%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO186+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:05:49 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO186+3 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 14:40:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(convergent_lines_type, type, (
% 0.19/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_U_1_type, type, (
% 0.19/0.39 tptp_fun_U_1: $i)).
% 0.19/0.39 tff(distinct_lines_type, type, (
% 0.19/0.39 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_V_0_type, type, (
% 0.19/0.39 tptp_fun_V_0: $i)).
% 0.19/0.39 tff(apart_point_and_line_type, type, (
% 0.19/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_X_3_type, type, (
% 0.19/0.39 tptp_fun_X_3: $i)).
% 0.19/0.39 tff(incident_point_and_line_type, type, (
% 0.19/0.39 incident_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.39 tff(distinct_points_type, type, (
% 0.19/0.39 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.39 tptp_fun_Y_2: $i)).
% 0.19/0.39 tff(equal_points_type, type, (
% 0.19/0.39 equal_points: ( $i * $i ) > $o)).
% 0.19/0.39 tff(intersection_point_type, type, (
% 0.19/0.39 intersection_point: ( $i * $i ) > $i)).
% 0.19/0.39 tff(1,assumption,(~convergent_lines(U!1, U!1)), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (^[X: $i, Y: $i] : refl((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (^[X: $i, Y: $i] : trans(rewrite((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), rewrite((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), ((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.39 tff(7,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.39 tff(10,plain,(
% 0.19/0.39 ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[9])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(X!3, V!0) <=> incident_point_and_line(X!3, V!0)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (~(apart_point_and_line(X!3, V!0) <=> incident_point_and_line(X!3, V!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & incident_point_and_line(X, U) & incident_point_and_line(X, V))) | equal_points(X, intersection_point(U, V)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & incident_point_and_line(X, U) & incident_point_and_line(X, V))) | equal_points(X, intersection_point(U, V))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : ((((distinct_points(X, Y) & convergent_lines(U, V)) & incident_point_and_line(X, U)) & incident_point_and_line(X, V)) => equal_points(X, intersection_point(U, V)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & incident_point_and_line(X, U) & incident_point_and_line(X, V))) | equal_points(X, intersection_point(U, V))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : ((((distinct_points(X, Y) & convergent_lines(U, V)) & incident_point_and_line(X, U)) & incident_point_and_line(X, V)) => equal_points(X, intersection_point(U, V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & incident_point_and_line(X, U) & incident_point_and_line(X, V))) | equal_points(X, intersection_point(U, V)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & incident_point_and_line(X, U) & incident_point_and_line(X, V))) | equal_points(X, intersection_point(U, V)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & incident_point_and_line(X, U) & incident_point_and_line(X, V))) | equal_points(X, intersection_point(U, V)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & incident_point_and_line(X, U) & incident_point_and_line(X, V))) | equal_points(X, intersection_point(U, V)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.19/0.39 tff(21,plain,(
% 0.19/0.39 ~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & incident_point_and_line(X!3, U!1) & incident_point_and_line(X!3, V!0))) | equal_points(X!3, intersection_point(U!1, V!0)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & incident_point_and_line(X!3, U!1) & incident_point_and_line(X!3, V!0)),
% 0.19/0.39 inference(or_elim,[status(thm)],[21])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (incident_point_and_line(X!3, V!0)),
% 0.19/0.39 inference(and_elim,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 ((apart_point_and_line(X!3, V!0) <=> incident_point_and_line(X!3, V!0)) | (~apart_point_and_line(X!3, V!0)) | (~incident_point_and_line(X!3, V!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((apart_point_and_line(X!3, V!0) <=> incident_point_and_line(X!3, V!0)) | (~apart_point_and_line(X!3, V!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (~apart_point_and_line(X!3, V!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[25, 13])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(X!3, U!1) <=> incident_point_and_line(X!3, U!1)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (~(apart_point_and_line(X!3, U!1) <=> incident_point_and_line(X!3, U!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[27, 11])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (incident_point_and_line(X!3, U!1)),
% 0.19/0.39 inference(and_elim,[status(thm)],[22])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((apart_point_and_line(X!3, U!1) <=> incident_point_and_line(X!3, U!1)) | (~apart_point_and_line(X!3, U!1)) | (~incident_point_and_line(X!3, U!1))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((apart_point_and_line(X!3, U!1) <=> incident_point_and_line(X!3, U!1)) | (~apart_point_and_line(X!3, U!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (~apart_point_and_line(X!3, U!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[31, 28])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (^[X: $i, Y: $i] : refl((~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.39 tff(38,axiom,(![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','ax1')).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.39 tff(41,plain,(
% 0.19/0.39 ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[40])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))) | (~(distinct_points(X!3, intersection_point(U!1, V!0)) <=> equal_points(X!3, intersection_point(U!1, V!0))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (~(distinct_points(X!3, intersection_point(U!1, V!0)) <=> equal_points(X!3, intersection_point(U!1, V!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (~equal_points(X!3, intersection_point(U!1, V!0))),
% 0.19/0.39 inference(or_elim,[status(thm)],[21])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((distinct_points(X!3, intersection_point(U!1, V!0)) <=> equal_points(X!3, intersection_point(U!1, V!0))) | distinct_points(X!3, intersection_point(U!1, V!0)) | equal_points(X!3, intersection_point(U!1, V!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((distinct_points(X!3, intersection_point(U!1, V!0)) <=> equal_points(X!3, intersection_point(U!1, V!0))) | distinct_points(X!3, intersection_point(U!1, V!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (distinct_points(X!3, intersection_point(U!1, V!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (convergent_lines(U!1, V!0)),
% 0.19/0.39 inference(and_elim,[status(thm)],[22])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.40 tff(55,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.40 tff(58,plain,(
% 0.19/0.40 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[57])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (~apart_point_and_line(intersection_point(U!1, V!0), U!1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[62, 59, 49])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.40 tff(69,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.40 tff(72,plain,(
% 0.19/0.40 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[71])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 73, 49])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (![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_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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (![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)))) <=> ![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (![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)))) <=> ![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.40 tff(85,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.40 tff(88,plain,(
% 0.19/0.40 ![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))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[87])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(X!3, intersection_point(U!1, V!0)))) <=> (apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(X!3, intersection_point(U!1, V!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(X!3, intersection_point(U!1, V!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[93, 91])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(X!3, intersection_point(U!1, V!0))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (~distinct_lines(V!0, U!1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[96, 90, 77, 63, 48, 32, 26])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.40 tff(103,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.19/0.41 tff(106,plain,(
% 0.19/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[105])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 ((distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0))) <=> ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))),
% 0.19/0.41 inference(transitivity,[status(thm)],[110, 108])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[113, 107, 49, 97, 1])).
% 0.19/0.41 tff(115,plain,(convergent_lines(U!1, U!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(119,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.41 tff(121,plain,(
% 0.19/0.41 ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.41 inference(skolemize,[status(sab)],[120])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(U!1, U!1))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[123, 122, 115])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------