%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO175+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:05:45 AM UTC 2025
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO175+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 14:43:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 tff(convergent_lines_type, type, (
% 0.19/0.48 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.48 tff(tptp_fun_U_1_type, type, (
% 0.19/0.48 tptp_fun_U_1: $i)).
% 0.19/0.48 tff(parallel_through_point_type, type, (
% 0.19/0.48 parallel_through_point: ( $i * $i ) > $i)).
% 0.19/0.48 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.48 tptp_fun_Y_2: $i)).
% 0.19/0.48 tff(tptp_fun_V_0_type, type, (
% 0.19/0.48 tptp_fun_V_0: $i)).
% 0.19/0.48 tff(distinct_lines_type, type, (
% 0.19/0.48 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.48 tff(apart_point_and_line_type, type, (
% 0.19/0.48 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.48 tff(intersection_point_type, type, (
% 0.19/0.48 intersection_point: ( $i * $i ) > $i)).
% 0.19/0.48 tff(distinct_points_type, type, (
% 0.19/0.48 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.48 tff(tptp_fun_X_3_type, type, (
% 0.19/0.48 tptp_fun_X_3: $i)).
% 0.19/0.48 tff(1,plain,
% 0.19/0.48 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(2,plain,
% 0.19/0.48 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.48 tff(3,plain,
% 0.19/0.48 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(4,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.19/0.48 tff(5,plain,
% 0.19/0.48 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.48 tff(6,plain,(
% 0.19/0.48 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.48 inference(skolemize,[status(sab)],[5])).
% 0.19/0.48 tff(7,plain,
% 0.19/0.48 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.48 tff(8,plain,
% 0.19/0.48 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(V!0, Y!2), V!0))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(9,plain,
% 0.19/0.48 (~convergent_lines(parallel_through_point(V!0, Y!2), V!0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.48 tff(10,plain,
% 0.19/0.48 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(11,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.48 tff(12,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(13,plain,
% 0.19/0.48 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(14,plain,
% 0.19/0.48 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.48 tff(15,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.19/0.48 tff(16,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.48 tff(17,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.48 tff(18,plain,(
% 0.19/0.48 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.48 inference(skolemize,[status(sab)],[17])).
% 0.19/0.48 tff(19,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.48 tff(20,plain,
% 0.19/0.48 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(V!0, Y!2), V!0)) | convergent_lines(parallel_through_point(V!0, Y!2), V!0))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(V!0, Y!2), V!0)) | convergent_lines(parallel_through_point(V!0, Y!2), V!0))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(21,plain,
% 0.19/0.48 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(V!0, Y!2), V!0)) | convergent_lines(parallel_through_point(V!0, Y!2), V!0))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(22,plain,
% 0.19/0.48 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(V!0, Y!2), V!0)) | convergent_lines(parallel_through_point(V!0, Y!2), V!0)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.48 tff(23,plain,
% 0.19/0.48 (~distinct_lines(parallel_through_point(V!0, Y!2), V!0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.19/0.48 tff(24,plain,
% 0.19/0.48 ((~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & distinct_points(X!3, intersection_point(U!1, V!0)))))) <=> (~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & distinct_points(X!3, intersection_point(U!1, V!0))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(25,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V)))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(26,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & distinct_points(X, intersection_point(U, V))) => (apart_point_and_line(X, U) | apart_point_and_line(X, V)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(27,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & distinct_points(X, intersection_point(U, V))) => (apart_point_and_line(X, U) | apart_point_and_line(X, V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.48 tff(28,plain,
% 0.19/0.48 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.48 tff(29,plain,
% 0.19/0.48 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.19/0.48 tff(30,plain,
% 0.19/0.48 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.48 tff(31,plain,
% 0.19/0.48 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.19/0.48 tff(32,plain,(
% 0.19/0.48 ~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & distinct_points(X!3, intersection_point(U!1, V!0)))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[31])).
% 0.19/0.48 tff(33,plain,
% 0.19/0.48 (~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & distinct_points(X!3, intersection_point(U!1, V!0)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.19/0.48 tff(34,plain,
% 0.19/0.48 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & distinct_points(X!3, intersection_point(U!1, V!0))),
% 0.19/0.48 inference(or_elim,[status(thm)],[33])).
