%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO202+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:05:54 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO202+1 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 14:40:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(convergent_lines_type, type, (
% 0.12/0.38 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.38 tff(line_connecting_type, type, (
% 0.12/0.38 line_connecting: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.38 tptp_fun_Y_1: $i)).
% 0.12/0.38 tff(tptp_fun_X_2_type, type, (
% 0.12/0.38 tptp_fun_X_2: $i)).
% 0.12/0.38 tff(tptp_fun_Z_0_type, type, (
% 0.12/0.38 tptp_fun_Z_0: $i)).
% 0.12/0.38 tff(distinct_lines_type, type, (
% 0.12/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.38 tff(apart_point_and_line_type, type, (
% 0.12/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.38 tff(intersection_point_type, type, (
% 0.12/0.38 intersection_point: ( $i * $i ) > $i)).
% 0.12/0.38 tff(distinct_points_type, type, (
% 0.12/0.38 distinct_points: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,(
% 0.12/0.38 ![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.38 inference(skolemize,[status(sab)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X)) | (~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X)) | (~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~![X: $i, Y: $i, Z: $i] : (((distinct_points(X, Y) & distinct_points(X, Z)) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z))) => (~distinct_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X)) | (~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(12,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))) => (~distinct_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X)) | (~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X)) | (~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X)) | (~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(intersection_point(line_connecting(X, Y), line_connecting(X, Z)), X)) | (~(distinct_points(X, Y) & distinct_points(X, Z) & convergent_lines(line_connecting(X, Y), line_connecting(X, Z)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.12/0.39 tff(17,plain,(
% 0.12/0.39 ~((~distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)) | (~(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)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[16])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (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))),
% 0.12/0.39 inference(or_elim,[status(thm)],[17])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))),
% 0.12/0.39 inference(and_elim,[status(thm)],[18])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.39 tff(25,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')).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.12/0.39 tff(28,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[27])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (((~![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 ((~![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))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ((~![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (~apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Y!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[32, 29, 19])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.39 tff(39,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')).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.12/0.39 tff(42,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[41])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (((~![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 ((~![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))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 ((~![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (~apart_point_and_line(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), line_connecting(X!2, Z!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[46, 43, 19])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (distinct_points(X!2, Z!0)),
% 0.12/0.39 inference(and_elim,[status(thm)],[18])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.39 tff(54,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')).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.12/0.39 tff(57,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[56])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (((~![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 ((~![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))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 ((~![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[61, 58, 48])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (distinct_points(X!2, Y!1)),
% 0.12/0.39 inference(and_elim,[status(thm)],[18])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (((~![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~![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))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[66, 58, 63])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (distinct_points(intersection_point(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)), X!2)),
% 0.12/0.39 inference(or_elim,[status(thm)],[17])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (^[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_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_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, 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) | (~(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_points(X, Y)) | (~distinct_lines(U, V)))))), 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_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_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_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_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[71])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[74])).
% 0.12/0.39 tff(76,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')).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.12/0.40 tff(79,plain,(
% 0.12/0.40 ![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))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[78])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (((~![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)))) | ((~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_lines(line_connecting(X!2, 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_points(X, Y)) | (~distinct_lines(U, V)))) | (~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_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 ((apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, 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)) | 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, Y!1), line_connecting(X!2, Z!0)))) <=> ((~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_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 (((~![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)))) | (apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, 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)) | 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, 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_points(X, Y)) | (~distinct_lines(U, V)))) | ((~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_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[83])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (((~![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)))) | (apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, 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)) | 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, 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_points(X, Y)) | (~distinct_lines(U, V)))) | (~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_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[84, 82])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 ((~![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)))) | (apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, 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)) | 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, Y!1), line_connecting(X!2, Z!0))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 ((~![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)))) | (~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_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[87, 81, 68, 67, 62, 47, 33])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[92])).
% 0.12/0.40 tff(94,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')).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.12/0.40 tff(97,plain,(
% 0.12/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[96])).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0)) | (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))) <=> (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0)) | (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[100])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0)) | (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[101, 99])).
% 0.12/0.40 tff(103,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0)) | (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Z!0))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 (~convergent_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[104, 98, 88, 9])).
% 0.12/0.40 tff(106,plain,
% 0.12/0.40 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[106])).
% 0.12/0.40 tff(108,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(109,plain,
% 0.12/0.40 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(110,plain,
% 0.12/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[109])).
% 0.12/0.41 tff(111,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.12/0.41 tff(112,plain,
% 0.12/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.12/0.41 tff(113,plain,
% 0.12/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.12/0.41 tff(114,plain,(
% 0.12/0.41 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[113])).
% 0.12/0.41 tff(115,plain,
% 0.12/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.12/0.41 tff(116,plain,
% 0.12/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_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))) | convergent_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] : (convergent_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))) | convergent_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)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(117,plain,
% 0.12/0.41 ((convergent_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))) | convergent_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)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(118,plain,
% 0.12/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_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] : (convergent_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))) | convergent_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))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[117])).
% 0.12/0.41 tff(119,plain,
% 0.12/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_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] : (convergent_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))) | convergent_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)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[118, 116])).
% 0.12/0.41 tff(120,plain,
% 0.12/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_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))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(121,plain,
% 0.12/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_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))) | convergent_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))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.12/0.41 tff(122,plain,
% 0.12/0.41 (convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[121, 115, 19, 105])).
% 0.12/0.41 tff(123,plain,
% 0.12/0.41 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(124,plain,
% 0.12/0.41 ($false),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[123, 7, 122])).
% 0.12/0.41 % SZS output end Proof
% 0.12/0.41 % E exiting
%------------------------------------------------------------------------------