TSTP Solution File: GEO201+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO201+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 20:35:35 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO201+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 06:51:11 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(distinct_lines_type, type, (
% 0.21/0.42 distinct_lines: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_X_1_type, type, (
% 0.21/0.42 tptp_fun_X_1: $i)).
% 0.21/0.42 tff(tptp_fun_Y_0_type, type, (
% 0.21/0.42 tptp_fun_Y_0: $i)).
% 0.21/0.42 tff(convergent_lines_type, type, (
% 0.21/0.42 convergent_lines: ( $i * $i ) > $o)).
% 0.21/0.42 tff(distinct_points_type, type, (
% 0.21/0.42 distinct_points: ( $i * $i ) > $o)).
% 0.21/0.42 tff(intersection_point_type, type, (
% 0.21/0.42 intersection_point: ( $i * $i ) > $i)).
% 0.21/0.42 tff(line_connecting_type, type, (
% 0.21/0.42 line_connecting: ( $i * $i ) > $i)).
% 0.21/0.42 tff(apart_point_and_line_type, type, (
% 0.21/0.42 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.42 tff(1,assumption,(convergent_lines(X!1, X!1)), introduced(assumption)).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.42 tff(7,plain,(
% 0.21/0.42 ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.42 inference(skolemize,[status(sab)],[6])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!1, X!1))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.42 tff(11,plain,(~convergent_lines(X!1, X!1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))) <=> (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (convergent_lines(X, Y) => (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))) <=> (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(14,axiom,(~![X: $i, Y: $i] : (convergent_lines(X, Y) => (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.21/0.42 tff(22,plain,(
% 0.21/0.42 ~((~convergent_lines(X!1, Y!0)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[21])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (convergent_lines(X!1, Y!0)),
% 0.21/0.42 inference(or_elim,[status(thm)],[22])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (^[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)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.42 tff(29,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')).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.42 tff(32,plain,(
% 0.21/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[31])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (((~![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))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 ((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))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (((~![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)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[35])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (((~![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))),
% 0.21/0.43 inference(transitivity,[status(thm)],[36, 34])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 ((~![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)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 ((~![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)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (distinct_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[39, 33, 23])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (distinct_lines(Y!0, X!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[40, 11])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.43 tff(47,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')).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.43 tff(50,plain,(
% 0.21/0.43 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[49])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (((~![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))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 ((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))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (((~![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)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (((~![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))),
% 0.21/0.43 inference(transitivity,[status(thm)],[54, 52])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 ((~![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)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 ((~![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)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[57, 51, 23])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (convergent_lines(Y!0, X!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[58, 11])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.43 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')).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.43 tff(68,plain,(
% 0.21/0.43 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[67])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (((~![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 ((~![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)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 ((~![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))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (~apart_point_and_line(intersection_point(Y!0, X!1), X!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[73, 59])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.43 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')).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.21/0.43 tff(83,plain,(
% 0.21/0.43 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[82])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (((~![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 ((~![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)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 ((~![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))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 (~apart_point_and_line(intersection_point(X!1, Y!0), X!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[87, 84, 23])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (((~![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 ((~![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)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 ((~![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))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[91, 69, 23])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (![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_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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (![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_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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (![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_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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (^[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))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.44 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')).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 (![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_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 (![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_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.21/0.44 tff(103,plain,(
% 0.21/0.44 ![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_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[102])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (![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_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (![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_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (((~![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_points(X, Y)) | (~distinct_lines(U, V)))) | (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_points(X, Y)) | (~distinct_lines(U, V)))) | 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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 ((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_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))) | (~distinct_lines(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) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, X!1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (((~![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_points(X, Y)) | (~distinct_lines(U, V)))) | (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_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_points(X, Y)) | (~distinct_lines(U, V)))) | (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))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[107])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 (((~![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_points(X, Y)) | (~distinct_lines(U, V)))) | (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_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_points(X, Y)) | (~distinct_lines(U, V)))) | 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)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[108, 106])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 ((~![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_points(X, Y)) | (~distinct_lines(U, V)))) | (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_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, X!1)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 ((~![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_points(X, Y)) | (~distinct_lines(U, V)))) | 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))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, X!1))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[111, 105, 92, 88])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[112, 41])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))),
% 0.21/0.44 inference(or_elim,[status(thm)],[22])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[118])).
% 0.21/0.44 tff(120,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')).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.21/0.44 tff(123,plain,(
% 0.21/0.44 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[122])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (((~![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(Y!0, X!1), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(X!1, Y!0), 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(Y!0, X!1), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 ((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(Y!0, X!1), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (((~![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(Y!0, X!1), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (((~![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(Y!0, X!1), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[127, 125])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 ((~![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))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 ((~![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(Y!0, X!1), intersection_point(X!1, Y!0)) | distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 (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))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[130, 124, 114])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[131, 113])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[133])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[136])).