% 0.19/0.48 tff(35,plain,
% 0.19/0.48 (convergent_lines(U!1, V!0)),
% 0.19/0.48 inference(and_elim,[status(thm)],[34])).
% 0.19/0.48 tff(36,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(37,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.48 tff(38,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(39,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(40,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.48 tff(41,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')).
% 0.19/0.48 tff(42,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.48 tff(43,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.48 tff(44,plain,(
% 0.19/0.48 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[43])).
% 0.19/0.48 tff(45,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.48 tff(46,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(47,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(48,plain,
% 0.19/0.48 ((~![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))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.48 tff(49,plain,
% 0.19/0.48 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[48, 45, 35])).
% 0.19/0.48 tff(50,plain,
% 0.19/0.48 (distinct_points(X!3, intersection_point(U!1, V!0))),
% 0.19/0.48 inference(and_elim,[status(thm)],[34])).
% 0.19/0.48 tff(51,plain,
% 0.19/0.48 (~apart_point_and_line(X!3, V!0)),
% 0.19/0.48 inference(or_elim,[status(thm)],[33])).
% 0.19/0.48 tff(52,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(53,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.49 tff(54,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(55,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.49 tff(56,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(57,plain,
% 0.19/0.49 (^[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))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(58,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.49 tff(59,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.19/0.49 tff(60,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.49 tff(61,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.49 tff(62,plain,(
% 0.19/0.49 ![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))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[61])).
% 0.19/0.49 tff(63,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.19/0.49 tff(64,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.19/0.49 tff(65,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(X!3, V!0) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, 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(X!3, V!0) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, V!0)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(66,plain,
% 0.19/0.49 ((apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, V!0)) | (~distinct_points(X!3, intersection_point(U!1, V!0)))) <=> (apart_point_and_line(X!3, V!0) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, V!0)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(67,plain,
% 0.19/0.49 (((~![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), V!0) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, V!0)) | (~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(X!3, V!0) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, V!0))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.49 tff(68,plain,
% 0.19/0.49 (((~![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), V!0) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, V!0)) | (~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(X!3, V!0) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, V!0)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.49 tff(69,plain,
% 0.19/0.49 ((~![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), V!0) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, V!0)) | (~distinct_points(X!3, intersection_point(U!1, V!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(70,plain,
% 0.19/0.49 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(X!3, V!0) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, V!0))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.49 tff(71,plain,
% 0.19/0.49 (~distinct_lines(V!0, V!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[70, 64, 51, 50, 49])).
% 0.19/0.49 tff(72,plain,
% 0.19/0.49 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(73,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.49 tff(74,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(75,plain,
% 0.19/0.49 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(76,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.49 tff(77,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.19/0.49 tff(78,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.49 tff(79,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.49 tff(80,plain,(
% 0.19/0.49 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[79])).
% 0.19/0.49 tff(81,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.19/0.49 tff(82,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(V!0, V!0) | distinct_lines(parallel_through_point(V!0, Y!2), V!0) | (~distinct_lines(V!0, parallel_through_point(V!0, Y!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(V!0, V!0) | distinct_lines(parallel_through_point(V!0, Y!2), V!0) | (~distinct_lines(V!0, parallel_through_point(V!0, Y!2))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(83,plain,
% 0.19/0.49 ((distinct_lines(parallel_through_point(V!0, Y!2), V!0) | distinct_lines(V!0, V!0) | (~distinct_lines(V!0, parallel_through_point(V!0, Y!2)))) <=> (distinct_lines(V!0, V!0) | distinct_lines(parallel_through_point(V!0, Y!2), V!0) | (~distinct_lines(V!0, parallel_through_point(V!0, Y!2))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(84,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(V!0, Y!2), V!0) | distinct_lines(V!0, V!0) | (~distinct_lines(V!0, parallel_through_point(V!0, Y!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(V!0, V!0) | distinct_lines(parallel_through_point(V!0, Y!2), V!0) | (~distinct_lines(V!0, parallel_through_point(V!0, Y!2)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.49 tff(85,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(V!0, Y!2), V!0) | distinct_lines(V!0, V!0) | (~distinct_lines(V!0, parallel_through_point(V!0, Y!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(V!0, V!0) | distinct_lines(parallel_through_point(V!0, Y!2), V!0) | (~distinct_lines(V!0, parallel_through_point(V!0, Y!2))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.49 tff(86,plain,
% 0.19/0.49 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(V!0, Y!2), V!0) | distinct_lines(V!0, V!0) | (~distinct_lines(V!0, parallel_through_point(V!0, Y!2))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(87,plain,
% 0.19/0.49 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(V!0, V!0) | distinct_lines(parallel_through_point(V!0, Y!2), V!0) | (~distinct_lines(V!0, parallel_through_point(V!0, Y!2)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.49 tff(88,plain,
% 0.19/0.49 (~distinct_lines(V!0, parallel_through_point(V!0, Y!2))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[87, 81, 71, 23])).
