TSTP Solution File: GEO203+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO203+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 20:35:37 EDT 2022
% Result : Theorem 0.23s 0.44s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO203+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 31 06:57:35 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 0.23/0.44 % SZS status Theorem
% 0.23/0.44 % SZS output start Proof
% 0.23/0.44 tff(distinct_points_type, type, (
% 0.23/0.44 distinct_points: ( $i * $i ) > $o)).
% 0.23/0.44 tff(intersection_point_type, type, (
% 0.23/0.44 intersection_point: ( $i * $i ) > $i)).
% 0.23/0.44 tff(tptp_fun_Z_0_type, type, (
% 0.23/0.44 tptp_fun_Z_0: $i)).
% 0.23/0.44 tff(tptp_fun_X_2_type, type, (
% 0.23/0.44 tptp_fun_X_2: $i)).
% 0.23/0.44 tff(tptp_fun_Y_1_type, type, (
% 0.23/0.44 tptp_fun_Y_1: $i)).
% 0.23/0.44 tff(apart_point_and_line_type, type, (
% 0.23/0.44 apart_point_and_line: ( $i * $i ) > $o)).
% 0.23/0.44 tff(line_connecting_type, type, (
% 0.23/0.44 line_connecting: ( $i * $i ) > $i)).
% 0.23/0.44 tff(convergent_lines_type, type, (
% 0.23/0.44 convergent_lines: ( $i * $i ) > $o)).
% 0.23/0.44 tff(distinct_lines_type, type, (
% 0.23/0.44 distinct_lines: ( $i * $i ) > $o)).
% 0.23/0.44 tff(1,assumption,(distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), introduced(assumption)).
% 0.23/0.44 tff(2,plain,
% 0.23/0.44 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(3,plain,
% 0.23/0.44 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.23/0.44 tff(4,plain,
% 0.23/0.44 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.23/0.44 tff(6,plain,
% 0.23/0.44 (![X: $i] : (~distinct_points(X, X))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.23/0.44 tff(7,plain,(
% 0.23/0.44 ![X: $i] : (~distinct_points(X, X))),
% 0.23/0.44 inference(skolemize,[status(sab)],[6])).
% 0.23/0.44 tff(8,plain,
% 0.23/0.44 (![X: $i] : (~distinct_points(X, X))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.23/0.44 tff(9,plain,
% 0.23/0.44 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(10,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.23/0.44 tff(11,plain,(~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(12,plain,
% 0.23/0.44 (((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(13,plain,
% 0.23/0.44 ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.23/0.44 tff(14,assumption,(distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0))), introduced(assumption)).
% 0.23/0.44 tff(15,plain,
% 0.23/0.44 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(16,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[15, 8, 14])).
% 0.23/0.44 tff(17,plain,(~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(18,plain,
% 0.23/0.44 (((~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)))) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(19,plain,
% 0.23/0.44 ((~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.23/0.44 tff(20,assumption,(apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))), introduced(assumption)).
% 0.23/0.44 tff(21,plain,
% 0.23/0.44 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)) | (~(convergent_lines(X, Y) & convergent_lines(X, Z) & distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)) | (~(convergent_lines(X, Y) & convergent_lines(X, Z) & distinct_points(intersection_point(X, Y), intersection_point(X, Z))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(22,plain,
% 0.23/0.44 ((~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & convergent_lines(X, Z)) & distinct_points(intersection_point(X, Y), intersection_point(X, Z))) => (~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)) | (~(convergent_lines(X, Y) & convergent_lines(X, Z) & distinct_points(intersection_point(X, Y), intersection_point(X, Z))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(23,axiom,(~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & convergent_lines(X, Z)) & distinct_points(intersection_point(X, Y), intersection_point(X, Z))) => (~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.23/0.44 tff(24,plain,
% 0.23/0.44 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)) | (~(convergent_lines(X, Y) & convergent_lines(X, Z) & distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.23/0.44 tff(25,plain,
% 0.23/0.44 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)) | (~(convergent_lines(X, Y) & convergent_lines(X, Z) & distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.23/0.44 tff(26,plain,
% 0.23/0.44 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)) | (~(convergent_lines(X, Y) & convergent_lines(X, Z) & distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.23/0.44 tff(27,plain,
% 0.23/0.44 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)) | (~(convergent_lines(X, Y) & convergent_lines(X, Z) & distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.23/0.44 tff(28,plain,
% 0.23/0.44 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)) | (~(convergent_lines(X, Y) & convergent_lines(X, Z) & distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.23/0.44 tff(29,plain,
% 0.23/0.44 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)) | (~(convergent_lines(X, Y) & convergent_lines(X, Z) & distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.23/0.44 tff(30,plain,
% 0.23/0.44 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(line_connecting(intersection_point(X, Y), intersection_point(X, Z)), X)) | (~(convergent_lines(X, Y) & convergent_lines(X, Z) & distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.23/0.44 tff(31,plain,(
% 0.23/0.44 ~((~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(X!2, Z!0) & distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 0.23/0.44 inference(skolemize,[status(sab)],[30])).
