%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO202+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:55 AM UTC 2025
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO202+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:41:24 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(convergent_lines_type, type, (
% 0.18/0.40 convergent_lines: ( $i * $i ) > $o)).
% 0.18/0.40 tff(line_connecting_type, type, (
% 0.18/0.40 line_connecting: ( $i * $i ) > $i)).
% 0.18/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.18/0.40 tptp_fun_Y_1: $i)).
% 0.18/0.40 tff(tptp_fun_X_2_type, type, (
% 0.18/0.40 tptp_fun_X_2: $i)).
% 0.18/0.40 tff(distinct_lines_type, type, (
% 0.18/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.18/0.40 tff(tptp_fun_Z_0_type, type, (
% 0.18/0.40 tptp_fun_Z_0: $i)).
% 0.18/0.40 tff(distinct_points_type, type, (
% 0.18/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.18/0.40 tff(intersection_point_type, type, (
% 0.18/0.40 intersection_point: ( $i * $i ) > $i)).
% 0.18/0.40 tff(equal_points_type, type, (
% 0.18/0.40 equal_points: ( $i * $i ) > $o)).
% 0.18/0.40 tff(apart_point_and_line_type, type, (
% 0.18/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.40 tff(1,plain,
% 0.18/0.40 (^[X: $i, Y: $i] : refl((~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(5,plain,
% 0.18/0.40 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.40 tff(6,axiom,(![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax1')).
% 0.18/0.40 tff(7,plain,
% 0.18/0.40 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.40 tff(9,plain,(
% 0.18/0.40 ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[8])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.40 tff(11,plain,
% 0.18/0.40 ((~![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))) | (~(distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2) <=> equal_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(12,plain,
% 0.18/0.40 (~(distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2) <=> equal_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))) | equal_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))) | equal_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : (((distinct_points(X, Y) & distinct_points(X, Z)) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z))) => equal_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))) | equal_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(15,axiom,(~![X: $i, Y: $i, Z: $i] : (((distinct_points(X, Y) & distinct_points(X, Z)) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z))) => equal_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))) | equal_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.40 tff(17,plain,
% 0.18/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))) | equal_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))) | equal_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))) | equal_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.18/0.40 tff(20,plain,(
% 0.18/0.40 ~((~(distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))) | equal_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2))),
% 0.18/0.40 inference(skolemize,[status(sab)],[19])).
% 0.18/0.40 tff(21,plain,
% 0.18/0.40 (~equal_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)),
% 0.18/0.40 inference(or_elim,[status(thm)],[20])).
% 0.18/0.40 tff(22,plain,
% 0.18/0.40 ((distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2) <=> equal_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)) | distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2) | equal_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 ((distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2) <=> equal_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)) | distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 (distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[23, 12])).
% 0.18/0.40 tff(25,plain,
% 0.18/0.40 (distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))),
% 0.18/0.40 inference(or_elim,[status(thm)],[20])).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 (convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))),
% 0.18/0.40 inference(and_elim,[status(thm)],[25])).
% 0.18/0.40 tff(27,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(28,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.40 tff(29,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(30,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.40 tff(32,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')).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.18/0.40 tff(35,plain,(
% 0.18/0.40 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[34])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(39,plain,
% 0.18/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (~apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[39, 36, 26])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(45,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.41 tff(46,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')).
% 0.18/0.41 tff(47,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.41 tff(48,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.18/0.41 tff(49,plain,(
% 0.18/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[48])).
% 0.18/0.41 tff(50,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.18/0.41 tff(51,plain,
% 0.18/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(X!2, 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(X!2, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(52,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(53,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | (~apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.18/0.41 tff(54,plain,
% 0.18/0.41 (~apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[53, 50, 26])).
% 0.18/0.41 tff(55,plain,
% 0.18/0.41 (distinct_points(X!2, Z!0)),
% 0.18/0.41 inference(and_elim,[status(thm)],[25])).
% 0.18/0.41 tff(56,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(57,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.18/0.41 tff(58,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(59,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(60,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.41 tff(61,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.18/0.41 tff(62,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.18/0.41 tff(63,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.18/0.41 tff(64,plain,(
% 0.18/0.41 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[63])).
% 0.18/0.41 tff(65,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.18/0.41 tff(66,plain,
% 0.18/0.41 (((~![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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(67,plain,
% 0.18/0.41 ((~![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))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(68,plain,
% 0.18/0.41 ((~![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)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.41 tff(69,plain,
% 0.18/0.41 (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[68, 65, 55])).
% 0.18/0.41 tff(70,plain,
% 0.18/0.41 (distinct_points(X!2, Y!1)),
% 0.18/0.41 inference(and_elim,[status(thm)],[25])).
% 0.18/0.41 tff(71,plain,
% 0.18/0.41 (((~![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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(72,plain,
% 0.18/0.41 ((~![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))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(73,plain,
% 0.18/0.41 ((~![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)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.18/0.41 tff(74,plain,
% 0.18/0.41 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[73, 65, 70])).
% 0.18/0.41 tff(75,plain,
% 0.18/0.41 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.18/0.41 tff(77,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[77])).
% 0.18/0.41 tff(79,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(80,plain,
% 0.18/0.41 (^[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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.41 tff(82,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')).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.19/0.41 tff(85,plain,(
% 0.19/0.41 ![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))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[84])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (((~![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)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1)) | (~distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)) | (~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)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1)) | (~distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2))) <=> (apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1)) | (~distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (((~![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)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), 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(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1)) | (~distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (((~![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)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), 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(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1)) | (~distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[90, 88])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~![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)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((~![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)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0)) | apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1)) | (~distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[93, 87, 74, 69, 54, 40, 24])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.42 tff(100,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')).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.42 tff(103,plain,(
% 0.19/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[102])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 ((distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))) <=> ((~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[107, 105])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[110, 104, 26, 94])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(115,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.42 tff(117,plain,(
% 0.19/0.42 ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.42 inference(skolemize,[status(sab)],[116])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[119, 118, 111])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------