% 0.19/0.49 tff(89,plain,
% 0.19/0.49 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(90,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.49 tff(91,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(92,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(93,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.49 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')).
% 0.19/0.49 tff(95,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.49 tff(96,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.19/0.49 tff(97,plain,(
% 0.19/0.49 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[96])).
% 0.19/0.49 tff(98,plain,
% 0.19/0.49 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.19/0.49 tff(99,plain,
% 0.19/0.49 (((~![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, parallel_through_point(V!0, Y!2)) | convergent_lines(U!1, parallel_through_point(V!0, Y!2)))) <=> ((~![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, parallel_through_point(V!0, Y!2)) | convergent_lines(U!1, parallel_through_point(V!0, Y!2)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(100,plain,
% 0.19/0.49 ((distinct_lines(V!0, parallel_through_point(V!0, Y!2)) | convergent_lines(U!1, parallel_through_point(V!0, Y!2)) | (~convergent_lines(U!1, V!0))) <=> ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, parallel_through_point(V!0, Y!2)) | convergent_lines(U!1, parallel_through_point(V!0, Y!2)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(101,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, parallel_through_point(V!0, Y!2)) | convergent_lines(U!1, parallel_through_point(V!0, Y!2)) | (~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, parallel_through_point(V!0, Y!2)) | convergent_lines(U!1, parallel_through_point(V!0, Y!2))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[100])).
% 0.19/0.49 tff(102,plain,
% 0.19/0.49 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, parallel_through_point(V!0, Y!2)) | convergent_lines(U!1, parallel_through_point(V!0, Y!2)) | (~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, parallel_through_point(V!0, Y!2)) | convergent_lines(U!1, parallel_through_point(V!0, Y!2)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[101, 99])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, parallel_through_point(V!0, Y!2)) | convergent_lines(U!1, parallel_through_point(V!0, Y!2)) | (~convergent_lines(U!1, V!0)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(104,plain,
% 0.19/0.49 ((~![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, parallel_through_point(V!0, Y!2)) | convergent_lines(U!1, parallel_through_point(V!0, Y!2))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.49 tff(105,plain,
% 0.19/0.49 (convergent_lines(U!1, parallel_through_point(V!0, Y!2))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[104, 98, 35, 88])).
% 0.19/0.49 tff(106,plain,
% 0.19/0.49 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(107,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.49 tff(108,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.50 tff(111,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')).
% 0.19/0.50 tff(112,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.50 tff(113,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.19/0.50 tff(114,plain,(
% 0.19/0.50 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[113])).
% 0.19/0.50 tff(115,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.19/0.50 tff(116,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(117,plain,
% 0.19/0.50 ((~![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)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(118,plain,
% 0.19/0.50 ((~![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))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.50 tff(119,plain,
% 0.19/0.50 (~apart_point_and_line(intersection_point(U!1, V!0), U!1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[118, 115, 35])).
% 0.19/0.50 tff(120,plain,
% 0.19/0.50 (~apart_point_and_line(X!3, U!1)),
% 0.19/0.50 inference(or_elim,[status(thm)],[33])).
