident_point_and_line(X!2, line_connecting(Z!0, Y!1))),
% 0.21/0.43 inference(or_elim,[status(thm)],[37])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 ((apart_point_and_line(X!2, line_connecting(Z!0, Y!1)) <=> incident_point_and_line(X!2, line_connecting(Z!0, Y!1))) | apart_point_and_line(X!2, line_connecting(Z!0, Y!1)) | incident_point_and_line(X!2, line_connecting(Z!0, Y!1))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 ((apart_point_and_line(X!2, line_connecting(Z!0, Y!1)) <=> incident_point_and_line(X!2, line_connecting(Z!0, Y!1))) | apart_point_and_line(X!2, line_connecting(Z!0, Y!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (apart_point_and_line(X!2, line_connecting(Z!0, Y!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[40, 29])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & incident_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.21/0.43 inference(or_elim,[status(thm)],[37])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (distinct_points(X!2, Z!0)),
% 0.21/0.43 inference(and_elim,[status(thm)],[42])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.43 tff(49,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.43 tff(52,plain,(
% 0.21/0.43 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[51])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[56, 53, 43])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.43 tff(63,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.21/0.44 tff(66,plain,(
% 0.21/0.44 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[65])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 ((distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1)))) <=> (apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[70, 68])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.44 tff(74,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[73, 67, 57, 41, 17])).
% 0.21/0.44 tff(75,plain,(distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(76,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(79,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[79])).
% 0.21/0.44 tff(81,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.21/0.44 tff(84,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.44 inference(skolemize,[status(sab)],[83])).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(87,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(88,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.44 tff(89,plain,
% 0.21/0.44 (convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[88, 85, 75])).
% 0.21/0.44 tff(90,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(91,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.44 tff(92,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.44 tff(95,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.21/0.44 tff(98,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[97])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (~apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[102, 99, 89])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.44 tff(109,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.21/0.44 tff(112,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[111])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (~apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[116, 113, 89])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> incident_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (~(apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> incident_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[118, 27])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (incident_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.21/0.44 inference(and_elim,[status(thm)],[42])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 ((apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> incident_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~incident_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 ((apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> incident_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[122, 119])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[126, 11, 43])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (distinct_points(X!2, Y!1)),
% 0.21/0.44 inference(and_elim,[status(thm)],[42])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[131, 53, 128])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[133])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))))), rewrite((~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[138])).
% 0.21/0.45 tff(140,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.21/0.45 tff(141,plain,
% 0.21/0.45 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.45 tff(142,plain,
% 0.21/0.45 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.21/0.45 tff(143,plain,(
% 0.21/0.45 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[142])).
% 0.21/0.45 tff(144,plain,
% 0.21/0.45 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[144, 134])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 ((apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Z!0))) <=> (apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(148,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Z!0)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Z!0)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[148, 146])).
% 0.21/0.45 tff(150,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Z!0)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(151,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.45 tff(152,plain,
% 0.21/0.45 (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[151, 145, 43, 132, 127, 57, 123])).
% 0.21/0.45 tff(153,plain,
% 0.21/0.45 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(154,plain,
% 0.21/0.45 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(155,plain,
% 0.21/0.45 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.21/0.45 tff(156,plain,
% 0.21/0.45 (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[155, 11, 128])).
% 0.21/0.45 tff(157,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(158,plain,
% 0.21/0.45 ((distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0)))) <=> (apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(159,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[158])).
% 0.21/0.45 tff(160,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[159, 157])).
% 0.21/0.45 tff(161,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(162,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.45 tff(163,plain,
% 0.21/0.45 (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[162, 67, 156, 152])).
% 0.21/0.45 tff(164,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 ((apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))) <=> (apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(166,plain,
% 0.21/0.46 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[165])).
% 0.21/0.46 tff(167,plain,
% 0.21/0.46 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[166, 164])).
% 0.21/0.46 tff(168,plain,
% 0.21/0.46 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(169,plain,
% 0.21/0.46 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.21/0.46 tff(170,plain,
% 0.21/0.46 (apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[169, 145, 163, 75, 117, 103])).
% 0.21/0.46 tff(171,plain,
% 0.21/0.46 (~distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[170, 16])).
