TSTP Solution File: GEO188+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO188+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 20:35:26 EDT 2022
% Result : Theorem 0.16s 0.37s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GEO188+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n026.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
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 31 07:03:36 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.
% 0.16/0.37 % SZS status Theorem
% 0.16/0.37 % SZS output start Proof
% 0.16/0.37 tff(distinct_points_type, type, (
% 0.16/0.37 distinct_points: ( $i * $i ) > $o)).
% 0.16/0.37 tff(tptp_fun_Z_0_type, type, (
% 0.16/0.37 tptp_fun_Z_0: $i)).
% 0.16/0.37 tff(apart_point_and_line_type, type, (
% 0.16/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.16/0.37 tff(line_connecting_type, type, (
% 0.16/0.37 line_connecting: ( $i * $i ) > $i)).
% 0.16/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.16/0.37 tptp_fun_Y_1: $i)).
% 0.16/0.37 tff(tptp_fun_X_2_type, type, (
% 0.16/0.37 tptp_fun_X_2: $i)).
% 0.16/0.37 tff(distinct_lines_type, type, (
% 0.16/0.37 distinct_lines: ( $i * $i ) > $o)).
% 0.16/0.37 tff(1,assumption,(distinct_points(Y!1, Y!1)), introduced(assumption)).
% 0.16/0.37 tff(2,plain,
% 0.16/0.37 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(3,plain,
% 0.16/0.37 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.16/0.37 tff(4,plain,
% 0.16/0.37 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.16/0.37 tff(6,plain,
% 0.16/0.37 (![X: $i] : (~distinct_points(X, X))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.16/0.37 tff(7,plain,(
% 0.16/0.37 ![X: $i] : (~distinct_points(X, X))),
% 0.16/0.37 inference(skolemize,[status(sab)],[6])).
% 0.16/0.37 tff(8,plain,
% 0.16/0.37 (![X: $i] : (~distinct_points(X, X))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.16/0.37 tff(9,plain,
% 0.16/0.37 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!1, Y!1))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(10,plain,
% 0.16/0.37 ($false),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.16/0.37 tff(11,plain,(~distinct_points(Y!1, Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.37 tff(12,plain,
% 0.16/0.37 (((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1))) | distinct_points(Y!1, Y!1)),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(13,plain,
% 0.16/0.37 ((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.16/0.37 tff(14,assumption,(apart_point_and_line(Y!1, line_connecting(X!2, Y!1))), introduced(assumption)).
% 0.16/0.37 tff(15,plain,
% 0.16/0.37 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y)))))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(16,plain,
% 0.16/0.37 ((~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & (~apart_point_and_line(Z, line_connecting(X, Y)))) => (~apart_point_and_line(X, line_connecting(Z, Y))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y)))))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(17,axiom,(~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & (~apart_point_and_line(Z, line_connecting(X, Y)))) => (~apart_point_and_line(X, line_connecting(Z, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.16/0.37 tff(18,plain,
% 0.16/0.37 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.16/0.37 tff(19,plain,
% 0.16/0.37 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.16/0.37 tff(20,plain,
% 0.16/0.37 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.16/0.37 tff(21,plain,
% 0.16/0.37 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.16/0.37 tff(22,plain,
% 0.16/0.37 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.16/0.37 tff(23,plain,
% 0.16/0.37 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.16/0.37 tff(24,plain,
% 0.16/0.37 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.16/0.37 tff(25,plain,(
% 0.16/0.37 ~((~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | (~(distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))))),
% 0.16/0.37 inference(skolemize,[status(sab)],[24])).
% 0.16/0.37 tff(26,plain,
% 0.16/0.37 (distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.16/0.37 inference(or_elim,[status(thm)],[25])).
% 0.16/0.37 tff(27,plain,
% 0.16/0.37 (distinct_points(X!2, Y!1)),
% 0.16/0.37 inference(and_elim,[status(thm)],[26])).
