TSTP Solution File: GEO200+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO200+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:35:35 EDT 2022
% Result : Theorem 0.15s 0.35s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GEO200+2 : TPTP v8.1.0. Released v3.3.0.
% 0.05/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n027.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Wed Aug 31 07:08:32 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.15/0.35 % SZS status Theorem
% 0.15/0.35 % SZS output start Proof
% 0.15/0.35 tff(distinct_points_type, type, (
% 0.15/0.35 distinct_points: ( $i * $i ) > $o)).
% 0.15/0.35 tff(tptp_fun_Y_0_type, type, (
% 0.15/0.35 tptp_fun_Y_0: $i)).
% 0.15/0.35 tff(tptp_fun_X_1_type, type, (
% 0.15/0.35 tptp_fun_X_1: $i)).
% 0.15/0.35 tff(apart_point_and_line_type, type, (
% 0.15/0.35 apart_point_and_line: ( $i * $i ) > $o)).
% 0.15/0.35 tff(line_connecting_type, type, (
% 0.15/0.35 line_connecting: ( $i * $i ) > $i)).
% 0.15/0.35 tff(distinct_lines_type, type, (
% 0.15/0.35 distinct_lines: ( $i * $i ) > $o)).
% 0.15/0.35 tff(1,assumption,(distinct_points(Y!0, Y!0)), introduced(assumption)).
% 0.15/0.35 tff(2,plain,
% 0.15/0.35 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(3,plain,
% 0.15/0.35 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[2])).
% 0.15/0.35 tff(4,plain,
% 0.15/0.35 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.15/0.35 tff(6,plain,
% 0.15/0.35 (![X: $i] : (~distinct_points(X, X))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.15/0.35 tff(7,plain,(
% 0.15/0.35 ![X: $i] : (~distinct_points(X, X))),
% 0.15/0.35 inference(skolemize,[status(sab)],[6])).
% 0.15/0.35 tff(8,plain,
% 0.15/0.35 (![X: $i] : (~distinct_points(X, X))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.15/0.35 tff(9,plain,
% 0.15/0.35 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!0, Y!0))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(10,plain,
% 0.15/0.35 ($false),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.15/0.35 tff(11,plain,(~distinct_points(Y!0, Y!0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.35 tff(12,plain,
% 0.15/0.35 (((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0))) | distinct_points(Y!0, Y!0)),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(13,plain,
% 0.15/0.35 ((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.15/0.35 tff(14,assumption,(distinct_points(X!1, X!1)), introduced(assumption)).
% 0.15/0.35 tff(15,plain,
% 0.15/0.35 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(X!1, X!1))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(16,plain,
% 0.15/0.35 ($false),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[15, 8, 14])).
% 0.15/0.35 tff(17,plain,(~distinct_points(X!1, X!1)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.35 tff(18,plain,
% 0.15/0.35 (((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!0))) | distinct_points(X!1, X!1)),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(19,plain,
% 0.15/0.35 ((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!0))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.15/0.35 tff(20,assumption,(apart_point_and_line(X!1, line_connecting(X!1, Y!0))), introduced(assumption)).
% 0.15/0.35 tff(21,plain,
% 0.15/0.35 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))) <=> (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X)))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(22,plain,
% 0.15/0.35 ((~![X: $i, Y: $i] : (distinct_points(X, Y) => (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))) <=> (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X)))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(23,axiom,(~![X: $i, Y: $i] : (distinct_points(X, Y) => (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.15/0.35 tff(24,plain,
% 0.15/0.35 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.15/0.35 tff(25,plain,
% 0.15/0.35 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.15/0.35 tff(26,plain,
% 0.15/0.35 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.15/0.35 tff(27,plain,
% 0.15/0.35 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.15/0.35 tff(28,plain,
% 0.15/0.35 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.15/0.35 tff(29,plain,
% 0.15/0.35 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.15/0.35 tff(30,plain,
% 0.15/0.35 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.15/0.35 tff(31,plain,(
% 0.15/0.35 ~((~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))))),
% 0.15/0.35 inference(skolemize,[status(sab)],[30])).
% 0.15/0.35 tff(32,plain,
% 0.15/0.35 (distinct_points(X!1, Y!0)),
% 0.15/0.35 inference(or_elim,[status(thm)],[31])).