% 0.21/0.46 tff(172,plain,
% 0.21/0.46 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(173,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(174,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.21/0.46 tff(175,plain,
% 0.21/0.46 ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[174, 53])).
% 0.21/0.46 tff(176,plain,
% 0.21/0.46 (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[175, 1])).
% 0.21/0.46 tff(177,plain,
% 0.21/0.46 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(178,plain,
% 0.21/0.46 ((apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))) <=> (apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(179,plain,
% 0.21/0.46 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[178])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[179, 177])).
% 0.21/0.47 tff(181,plain,
% 0.21/0.47 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(182,plain,
% 0.21/0.47 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)), line_connecting(Z!0, Y!1)) | (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.21/0.47 tff(183,plain,
% 0.21/0.47 (apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[182, 145, 127, 75, 117, 103])).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 (~distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[183, 176])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(186,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[185])).
% 0.21/0.47 tff(187,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(188,plain,
% 0.21/0.47 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | distinct_points(Y, Z)) <=> (distinct_points(Y, Z) | distinct_points(X, Z))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))))), rewrite((distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(189,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[188])).
% 0.21/0.47 tff(190,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart4')).
% 0.21/0.47 tff(191,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.21/0.47 tff(192,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.21/0.47 tff(193,plain,(
% 0.21/0.47 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[192])).
% 0.21/0.47 tff(194,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.21/0.47 tff(195,plain,
% 0.21/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(Z!0, Y!1)) | distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Z!0, Y!1)) | distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(196,plain,
% 0.21/0.47 ((distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Z!0, Y!1))) <=> ((~distinct_points(Z!0, Y!1)) | distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(197,plain,
% 0.21/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(Z!0, Y!1)) | distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[196])).
% 0.21/0.47 tff(198,plain,
% 0.21/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Z!0, Y!1)) | distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[197, 195])).
% 0.21/0.47 tff(199,plain,
% 0.21/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(Z!0, Y!1)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(200,plain,
% 0.21/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Z!0, Y!1)) | distinct_points(Z!0, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0))) | distinct_points(Y!1, intersection_point(line_connecting(Z!0, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.21/0.47 tff(201,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[200, 194, 1, 184, 171])).
% 0.21/0.47 tff(202,plain,(~distinct_points(Z!0, Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(203,assumption,(~distinct_points(Y!1, Y!1)), introduced(assumption)).
% 0.21/0.47 tff(204,assumption,(~distinct_points(Z!0, Y!1)), introduced(assumption)).
% 0.21/0.47 tff(205,plain,
% 0.21/0.47 (distinct_points(Y!1, Z!0)),
% 0.21/0.47 inference(and_elim,[status(thm)],[42])).
% 0.21/0.47 tff(206,plain,
% 0.21/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(207,plain,
% 0.21/0.47 ((distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0))) <=> ((~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(208,plain,
% 0.21/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[207])).
% 0.21/0.47 tff(209,plain,
% 0.21/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1))),
% 0.21/0.47 inference(transitivity,[status(thm)],[208, 206])).
% 0.21/0.47 tff(210,plain,
% 0.21/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(211,plain,
% 0.21/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.21/0.47 tff(212,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[211, 194, 205, 204, 203])).
% 0.21/0.47 tff(213,plain,(distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(214,plain,
% 0.21/0.47 (distinct_points(Y!1, Y!1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[213, 202])).
% 0.21/0.47 tff(215,plain,
% 0.21/0.47 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(216,plain,
% 0.21/0.47 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[215])).
% 0.21/0.47 tff(217,plain,
% 0.21/0.47 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(218,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart1')).
% 0.21/0.47 tff(219,plain,
% 0.21/0.47 (![X: $i] : (~distinct_points(X, X))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.21/0.47 tff(220,plain,(
% 0.21/0.47 ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.47 inference(skolemize,[status(sab)],[219])).
% 0.21/0.47 tff(221,plain,
% 0.21/0.47 (![X: $i] : (~distinct_points(X, X))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.21/0.47 tff(222,plain,
% 0.21/0.47 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!1, Y!1))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(223,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[222, 221, 214])).
% 0.21/0.47 % SZS output end Proof
% 0.21/0.48 % E exiting
%------------------------------------------------------------------------------