% 0.19/0.50 tff(121,plain,
% 0.19/0.50 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, 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) | (~distinct_lines(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(X!3, V!0) | apart_point_and_line(X!3, 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) | (~distinct_lines(U!1, V!0)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(122,plain,
% 0.19/0.50 ((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, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_lines(U!1, V!0)) | (~distinct_points(X!3, intersection_point(U!1, V!0)))) <=> (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, 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) | (~distinct_lines(U!1, V!0)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(123,plain,
% 0.19/0.50 (((~![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, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_lines(U!1, V!0)) | (~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(X!3, V!0) | apart_point_and_line(X!3, 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) | (~distinct_lines(U!1, V!0))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.50 tff(124,plain,
% 0.19/0.50 (((~![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, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_lines(U!1, V!0)) | (~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(X!3, V!0) | apart_point_and_line(X!3, 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) | (~distinct_lines(U!1, V!0)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[123, 121])).
% 0.19/0.50 tff(125,plain,
% 0.19/0.50 ((~![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, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_lines(U!1, V!0)) | (~distinct_points(X!3, intersection_point(U!1, V!0))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(126,plain,
% 0.19/0.50 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, 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) | (~distinct_lines(U!1, V!0))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.50 tff(127,plain,
% 0.19/0.50 (~distinct_lines(U!1, V!0)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[126, 64, 51, 120, 50, 49, 119])).
% 0.19/0.50 tff(128,plain,
% 0.19/0.50 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(U!1, V!0) | convergent_lines(parallel_through_point(V!0, Y!2), V!0) | (~convergent_lines(parallel_through_point(V!0, Y!2), U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(U!1, V!0) | convergent_lines(parallel_through_point(V!0, Y!2), V!0) | (~convergent_lines(parallel_through_point(V!0, Y!2), U!1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(129,plain,
% 0.19/0.50 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(U!1, V!0) | convergent_lines(parallel_through_point(V!0, Y!2), V!0) | (~convergent_lines(parallel_through_point(V!0, Y!2), U!1)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(130,plain,
% 0.19/0.50 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(U!1, V!0) | convergent_lines(parallel_through_point(V!0, Y!2), V!0) | (~convergent_lines(parallel_through_point(V!0, Y!2), U!1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.50 tff(131,plain,
% 0.19/0.50 (~convergent_lines(parallel_through_point(V!0, Y!2), U!1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[130, 98, 127, 9])).
% 0.19/0.50 tff(132,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(133,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[132])).
% 0.19/0.50 tff(134,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(135,plain,
% 0.19/0.50 (^[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)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(136,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[135])).
% 0.19/0.50 tff(137,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')).
% 0.19/0.50 tff(138,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.50 tff(139,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.19/0.50 tff(140,plain,(
% 0.19/0.50 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[139])).
% 0.19/0.50 tff(141,plain,
% 0.19/0.50 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.19/0.50 tff(142,plain,
% 0.19/0.50 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(V!0, Y!2), U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, parallel_through_point(V!0, Y!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(parallel_through_point(V!0, Y!2), U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, parallel_through_point(V!0, Y!2))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(143,plain,
% 0.19/0.50 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(V!0, Y!2), U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, parallel_through_point(V!0, Y!2))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(144,plain,
% 0.19/0.50 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(parallel_through_point(V!0, Y!2), U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, parallel_through_point(V!0, Y!2)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.50 tff(145,plain,
% 0.19/0.50 (convergent_lines(U!1, U!1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[144, 141, 131, 105])).
% 0.19/0.50 tff(146,plain,
% 0.19/0.50 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(147,plain,
% 0.19/0.50 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.50 tff(148,plain,
% 0.19/0.50 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(149,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.19/0.50 tff(150,plain,
% 0.19/0.50 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.50 tff(151,plain,(
% 0.19/0.50 ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.50 inference(skolemize,[status(sab)],[150])).
% 0.19/0.50 tff(152,plain,
% 0.19/0.50 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.19/0.50 tff(153,plain,
% 0.19/0.50 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(U!1, U!1))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(154,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[153, 152, 145])).
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50 % E exiting
%------------------------------------------------------------------------------