% 0.15/0.35 tff(33,plain,
% 0.15/0.35 (^[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))))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(34,plain,
% 0.15/0.35 (![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)))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[33])).
% 0.15/0.35 tff(35,plain,
% 0.15/0.35 (^[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)))))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(36,plain,
% 0.15/0.35 (![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)))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[35])).
% 0.15/0.35 tff(37,plain,
% 0.15/0.35 (![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))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(38,plain,
% 0.15/0.35 (^[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))))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(39,plain,
% 0.15/0.36 (![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))))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[38])).
% 0.15/0.36 tff(40,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')).
% 0.15/0.36 tff(41,plain,
% 0.15/0.36 (![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))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.15/0.36 tff(42,plain,
% 0.15/0.36 (![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))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.15/0.36 tff(43,plain,(
% 0.15/0.36 ![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))))),
% 0.15/0.36 inference(skolemize,[status(sab)],[42])).
% 0.15/0.36 tff(44,plain,
% 0.15/0.36 (![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)))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.15/0.36 tff(45,plain,
% 0.15/0.36 (![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)))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.15/0.36 tff(46,plain,
% 0.15/0.36 (((~![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!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))) | (~((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!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(X!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))) | (~((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!0)))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(47,plain,
% 0.15/0.36 ((~![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!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))) | (~((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!0)))))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(48,plain,
% 0.15/0.36 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))) | (~((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!0))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.15/0.36 tff(49,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[48, 45, 32, 20, 19])).
% 0.15/0.36 tff(50,plain,(~apart_point_and_line(X!1, line_connecting(X!1, Y!0))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.36 tff(51,assumption,(apart_point_and_line(Y!0, line_connecting(X!1, Y!0))), introduced(assumption)).
% 0.15/0.36 tff(52,plain,
% 0.15/0.36 (((~![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!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!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(X!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0)))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(53,plain,
% 0.15/0.36 ((~![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!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0)))))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(54,plain,
% 0.15/0.36 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.15/0.36 tff(55,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[54, 45, 32, 51, 13])).
% 0.15/0.36 tff(56,plain,(~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.36 tff(57,plain,
% 0.15/0.36 (((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!1))) | distinct_points(X!1, X!1)),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(58,plain,
% 0.15/0.36 ((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!1))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[57, 17])).
% 0.15/0.36 tff(59,assumption,(apart_point_and_line(X!1, line_connecting(Y!0, X!1))), introduced(assumption)).
% 0.15/0.36 tff(60,plain,
% 0.15/0.36 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(61,plain,
% 0.15/0.36 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[60])).
% 0.15/0.36 tff(62,plain,
% 0.15/0.36 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(63,plain,
% 0.15/0.36 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | distinct_points(Y, Z)) <=> (distinct_points(Y, Z) | distinct_points(X, Z))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))))), rewrite((distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(64,plain,
% 0.15/0.36 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[63])).
% 0.15/0.36 tff(65,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart4')).
% 0.15/0.36 tff(66,plain,
% 0.15/0.36 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.15/0.36 tff(67,plain,
% 0.15/0.36 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.15/0.36 tff(68,plain,(
% 0.15/0.36 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.15/0.36 inference(skolemize,[status(sab)],[67])).
% 0.15/0.36 tff(69,plain,
% 0.15/0.36 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.15/0.36 tff(70,plain,
% 0.15/0.36 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(71,plain,
% 0.15/0.36 ((distinct_points(Y!0, X!1) | distinct_points(X!1, X!1) | (~distinct_points(X!1, Y!0))) <=> ((~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(72,plain,
% 0.15/0.36 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!0, X!1) | distinct_points(X!1, X!1) | (~distinct_points(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1)))),
% 0.15/0.36 inference(monotonicity,[status(thm)],[71])).
% 0.15/0.36 tff(73,plain,
% 0.15/0.36 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!0, X!1) | distinct_points(X!1, X!1) | (~distinct_points(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1))),
% 0.15/0.36 inference(transitivity,[status(thm)],[72, 70])).
% 0.15/0.36 tff(74,plain,
% 0.15/0.36 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!0, X!1) | distinct_points(X!1, X!1) | (~distinct_points(X!1, Y!0)))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(75,plain,
% 0.15/0.36 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1)),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.15/0.36 tff(76,plain,
% 0.15/0.36 (distinct_points(Y!0, X!1) | distinct_points(X!1, X!1)),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[75, 69, 32])).