% 0.23/0.44 tff(32,plain,
% 0.23/0.44 (convergent_lines(X!2, Y!1) & convergent_lines(X!2, Z!0) & distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.23/0.44 inference(or_elim,[status(thm)],[31])).
% 0.23/0.44 tff(33,plain,
% 0.23/0.44 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.23/0.44 inference(and_elim,[status(thm)],[32])).
% 0.23/0.44 tff(34,plain,
% 0.23/0.44 (^[X: $i, Y: $i, Z: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(35,plain,
% 0.23/0.44 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[34])).
% 0.23/0.44 tff(36,plain,
% 0.23/0.44 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(Z, X) & distinct_points(Z, Y)) <=> (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))), rewrite(((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(37,plain,
% 0.23/0.44 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[36])).
% 0.23/0.44 tff(38,plain,
% 0.23/0.44 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(39,plain,
% 0.23/0.44 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))) <=> ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> (distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))))), rewrite((distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(40,plain,
% 0.23/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[39])).
% 0.23/0.44 tff(41,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.23/0.45 tff(42,plain,
% 0.23/0.45 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.23/0.45 tff(43,plain,
% 0.23/0.45 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.23/0.45 tff(44,plain,(
% 0.23/0.45 ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[43])).
% 0.23/0.45 tff(45,plain,
% 0.23/0.45 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.23/0.45 tff(46,plain,
% 0.23/0.45 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.23/0.45 tff(47,plain,
% 0.23/0.45 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~((~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~((~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0))))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(48,plain,
% 0.23/0.45 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~((~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0))))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(49,plain,
% 0.23/0.45 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~((~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.23/0.45 tff(50,plain,
% 0.23/0.45 ($false),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[49, 46, 33, 20, 19])).
% 0.23/0.45 tff(51,plain,(~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.45 tff(52,plain,
% 0.23/0.45 (convergent_lines(X!2, Z!0)),
% 0.23/0.45 inference(and_elim,[status(thm)],[32])).
% 0.23/0.45 tff(53,plain,
% 0.23/0.45 (^[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)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(54,plain,
% 0.23/0.45 (![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))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[53])).
% 0.23/0.45 tff(55,plain,
% 0.23/0.45 (![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))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(56,plain,
% 0.23/0.45 (^[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))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(57,plain,
% 0.23/0.45 (![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))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[56])).
% 0.23/0.45 tff(58,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')).
% 0.23/0.45 tff(59,plain,
% 0.23/0.45 (![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))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.23/0.45 tff(60,plain,
% 0.23/0.45 (![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))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.23/0.45 tff(61,plain,(
% 0.23/0.45 ![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))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[60])).
% 0.23/0.45 tff(62,plain,
% 0.23/0.45 (![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))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.23/0.45 tff(63,plain,
% 0.23/0.45 (((~![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!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!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(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(64,plain,
% 0.23/0.45 ((distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))) <=> ((~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(65,plain,
% 0.23/0.45 ((~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2))) <=> (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(66,plain,
% 0.23/0.45 ((distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2)))) <=> (distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[65])).
% 0.23/0.45 tff(67,plain,
% 0.23/0.45 ((distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2)))) <=> ((~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)))),
% 0.23/0.45 inference(transitivity,[status(thm)],[66, 64])).
% 0.23/0.45 tff(68,plain,
% 0.23/0.45 (((~![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!2, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2))))) <=> ((~![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!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0))))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[67])).
% 0.23/0.45 tff(69,plain,
% 0.23/0.45 (((~![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!2, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2))))) <=> ((~![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!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)))),
% 0.23/0.45 inference(transitivity,[status(thm)],[68, 63])).