% 0.16/0.37 tff(28,plain,
% 0.16/0.37 (^[X: $i, Y: $i, Z: $i] : refl(((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(29,plain,
% 0.16/0.37 (![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.16/0.37 tff(30,plain,
% 0.16/0.37 (^[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)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y))) <=> ((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y))))), rewrite(((~((~distinct_points(Z, X)) | (~distinct_points(Z, 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(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))), (((distinct_points(Z, X) & distinct_points(Z, 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(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(31,plain,
% 0.16/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.16/0.37 tff(32,plain,
% 0.16/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(33,plain,
% 0.16/0.37 (^[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)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(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)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(34,plain,
% 0.16/0.37 (![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)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.16/0.37 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/sandbox2/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.16/0.37 tff(36,plain,
% 0.16/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.16/0.37 tff(37,plain,
% 0.16/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.16/0.37 tff(38,plain,(
% 0.16/0.37 ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)))),
% 0.16/0.37 inference(skolemize,[status(sab)],[37])).
% 0.16/0.37 tff(39,plain,
% 0.16/0.37 (![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.16/0.37 tff(40,plain,
% 0.16/0.37 (![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.16/0.37 tff(41,plain,
% 0.16/0.37 (((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1)) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1)) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1)))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(42,plain,
% 0.16/0.37 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1)) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1)))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(43,plain,
% 0.16/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1)) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.16/0.38 tff(44,plain,
% 0.16/0.38 ($false),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[43, 40, 27, 14, 13])).
% 0.16/0.38 tff(45,plain,(~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.38 tff(46,assumption,(~distinct_points(Z!0, Z!0)), introduced(assumption)).
% 0.16/0.38 tff(47,plain,
% 0.16/0.38 (((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1))) | distinct_points(Z!0, Z!0)),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(48,plain,
% 0.16/0.38 ((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.16/0.38 tff(49,assumption,(~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))), introduced(assumption)).
% 0.16/0.38 tff(50,assumption,(~distinct_points(Y!1, Y!1)), introduced(assumption)).
% 0.16/0.38 tff(51,plain,
% 0.16/0.38 (((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0))) | distinct_points(Y!1, Y!1)),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(52,plain,
% 0.16/0.38 ((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.16/0.38 tff(53,assumption,(apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))), introduced(assumption)).
% 0.16/0.38 tff(54,plain,
% 0.16/0.38 (distinct_points(Y!1, Z!0)),
% 0.16/0.38 inference(and_elim,[status(thm)],[26])).
% 0.16/0.38 tff(55,plain,
% 0.16/0.38 (^[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))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(56,plain,
% 0.16/0.38 (![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)))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[55])).
% 0.16/0.38 tff(57,plain,
% 0.16/0.38 (![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)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(58,plain,
% 0.16/0.38 (^[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)))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(59,plain,
% 0.16/0.38 (![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)))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[58])).
% 0.16/0.38 tff(60,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart4')).
% 0.16/0.38 tff(61,plain,
% 0.16/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.16/0.38 tff(62,plain,
% 0.16/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.16/0.38 tff(63,plain,(
% 0.16/0.38 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.16/0.38 inference(skolemize,[status(sab)],[62])).
% 0.16/0.38 tff(64,plain,
% 0.16/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.16/0.38 tff(65,plain,
% 0.16/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(66,plain,
% 0.16/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0)))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(67,plain,
% 0.16/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.16/0.38 tff(68,plain,
% 0.16/0.38 (distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[67, 64, 54])).
% 0.16/0.38 tff(69,plain,
% 0.16/0.38 (distinct_points(Z!0, Y!1)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[68, 50])).
% 0.16/0.38 tff(70,plain,
% 0.16/0.38 (((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0)))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0)))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(71,plain,
% 0.16/0.38 (((~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))) | (~distinct_points(Z!0, Y!1)) | (~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0))))) <=> ((~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0)))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(72,plain,
% 0.16/0.38 ((~((~distinct_points(Y!1, Z!0)) | (~distinct_points(Y!1, Y!1)))) <=> (~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(73,plain,
% 0.16/0.38 (((~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))) | (~distinct_points(Z!0, Y!1)) | (~((~distinct_points(Y!1, Z!0)) | (~distinct_points(Y!1, Y!1))))) <=> ((~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))) | (~distinct_points(Z!0, Y!1)) | (~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0)))))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[72])).
