TSTP Solution File: GEO179+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 20:35:19 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:55:49 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.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(apart_point_and_line_type, type, (
% 0.20/0.41 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.41 tff(line_connecting_type, type, (
% 0.20/0.41 line_connecting: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_X_2_type, type, (
% 0.20/0.41 tptp_fun_X_2: $i)).
% 0.20/0.41 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.41 tptp_fun_Z_0: $i)).
% 0.20/0.41 tff(distinct_points_type, type, (
% 0.20/0.41 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.41 tptp_fun_Y_1: $i)).
% 0.20/0.41 tff(distinct_lines_type, type, (
% 0.20/0.41 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,assumption,(distinct_points(Z!0, Z!0)), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.41 tff(7,plain,(
% 0.20/0.41 ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.41 inference(skolemize,[status(sab)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Z!0, Z!0))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.41 tff(11,plain,(~distinct_points(Z!0, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0))) | distinct_points(Z!0, Z!0)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 ((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : ((distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y))) => (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(16,axiom,(~![X: $i, Y: $i, Z: $i] : ((distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y))) => (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.20/0.41 tff(24,plain,(
% 0.20/0.41 ~((~(distinct_points(X!2, Y!1) & apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) & distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[23])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (distinct_points(X!2, Y!1) & apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.20/0.41 inference(or_elim,[status(thm)],[24])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.20/0.41 inference(and_elim,[status(thm)],[25])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (distinct_points(X!2, Y!1)),
% 0.20/0.41 inference(and_elim,[status(thm)],[25])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (^[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))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![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)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (^[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)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![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)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (^[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))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.41 tff(35,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/sandbox/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.41 tff(38,plain,(
% 0.20/0.41 ![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))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[37])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (![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)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![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)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (((~![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(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))))) <=> ((~![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(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((~![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(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 ((~![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(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[43, 40, 27, 26])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))) | distinct_points(Z!0, X!2)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (distinct_points(Z!0, X!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, 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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (((~distinct_points(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, X!2))))) <=> ((~distinct_points(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, X!2)))))) <=> ((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, X!2)))))) <=> ((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 ((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, X!2)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 ((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 ((~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[52, 40, 46])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[53, 13])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0))) | distinct_points(Z!0, Z!0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[55, 11])).
% 0.20/0.42 tff(57,assumption,(apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))), introduced(assumption)).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))) | distinct_points(Z!0, Y!1)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (distinct_points(Z!0, Y!1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[58, 44])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (((~![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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, 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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1))))) <=> ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (((~![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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1)))))) <=> ((~![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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (((~![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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1)))))) <=> ((~![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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 ((~![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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[65, 40, 59, 57, 56])).
% 0.20/0.42 tff(67,plain,(~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.42 tff(73,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq2')).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.20/0.42 tff(76,plain,(
% 0.20/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[75])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) <=> (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[80, 78])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[83, 77, 26])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[84, 67])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 ((~(~((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))))) <=> ((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) & distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))) <=> (~((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 ((~(distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) & distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))) <=> (~(~((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[87])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 ((~(distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) & distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))) <=> ((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[88, 86])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (~(distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) & distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))),
% 0.20/0.43 inference(or_elim,[status(thm)],[24])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 ((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[91, 85])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) <=> (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[94])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[95, 93])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[98, 77, 26, 92, 54])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------