% 0.23/0.45 tff(70,plain,
% 0.23/0.45 ((~![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!2, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(71,plain,
% 0.23/0.45 ((~![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!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.23/0.45 tff(72,plain,
% 0.23/0.45 ((~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[71, 62, 52])).
% 0.23/0.45 tff(73,plain,
% 0.23/0.45 (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[72, 17])).
% 0.23/0.45 tff(74,plain,
% 0.23/0.45 ((apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(75,plain,
% 0.23/0.45 (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.23/0.45 tff(76,plain,
% 0.23/0.45 (convergent_lines(X!2, Y!1)),
% 0.23/0.45 inference(and_elim,[status(thm)],[32])).
% 0.23/0.45 tff(77,plain,
% 0.23/0.45 (((~![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!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![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!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(78,plain,
% 0.23/0.45 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(79,plain,
% 0.23/0.45 ((~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))) <=> (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(80,plain,
% 0.23/0.45 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[79])).
% 0.23/0.45 tff(81,plain,
% 0.23/0.45 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.23/0.45 inference(transitivity,[status(thm)],[80, 78])).
% 0.23/0.45 tff(82,plain,
% 0.23/0.45 (((~![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!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![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!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[81])).
% 0.23/0.45 tff(83,plain,
% 0.23/0.45 (((~![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!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![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!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.23/0.45 inference(transitivity,[status(thm)],[82, 77])).
% 0.23/0.45 tff(84,plain,
% 0.23/0.45 ((~![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!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(85,plain,
% 0.23/0.45 ((~![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!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.23/0.45 tff(86,plain,
% 0.23/0.45 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[85, 62, 76])).
% 0.23/0.45 tff(87,plain,
% 0.23/0.45 (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[86, 11])).
% 0.23/0.45 tff(88,plain,
% 0.23/0.45 ((apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(89,plain,
% 0.23/0.45 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.23/0.45 tff(90,plain,
% 0.23/0.45 (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2)),
% 0.23/0.45 inference(or_elim,[status(thm)],[31])).
% 0.23/0.45 tff(91,plain,
% 0.23/0.45 (^[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))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(92,plain,
% 0.23/0.45 (![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))) <=> ![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[91])).
% 0.23/0.45 tff(93,plain,
% 0.23/0.45 (^[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)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(94,plain,
% 0.23/0.45 (![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)))) <=> ![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[93])).
% 0.23/0.45 tff(95,plain,
% 0.23/0.45 (![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)))) <=> ![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))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(96,plain,
% 0.23/0.45 (^[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))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(97,plain,
% 0.23/0.45 (![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))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[96])).
% 0.23/0.45 tff(98,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')).
% 0.23/0.45 tff(99,plain,
% 0.23/0.45 (![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))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.23/0.45 tff(100,plain,
% 0.23/0.45 (![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))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.23/0.45 tff(101,plain,(
% 0.23/0.45 ![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))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[100])).
% 0.23/0.45 tff(102,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.23/0.45 tff(103,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[102, 92])).
% 0.23/0.45 tff(104,plain,
% 0.23/0.45 (((~![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)))) | ((~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(105,plain,
% 0.23/0.45 ((apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2))) <=> ((~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(106,plain,
% 0.23/0.45 (((~![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!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2)))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[105])).
% 0.23/0.46 tff(107,plain,
% 0.23/0.46 (((~![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!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2))),
% 0.23/0.46 inference(transitivity,[status(thm)],[106, 104])).
% 0.23/0.46 tff(108,plain,
% 0.23/0.46 ((~![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!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(109,plain,
% 0.23/0.46 ((~![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)))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), X!2)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.23/0.46 tff(110,plain,
% 0.23/0.46 (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[109, 103, 90, 33])).
% 0.23/0.46 tff(111,plain,
% 0.23/0.46 (apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[110, 89])).
% 0.23/0.46 tff(112,plain,
% 0.23/0.46 (apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[111, 75])).
% 0.23/0.46 tff(113,plain,
% 0.23/0.46 (apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[112, 51])).
% 0.23/0.46 tff(114,plain,
% 0.23/0.46 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(115,plain,
% 0.23/0.46 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(116,plain,
% 0.23/0.46 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.23/0.46 tff(117,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[116, 46, 33, 113, 13])).
% 0.23/0.46 % SZS output end Proof
%------------------------------------------------------------------------------