% 0.21/0.44 tff(138,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')).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.21/0.44 tff(141,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[140])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 (((~![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)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(144,plain,
% 0.21/0.45 ((~![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)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 ((~![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))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 (~apart_point_and_line(intersection_point(X!1, Y!0), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[145, 142, 114])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(148,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[147])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(150,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(151,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[150])).
% 0.21/0.45 tff(152,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')).
% 0.21/0.45 tff(153,plain,
% 0.21/0.45 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.45 tff(154,plain,
% 0.21/0.45 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.21/0.45 tff(155,plain,(
% 0.21/0.45 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[154])).
% 0.21/0.45 tff(156,plain,
% 0.21/0.45 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.21/0.45 tff(157,plain,
% 0.21/0.45 (((~![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)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(158,plain,
% 0.21/0.45 ((~![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)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(159,plain,
% 0.21/0.45 ((~![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))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.21/0.45 tff(160,plain,
% 0.21/0.45 (~apart_point_and_line(intersection_point(Y!0, X!1), line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[159, 156, 114])).
% 0.21/0.45 tff(161,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(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))) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | 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)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(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))) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | 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)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(162,plain,
% 0.21/0.45 ((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_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))))) <=> (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))) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | 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)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(163,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(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_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_points(X, Y)) | (~distinct_lines(U, V)))) | (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))) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | 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))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[162])).
% 0.21/0.45 tff(164,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(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_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_points(X, Y)) | (~distinct_lines(U, V)))) | 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))) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | 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)))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[163, 161])).
% 0.21/0.45 tff(165,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(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_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)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(166,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(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))) | apart_point_and_line(intersection_point(X!1, Y!0), X!1) | 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))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.21/0.45 tff(167,plain,
% 0.21/0.45 (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))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[166, 105, 160, 146, 88])).
% 0.21/0.45 tff(168,plain,
% 0.21/0.45 (~distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[167, 132, 74])).
% 0.21/0.45 tff(169,plain,
% 0.21/0.45 (((~![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(170,plain,
% 0.21/0.45 ((~![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)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(171,plain,
% 0.21/0.45 ((~![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))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.21/0.45 tff(172,plain,
% 0.21/0.45 ((~convergent_lines(Y!0, X!1)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[171, 84])).
% 0.21/0.45 tff(173,plain,
% 0.21/0.45 (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[172, 59])).
% 0.21/0.45 tff(174,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(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))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, 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_points(X, Y)) | (~distinct_lines(U, V)))) | 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))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(175,plain,
% 0.21/0.46 ((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_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, line_connecting(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))) | 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), Y!0) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(176,plain,
% 0.21/0.46 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(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_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, 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_points(X, Y)) | (~distinct_lines(U, V)))) | (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))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[175])).
% 0.21/0.46 tff(177,plain,
% 0.21/0.46 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(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_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, 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_points(X, Y)) | (~distinct_lines(U, V)))) | 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))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[176, 174])).
% 0.21/0.46 tff(178,plain,
% 0.21/0.46 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(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_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(179,plain,
% 0.21/0.46 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(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))) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.46 tff(180,plain,
% 0.21/0.46 (apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(X!1, Y!0))) | (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[179, 105, 160, 146, 92])).
% 0.21/0.46 tff(181,plain,
% 0.21/0.46 (~distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[180, 132, 173])).
% 0.21/0.46 tff(182,plain,
% 0.21/0.46 (^[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))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(183,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[182])).
% 0.21/0.46 tff(184,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(185,plain,
% 0.21/0.46 (^[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)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(186,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[185])).
% 0.21/0.46 tff(187,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')).
% 0.21/0.46 tff(188,plain,
% 0.21/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.21/0.46 tff(189,plain,
% 0.21/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.21/0.46 tff(190,plain,(
% 0.21/0.46 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[189])).
% 0.21/0.46 tff(191,plain,
% 0.21/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[190, 183])).
% 0.21/0.46 tff(192,plain,
% 0.21/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (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))) | (~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, 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))) | (~distinct_lines(Y!0, X!1)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(193,plain,
% 0.21/0.46 ((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, 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))) | (~distinct_lines(Y!0, X!1)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(194,plain,
% 0.21/0.46 (((~![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, 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))) | (~distinct_lines(Y!0, X!1))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[193])).
% 0.21/0.46 tff(195,plain,
% 0.21/0.46 (((~![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, 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))) | (~distinct_lines(Y!0, X!1)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[194, 192])).
% 0.21/0.46 tff(196,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(197,plain,
% 0.21/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Y!0, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | distinct_lines(X!1, line_connecting(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(Y!0, X!1))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.21/0.47 tff(198,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[197, 191, 181, 168, 41])).
% 0.21/0.47 % SZS output end Proof
%------------------------------------------------------------------------------