TSTP Solution File: GEO201+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO201+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 20:35:36 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO201+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % 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 : Wed Aug 31 06:53:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(distinct_lines_type, type, (
% 0.19/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.40 tff(line_connecting_type, type, (
% 0.19/0.40 line_connecting: ( $i * $i ) > $i)).
% 0.19/0.40 tff(intersection_point_type, type, (
% 0.19/0.40 intersection_point: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_X_1_type, type, (
% 0.19/0.40 tptp_fun_X_1: $i)).
% 0.19/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.40 tptp_fun_Y_0: $i)).
% 0.19/0.40 tff(apart_point_and_line_type, type, (
% 0.19/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.40 tff(convergent_lines_type, type, (
% 0.19/0.40 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.40 tff(equal_points_type, type, (
% 0.19/0.40 equal_points: ( $i * $i ) > $o)).
% 0.19/0.40 tff(distinct_points_type, type, (
% 0.19/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.40 tff(1,assumption,(convergent_lines(X!1, X!1)), introduced(assumption)).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.40 tff(7,plain,(
% 0.19/0.40 ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.40 inference(skolemize,[status(sab)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!1, X!1))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.40 tff(11,plain,(~convergent_lines(X!1, X!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))) <=> (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : (convergent_lines(X, Y) => equal_points(intersection_point(X, Y), intersection_point(Y, X)))) <=> (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,axiom,(~![X: $i, Y: $i] : (convergent_lines(X, Y) => equal_points(intersection_point(X, Y), intersection_point(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | equal_points(intersection_point(X, Y), intersection_point(Y, X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.19/0.40 tff(22,plain,(
% 0.19/0.40 ~((~convergent_lines(X!1, Y!0)) | equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[21])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (convergent_lines(X!1, Y!0)),
% 0.19/0.41 inference(or_elim,[status(thm)],[22])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.41 tff(29,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.41 tff(32,plain,(
% 0.19/0.41 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[31])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 ((convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0))) <=> ((~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.19/0.41 inference(transitivity,[status(thm)],[36, 34])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[39, 33, 23])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (convergent_lines(Y!0, X!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[40, 11])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.41 tff(47,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.41 tff(50,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[49])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (~apart_point_and_line(intersection_point(Y!0, X!1), X!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[55, 41])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.41 tff(62,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.19/0.41 tff(65,plain,(
% 0.19/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[64])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0))) <=> ((~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.19/0.41 inference(transitivity,[status(thm)],[69, 67])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[72, 66, 23])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (distinct_lines(Y!0, X!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[73, 11])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.41 tff(80,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.41 tff(83,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[82])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), X!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), X!1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), X!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), X!1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (~apart_point_and_line(intersection_point(X!1, Y!0), X!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[87, 84, 23])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!1, Y!0)) | (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 51, 23])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))))), rewrite((~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (^[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))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.42 tff(100,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (![X: $i, Y: $i, 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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.42 tff(103,plain,(
% 0.19/0.42 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[102])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (![X: $i, Y: $i, 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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, X!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!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, X!1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 ((apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | (~distinct_lines(Y!0, X!1)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)))) <=> (apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, X!1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | (~distinct_lines(Y!0, X!1)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, X!1))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | (~distinct_lines(Y!0, X!1)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, X!1)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[108, 106])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | (~distinct_lines(Y!0, X!1)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, X!1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, X!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[111, 105, 92, 88])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[112, 74])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : refl((equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> (equal_points(X, Y) <=> (~distinct_points(X, Y))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(117,axiom,(![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','ax1')).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.42 tff(119,plain,(
% 0.19/0.42 ![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[118])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))) | (equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)) <=> (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)) <=> (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (~equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))),
% 0.19/0.42 inference(or_elim,[status(thm)],[22])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 ((~(equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)) <=> (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))) | equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)) | distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 ((~(equal_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)) <=> (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))) | distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | distinct_points(Y, Z)) <=> (distinct_points(Y, Z) | distinct_points(X, Z))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))))), rewrite((distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.42 tff(132,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart4')).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.19/0.42 tff(135,plain,(
% 0.19/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[134])).
% 0.19/0.43 tff(136,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.19/0.43 tff(137,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(138,plain,
% 0.19/0.43 ((distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) <=> ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(139,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[138])).
% 0.19/0.43 tff(140,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[139, 137])).
% 0.19/0.43 tff(141,plain,
% 0.19/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(142,plain,
% 0.19/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 (distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[142, 136, 126])).
% 0.19/0.43 tff(144,plain,
% 0.19/0.43 (distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[143, 113])).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[145])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[148])).
% 0.19/0.43 tff(150,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.19/0.43 tff(153,plain,(
% 0.19/0.43 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[152])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (~apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[157, 154, 126])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[159])).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(163,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[162])).
% 0.19/0.43 tff(164,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.43 tff(166,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.19/0.43 tff(167,plain,(
% 0.19/0.43 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[166])).
% 0.19/0.43 tff(168,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[167, 160])).
% 0.19/0.43 tff(169,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(170,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(171,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 (~apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[171, 168, 126])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 (((~![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!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!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!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 ((apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)))) <=> (apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(175,plain,
% 0.19/0.43 (((~![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!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[174])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 (((~![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!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[175, 173])).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 ((~![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!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 ((~![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!1, Y!0), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 (apart_point_and_line(intersection_point(Y!0, X!1), X!1) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[178, 105, 88, 172, 158])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[179, 144, 56])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(182,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(183,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.19/0.44 tff(184,plain,
% 0.19/0.44 ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[183, 84])).
% 0.19/0.44 tff(185,plain,
% 0.19/0.44 (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[184, 41])).
% 0.19/0.44 tff(186,plain,
% 0.19/0.44 (((~![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!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(187,plain,
% 0.19/0.44 ((apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)))) <=> (apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(188,plain,
% 0.19/0.44 (((~![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!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[187])).
% 0.19/0.44 tff(189,plain,
% 0.19/0.44 (((~![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!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[188, 186])).
% 0.19/0.44 tff(190,plain,
% 0.19/0.44 ((~![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!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(191,plain,
% 0.19/0.44 ((~![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!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.44 tff(192,plain,
% 0.19/0.44 (apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[191, 105, 92, 172, 158])).
% 0.19/0.44 tff(193,plain,
% 0.19/0.44 (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[192, 144, 185])).
% 0.19/0.44 tff(194,plain,
% 0.19/0.44 (^[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))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(195,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[194])).
% 0.19/0.44 tff(196,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(197,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(198,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[197])).
% 0.19/0.44 tff(199,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.19/0.44 tff(200,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.19/0.44 tff(201,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.19/0.44 tff(202,plain,(
% 0.19/0.44 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[201])).
% 0.19/0.44 tff(203,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[202, 195])).
% 0.19/0.44 tff(204,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | ((~distinct_lines(Y!0, X!1)) | distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (~distinct_lines(Y!0, X!1)) | distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(205,plain,
% 0.19/0.44 ((distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, X!1))) <=> ((~distinct_lines(Y!0, X!1)) | distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(206,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, X!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | ((~distinct_lines(Y!0, X!1)) | distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[205])).
% 0.19/0.44 tff(207,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, X!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (~distinct_lines(Y!0, X!1)) | distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[206, 204])).
% 0.19/0.44 tff(208,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, X!1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(209,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (~distinct_lines(Y!0, X!1)) | distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.19/0.44 tff(210,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[209, 203, 74, 193, 180])).
% 0.19/0.44 % SZS output end Proof
%------------------------------------------------------------------------------