%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO172+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:05:44 AM UTC 2025
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO172+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:39:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(convergent_lines_type, type, (
% 0.18/0.38 convergent_lines: ( $i * $i ) > $o)).
% 0.18/0.38 tff(tptp_fun_X_2_type, type, (
% 0.18/0.38 tptp_fun_X_2: $i)).
% 0.18/0.38 tff(distinct_lines_type, type, (
% 0.18/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.18/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.18/0.38 tptp_fun_Y_1: $i)).
% 0.18/0.38 tff(apart_point_and_line_type, type, (
% 0.18/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.38 tff(tptp_fun_Z_0_type, type, (
% 0.18/0.38 tptp_fun_Z_0: $i)).
% 0.18/0.38 tff(incident_point_and_line_type, type, (
% 0.18/0.38 incident_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.38 tff(equal_points_type, type, (
% 0.18/0.38 equal_points: ( $i * $i ) > $o)).
% 0.18/0.38 tff(intersection_point_type, type, (
% 0.18/0.38 intersection_point: ( $i * $i ) > $i)).
% 0.18/0.38 tff(distinct_points_type, type, (
% 0.18/0.38 distinct_points: ( $i * $i ) > $o)).
% 0.18/0.38 tff(1,plain,
% 0.18/0.38 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(4,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.18/0.38 tff(5,plain,
% 0.18/0.38 (![X: $i] : (~convergent_lines(X, X))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.38 tff(6,plain,(
% 0.18/0.38 ![X: $i] : (~convergent_lines(X, X))),
% 0.18/0.38 inference(skolemize,[status(sab)],[5])).
% 0.18/0.38 tff(7,plain,
% 0.18/0.38 (![X: $i] : (~convergent_lines(X, X))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.38 tff(8,plain,
% 0.18/0.38 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!2, X!2))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(9,plain,
% 0.18/0.38 (~convergent_lines(X!2, X!2)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 (^[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))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.38 tff(15,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.18/0.38 tff(18,plain,(
% 0.18/0.38 ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[17])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(Z!0, Y!1) <=> incident_point_and_line(Z!0, Y!1)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (~(apart_point_and_line(Z!0, Y!1) <=> incident_point_and_line(Z!0, Y!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 ((~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & incident_point_and_line(Z, X)) & incident_point_and_line(Z, Y)) => equal_points(Z, intersection_point(X, Y)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(24,axiom,(~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & incident_point_and_line(Z, X)) & incident_point_and_line(Z, Y)) => equal_points(Z, intersection_point(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.18/0.38 tff(29,plain,(
% 0.18/0.38 ~((~(convergent_lines(X!2, Y!1) & incident_point_and_line(Z!0, X!2) & incident_point_and_line(Z!0, Y!1))) | equal_points(Z!0, intersection_point(X!2, Y!1)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[28])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (convergent_lines(X!2, Y!1) & incident_point_and_line(Z!0, X!2) & incident_point_and_line(Z!0, Y!1)),
% 0.18/0.38 inference(or_elim,[status(thm)],[29])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (incident_point_and_line(Z!0, Y!1)),
% 0.18/0.38 inference(and_elim,[status(thm)],[30])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 ((apart_point_and_line(Z!0, Y!1) <=> incident_point_and_line(Z!0, Y!1)) | (~apart_point_and_line(Z!0, Y!1)) | (~incident_point_and_line(Z!0, Y!1))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 ((apart_point_and_line(Z!0, Y!1) <=> incident_point_and_line(Z!0, Y!1)) | (~apart_point_and_line(Z!0, Y!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (~apart_point_and_line(Z!0, Y!1)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[33, 21])).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(Z!0, X!2) <=> incident_point_and_line(Z!0, X!2)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (~(apart_point_and_line(Z!0, X!2) <=> incident_point_and_line(Z!0, X!2))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[35, 19])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (incident_point_and_line(Z!0, X!2)),
% 0.18/0.38 inference(and_elim,[status(thm)],[30])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 ((apart_point_and_line(Z!0, X!2) <=> incident_point_and_line(Z!0, X!2)) | (~apart_point_and_line(Z!0, X!2)) | (~incident_point_and_line(Z!0, X!2))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 ((apart_point_and_line(Z!0, X!2) <=> incident_point_and_line(Z!0, X!2)) | (~apart_point_and_line(Z!0, X!2))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (~apart_point_and_line(Z!0, X!2)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (^[X: $i, Y: $i] : refl((~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (^[X: $i, Y: $i] : trans(rewrite((equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y)))), rewrite((~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y)))), ((equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.38 tff(46,axiom,(![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax1')).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.18/0.38 tff(49,plain,(
% 0.18/0.38 ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[48])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))) | (~(distinct_points(Z!0, intersection_point(X!2, Y!1)) <=> equal_points(Z!0, intersection_point(X!2, Y!1))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 (~(distinct_points(Z!0, intersection_point(X!2, Y!1)) <=> equal_points(Z!0, intersection_point(X!2, Y!1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 (~equal_points(Z!0, intersection_point(X!2, Y!1))),