% 0.15/0.36 tff(77,plain,
% 0.15/0.36 (distinct_points(Y!0, X!1)),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[76, 17])).
% 0.15/0.36 tff(78,plain,
% 0.15/0.36 (((~![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(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))) | (~((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!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(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))) | (~((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!1)))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(79,plain,
% 0.15/0.36 ((~![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(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))) | (~((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!1)))))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(80,plain,
% 0.15/0.36 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))) | (~((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!1))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.15/0.36 tff(81,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[80, 45, 77, 59, 58])).
% 0.15/0.36 tff(82,plain,(~apart_point_and_line(X!1, line_connecting(Y!0, X!1))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.36 tff(83,plain,
% 0.15/0.36 (distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))),
% 0.15/0.36 inference(or_elim,[status(thm)],[31])).
% 0.15/0.36 tff(84,plain,
% 0.15/0.36 (^[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))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(85,plain,
% 0.15/0.36 (![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)))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[84])).
% 0.15/0.36 tff(86,plain,
% 0.15/0.36 (^[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)))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(87,plain,
% 0.15/0.36 (![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)))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[86])).
% 0.15/0.36 tff(88,plain,
% 0.15/0.36 (![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))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(89,plain,
% 0.15/0.36 (^[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))))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(90,plain,
% 0.15/0.36 (![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))))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[89])).
% 0.15/0.36 tff(91,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/sandbox/benchmark/Axioms/GEO008+0.ax','cu1')).
% 0.15/0.36 tff(92,plain,
% 0.15/0.36 (![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))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.15/0.36 tff(93,plain,
% 0.15/0.36 (![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))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.15/0.37 tff(94,plain,(
% 0.15/0.37 ![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))))),
% 0.15/0.37 inference(skolemize,[status(sab)],[93])).
% 0.15/0.37 tff(95,plain,
% 0.15/0.37 (![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)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.15/0.37 tff(96,plain,
% 0.15/0.37 (![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)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.15/0.37 tff(97,plain,
% 0.15/0.37 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(98,plain,
% 0.15/0.37 ((apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1)))) <=> ((~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(99,plain,
% 0.15/0.37 (((~![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(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1))))),
% 0.15/0.37 inference(monotonicity,[status(thm)],[98])).
% 0.15/0.37 tff(100,plain,
% 0.15/0.37 (((~![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(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)))),
% 0.15/0.37 inference(transitivity,[status(thm)],[99, 97])).
% 0.15/0.37 tff(101,plain,
% 0.15/0.37 ((~![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(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(102,plain,
% 0.15/0.37 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.15/0.37 tff(103,plain,
% 0.15/0.37 (apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[102, 96, 32, 83])).
% 0.15/0.37 tff(104,plain,
% 0.15/0.37 (apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[103, 82])).
% 0.15/0.37 tff(105,plain,
% 0.15/0.37 (apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[104, 56])).
% 0.15/0.37 tff(106,plain,
% 0.15/0.37 (apart_point_and_line(Y!0, line_connecting(Y!0, X!1))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[105, 50])).
% 0.15/0.37 tff(107,plain,
% 0.15/0.37 (((~![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(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!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(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0)))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(108,plain,
% 0.15/0.37 (((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, Y!0)) | (~distinct_points(Y!0, X!1))))) <=> ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0)))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(109,plain,
% 0.15/0.37 (((~![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(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, Y!0)) | (~distinct_points(Y!0, X!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(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0))))))),
% 0.15/0.37 inference(monotonicity,[status(thm)],[108])).
% 0.15/0.37 tff(110,plain,
% 0.15/0.37 (((~![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(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, Y!0)) | (~distinct_points(Y!0, X!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(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0)))))),
% 0.15/0.37 inference(transitivity,[status(thm)],[109, 107])).
% 0.15/0.37 tff(111,plain,
% 0.15/0.37 ((~![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(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, Y!0)) | (~distinct_points(Y!0, X!1)))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(112,plain,
% 0.15/0.37 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.15/0.37 tff(113,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[112, 45, 77, 106, 13])).
% 0.15/0.37 % SZS output end Proof
%------------------------------------------------------------------------------