TSTP Solution File: GEO172+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO172+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Fri Sep 16 20:35:14 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO172+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:47:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(convergent_lines_type, type, (
% 0.20/0.41 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_X_2_type, type, (
% 0.20/0.41 tptp_fun_X_2: $i)).
% 0.20/0.41 tff(distinct_lines_type, type, (
% 0.20/0.41 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.41 tptp_fun_Y_1: $i)).
% 0.20/0.41 tff(apart_point_and_line_type, type, (
% 0.20/0.41 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.41 tptp_fun_Z_0: $i)).
% 0.20/0.41 tff(incident_point_and_line_type, type, (
% 0.20/0.41 incident_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.41 tff(equal_points_type, type, (
% 0.20/0.41 equal_points: ( $i * $i ) > $o)).
% 0.20/0.41 tff(intersection_point_type, type, (
% 0.20/0.41 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.41 tff(distinct_points_type, type, (
% 0.20/0.41 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,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')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41 tff(6,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[5])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(Z!0, Y!1) <=> (~apart_point_and_line(Z!0, Y!1)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (incident_point_and_line(Z!0, Y!1) <=> (~apart_point_and_line(Z!0, Y!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & incident_point_and_line(Z, X)) & incident_point_and_line(Z, Y)) => equal_points(Z, intersection_point(X, Y)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(12,axiom,(~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & incident_point_and_line(Z, X)) & incident_point_and_line(Z, Y)) => equal_points(Z, intersection_point(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & incident_point_and_line(Z, X) & incident_point_and_line(Z, Y))) | equal_points(Z, intersection_point(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.20/0.42 tff(20,plain,(
% 0.20/0.42 ~((~(convergent_lines(X!2, Y!1) & incident_point_and_line(Z!0, X!2) & incident_point_and_line(Z!0, Y!1))) | equal_points(Z!0, intersection_point(X!2, Y!1)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[19])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (convergent_lines(X!2, Y!1) & incident_point_and_line(Z!0, X!2) & incident_point_and_line(Z!0, Y!1)),
% 0.20/0.42 inference(or_elim,[status(thm)],[20])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (incident_point_and_line(Z!0, Y!1)),
% 0.20/0.42 inference(and_elim,[status(thm)],[21])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((~(incident_point_and_line(Z!0, Y!1) <=> (~apart_point_and_line(Z!0, Y!1)))) | (~incident_point_and_line(Z!0, Y!1)) | (~apart_point_and_line(Z!0, Y!1))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 ((~(incident_point_and_line(Z!0, Y!1) <=> (~apart_point_and_line(Z!0, Y!1)))) | (~apart_point_and_line(Z!0, Y!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (~apart_point_and_line(Z!0, Y!1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[24, 9])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(Z!0, X!2) <=> (~apart_point_and_line(Z!0, X!2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (incident_point_and_line(Z!0, X!2) <=> (~apart_point_and_line(Z!0, X!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[26, 7])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (incident_point_and_line(Z!0, X!2)),
% 0.20/0.42 inference(and_elim,[status(thm)],[21])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 ((~(incident_point_and_line(Z!0, X!2) <=> (~apart_point_and_line(Z!0, X!2)))) | (~incident_point_and_line(Z!0, X!2)) | (~apart_point_and_line(Z!0, X!2))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 ((~(incident_point_and_line(Z!0, X!2) <=> (~apart_point_and_line(Z!0, X!2)))) | (~apart_point_and_line(Z!0, X!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (~apart_point_and_line(Z!0, X!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[30, 27])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl((equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> (equal_points(X, Y) <=> (~distinct_points(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,axiom,(![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','ax1')).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.42 tff(37,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[36])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))) | (equal_points(Z!0, intersection_point(X!2, Y!1)) <=> (~distinct_points(Z!0, intersection_point(X!2, Y!1))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (equal_points(Z!0, intersection_point(X!2, Y!1)) <=> (~distinct_points(Z!0, intersection_point(X!2, Y!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (~equal_points(Z!0, intersection_point(X!2, Y!1))),
% 0.20/0.42 inference(or_elim,[status(thm)],[20])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ((~(equal_points(Z!0, intersection_point(X!2, Y!1)) <=> (~distinct_points(Z!0, intersection_point(X!2, Y!1))))) | equal_points(Z!0, intersection_point(X!2, Y!1)) | distinct_points(Z!0, intersection_point(X!2, Y!1))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 ((~(equal_points(Z!0, intersection_point(X!2, Y!1)) <=> (~distinct_points(Z!0, intersection_point(X!2, Y!1))))) | distinct_points(Z!0, intersection_point(X!2, Y!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (distinct_points(Z!0, intersection_point(X!2, Y!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (convergent_lines(X!2, Y!1)),
% 0.20/0.42 inference(and_elim,[status(thm)],[21])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.42 tff(51,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')).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.42 tff(54,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[53])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[58, 55, 45])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.42 tff(65,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')).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.42 tff(68,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[67])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[72, 69, 45])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> ![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (^[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))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.42 tff(81,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')).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.20/0.42 tff(84,plain,(
% 0.20/0.42 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[83])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 ((apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(Z!0, intersection_point(X!2, Y!1)))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(Y!1, X!2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (~distinct_lines(Y!1, X!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[92, 86, 73, 59, 44, 31, 25])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.43 tff(99,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')).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.43 tff(102,plain,(
% 0.20/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[101])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.43 inference(transitivity,[status(thm)],[106, 104])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (convergent_lines(X!2, X!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[109, 103, 45, 93])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(114,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.43 tff(116,plain,(
% 0.20/0.43 ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43 inference(skolemize,[status(sab)],[115])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!2, X!2))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[118, 117, 110])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------