% 0.18/0.38 inference(or_elim,[status(thm)],[29])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 ((distinct_points(Z!0, intersection_point(X!2, Y!1)) <=> equal_points(Z!0, intersection_point(X!2, Y!1))) | distinct_points(Z!0, intersection_point(X!2, Y!1)) | equal_points(Z!0, intersection_point(X!2, Y!1))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(55,plain,
% 0.18/0.38 ((distinct_points(Z!0, intersection_point(X!2, Y!1)) <=> equal_points(Z!0, intersection_point(X!2, Y!1))) | distinct_points(Z!0, intersection_point(X!2, Y!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.18/0.38 tff(56,plain,
% 0.18/0.38 (distinct_points(Z!0, intersection_point(X!2, Y!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.18/0.38 tff(57,plain,
% 0.18/0.38 (convergent_lines(X!2, Y!1)),
% 0.18/0.38 inference(and_elim,[status(thm)],[30])).
% 0.18/0.38 tff(58,plain,
% 0.18/0.38 (^[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))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(59,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[58])).
% 0.18/0.38 tff(60,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (^[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))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.39 tff(63,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.18/0.39 tff(66,plain,(
% 0.18/0.39 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[65])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[70, 67, 57])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 (^[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))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[72])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 (^[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))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[75])).
% 0.18/0.39 tff(77,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.18/0.39 tff(80,plain,(
% 0.18/0.39 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[79])).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[84, 81, 57])).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 (^[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))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 (^[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)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[88])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[91])).
% 0.18/0.39 tff(93,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/sandbox/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.18/0.39 tff(94,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.39 tff(95,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.18/0.39 tff(96,plain,(
% 0.18/0.39 ![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))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[95])).
% 0.18/0.39 tff(97,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.18/0.39 tff(98,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[97, 87])).
% 0.18/0.39 tff(99,plain,
% 0.18/0.39 (((~![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(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(Z!0, X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)))) <=> ((~![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(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(Z!0, X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(100,plain,
% 0.18/0.39 ((apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(Z!0, intersection_point(X!2, Y!1)))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(Z!0, X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(101,plain,
% 0.18/0.39 (((~![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(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(Z!0, intersection_point(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(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(Z!0, X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[100])).
% 0.18/0.39 tff(102,plain,
% 0.18/0.39 (((~![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(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(Z!0, intersection_point(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(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(Z!0, X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[101, 99])).
% 0.18/0.39 tff(103,plain,
% 0.18/0.39 ((~![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(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(104,plain,
% 0.18/0.39 ((~![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(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(Z!0, X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.18/0.39 tff(105,plain,
% 0.18/0.39 (~distinct_lines(Y!1, X!2)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[104, 98, 85, 71, 56, 40, 34])).
% 0.18/0.39 tff(106,plain,
% 0.18/0.39 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(107,plain,
% 0.18/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[106])).
% 0.18/0.39 tff(108,plain,
% 0.18/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(109,plain,
% 0.18/0.39 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(110,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[109])).
% 0.18/0.40 tff(111,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.18/0.40 tff(112,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.18/0.40 tff(113,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.18/0.40 tff(114,plain,(
% 0.18/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[113])).
% 0.18/0.40 tff(115,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.18/0.40 tff(116,plain,
% 0.18/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(117,plain,
% 0.18/0.40 ((distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(118,plain,
% 0.18/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[117])).
% 0.18/0.40 tff(119,plain,
% 0.18/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.18/0.40 inference(transitivity,[status(thm)],[118, 116])).
% 0.18/0.40 tff(120,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(121,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.18/0.40 tff(122,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[121, 115, 57, 105, 9])).
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------