TSTP Solution File: GEO201+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:15:04 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.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(apart_point_and_line_type, type, (
% 0.20/0.45 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.45 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.45 tptp_fun_Y_0: $i)).
% 0.20/0.45 tff(intersection_point_type, type, (
% 0.20/0.45 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.45 tff(tptp_fun_X_1_type, type, (
% 0.20/0.45 tptp_fun_X_1: $i)).
% 0.20/0.45 tff(distinct_points_type, type, (
% 0.20/0.45 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.45 tff(convergent_lines_type, type, (
% 0.20/0.45 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.45 tff(distinct_lines_type, type, (
% 0.20/0.45 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.45 tff(1,assumption,(distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))), introduced(assumption)).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.45 tff(4,plain,
% 0.20/0.45 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.20/0.45 tff(6,plain,
% 0.20/0.45 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.45 tff(7,plain,(
% 0.20/0.45 ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.45 inference(skolemize,[status(sab)],[6])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.45 tff(11,plain,(~distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 ((~![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)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 ((~![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)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 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')).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~distinct_points(intersection_point(X, Y), intersection_point(Y, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.20/0.45 tff(22,plain,(
% 0.20/0.45 ~((~convergent_lines(X!1, Y!0)) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[21])).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (convergent_lines(X!1, Y!0)),
% 0.20/0.45 inference(or_elim,[status(thm)],[22])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) <=> (apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))))), rewrite(((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))))), rewrite((convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.45 tff(29,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.45 tff(32,plain,(
% 0.20/0.45 ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[31])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(X!1, Y!0)) | 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))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!1, Y!0)) | 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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 ((distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | (~convergent_lines(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)))) <=> ((~convergent_lines(X!1, Y!0)) | 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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 ((~(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) | apart_point_and_line(intersection_point(X!1, Y!0), X!1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 ((distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | (~convergent_lines(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)) | (~convergent_lines(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))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 ((distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | (~convergent_lines(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)))) <=> ((~convergent_lines(X!1, Y!0)) | 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))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[37, 35])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | (~convergent_lines(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))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(X!1, Y!0)) | 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)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | (~convergent_lines(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))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!1, Y!0)) | 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))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[39, 34])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!1, Y!0), intersection_point(X!1, Y!0)) | (~convergent_lines(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))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!1, Y!0)) | 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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (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)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[42, 33, 23])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (~(apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[43, 11])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 ((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))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 (~apart_point_and_line(intersection_point(X!1, Y!0), Y!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 ((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), X!1))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 (~apart_point_and_line(intersection_point(X!1, Y!0), X!1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.20/0.46 tff(49,assumption,(distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1))), introduced(assumption)).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[50, 8, 49])).
% 0.20/0.46 tff(52,plain,(~distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(53,assumption,(convergent_lines(X!1, X!1)), introduced(assumption)).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(57,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart3')).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.46 tff(59,plain,(
% 0.20/0.46 ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(skolemize,[status(sab)],[58])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!1, X!1))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[61, 60, 53])).
% 0.20/0.46 tff(63,plain,(~convergent_lines(X!1, X!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.46 tff(69,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/GEO008+0.ax','apart6')).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.46 tff(72,plain,(
% 0.20/0.46 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[71])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 (((~![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 ((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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (((~![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)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 (((~![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))),
% 0.20/0.46 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 ((~![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)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 ((~![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)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[79, 73, 23])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (convergent_lines(Y!0, X!1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[80, 63])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(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), Y!0))) | distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(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), Y!0))) | distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 ((distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1)) | (~convergent_lines(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), Y!0)))) <=> ((~convergent_lines(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), Y!0))) | distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1)) | (~convergent_lines(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), Y!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(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), Y!0))) | distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1)) | (~convergent_lines(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), Y!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(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), Y!0))) | distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[84, 82])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1)) | (~convergent_lines(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), Y!0))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(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), Y!0))) | distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 ((~(apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0))) | distinct_points(intersection_point(Y!0, X!1), intersection_point(Y!0, X!1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[87, 33, 81])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (~(apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[88, 52])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 ((apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0)) | (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (~apart_point_and_line(intersection_point(Y!0, X!1), Y!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 ((apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0)) | (~apart_point_and_line(intersection_point(Y!0, X!1), X!1))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (~apart_point_and_line(intersection_point(Y!0, X!1), X!1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[92, 89])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.47 tff(99,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.47 tff(102,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.47 inference(skolemize,[status(sab)],[101])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!1, Y!0)) | distinct_lines(X!1, Y!0))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!1, Y!0)) | distinct_lines(X!1, Y!0))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!1, Y!0)) | distinct_lines(X!1, Y!0))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!1, Y!0)) | distinct_lines(X!1, Y!0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (distinct_lines(X!1, Y!0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[106, 103, 23])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))),
% 0.20/0.47 inference(or_elim,[status(thm)],[22])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.47 tff(116,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/GEO008+0.ax','cu1')).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.20/0.47 tff(119,plain,(
% 0.20/0.47 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[118])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[120, 110])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (((~![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)))) | ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(X!1, Y!0)) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), 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))) <=> ((~![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)))) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(X!1, Y!0)) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), 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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 ((apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), 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(Y!0, X!1))) | (~distinct_lines(X!1, Y!0))) <=> ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(X!1, Y!0)) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), 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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (((~![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), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), 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(Y!0, X!1))) | (~distinct_lines(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_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(X!1, Y!0)) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), 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)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[123])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (((~![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), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), 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(Y!0, X!1))) | (~distinct_lines(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_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(X!1, Y!0)) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), 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))),
% 0.20/0.47 inference(transitivity,[status(thm)],[124, 122])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 ((~![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), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), 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(Y!0, X!1))) | (~distinct_lines(X!1, Y!0)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(intersection_point(X!1, Y!0), intersection_point(Y!0, X!1))) | (~distinct_lines(X!1, Y!0)) | apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (apart_point_and_line(intersection_point(Y!0, X!1), Y!0) | apart_point_and_line(intersection_point(Y!0, X!1), X!1) | apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[127, 121, 108, 107])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (apart_point_and_line(intersection_point(X!1, Y!0), Y!0) | apart_point_and_line(intersection_point(X!1, Y!0), X!1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[128, 93, 91])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[129, 48, 46])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------