% 0.16/0.38 tff(74,plain,
% 0.16/0.38 (((~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))) | (~distinct_points(Z!0, Y!1)) | (~((~distinct_points(Y!1, Z!0)) | (~distinct_points(Y!1, Y!1))))) <=> ((~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0)))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[73, 71])).
% 0.16/0.38 tff(75,plain,
% 0.16/0.38 (((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))) | (~distinct_points(Z!0, Y!1)) | (~((~distinct_points(Y!1, Z!0)) | (~distinct_points(Y!1, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0)))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)))))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[74])).
% 0.16/0.38 tff(76,plain,
% 0.16/0.38 (((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))) | (~distinct_points(Z!0, Y!1)) | (~((~distinct_points(Y!1, Z!0)) | (~distinct_points(Y!1, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0)))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[75, 70])).
% 0.16/0.38 tff(77,plain,
% 0.16/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))) | (~distinct_points(Z!0, Y!1)) | (~((~distinct_points(Y!1, Z!0)) | (~distinct_points(Y!1, Y!1)))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(78,plain,
% 0.16/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, Z!0)))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.16/0.38 tff(79,plain,
% 0.16/0.38 ($false),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[78, 40, 69, 53, 52])).
% 0.16/0.38 tff(80,plain,((~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))) | distinct_points(Y!1, Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.38 tff(81,plain,
% 0.16/0.38 (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[80, 50])).
% 0.16/0.38 tff(82,assumption,(distinct_points(X!2, X!2)), introduced(assumption)).
% 0.16/0.38 tff(83,plain,
% 0.16/0.38 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(X!2, X!2))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(84,plain,
% 0.16/0.38 ($false),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[83, 8, 82])).
% 0.16/0.38 tff(85,plain,(~distinct_points(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.38 tff(86,plain,
% 0.16/0.38 (((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1))) | distinct_points(X!2, X!2)),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(87,plain,
% 0.16/0.38 ((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.16/0.38 tff(88,assumption,(apart_point_and_line(X!2, line_connecting(X!2, Y!1))), introduced(assumption)).
% 0.16/0.38 tff(89,plain,
% 0.16/0.38 (((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!2, Y!1)) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!2, Y!1)) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(90,plain,
% 0.16/0.38 (((~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1)) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1))))) <=> ((~distinct_points(X!2, Y!1)) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(91,plain,
% 0.16/0.38 (((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1)) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!2, Y!1)) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1)))))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[90])).
% 0.16/0.38 tff(92,plain,
% 0.16/0.38 (((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1)) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!2, Y!1)) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[91, 89])).
% 0.16/0.38 tff(93,plain,
% 0.16/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1)) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(94,plain,
% 0.16/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!2, Y!1)) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.16/0.38 tff(95,plain,
% 0.16/0.38 ($false),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[94, 40, 27, 88, 87])).
% 0.16/0.38 tff(96,plain,(~apart_point_and_line(X!2, line_connecting(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.38 tff(97,plain,
% 0.16/0.38 (apart_point_and_line(X!2, line_connecting(Z!0, Y!1))),
% 0.16/0.38 inference(or_elim,[status(thm)],[25])).
% 0.16/0.38 tff(98,plain,
% 0.16/0.38 (^[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))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(99,plain,
% 0.16/0.38 (![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)))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[98])).
% 0.16/0.38 tff(100,plain,
% 0.16/0.38 (![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)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(101,plain,
% 0.16/0.38 (^[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)))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(102,plain,
% 0.16/0.39 (![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)))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[101])).
% 0.16/0.39 tff(103,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/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq2')).
% 0.16/0.39 tff(104,plain,
% 0.16/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.16/0.39 tff(105,plain,
% 0.16/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.16/0.39 tff(106,plain,(
% 0.16/0.39 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.39 inference(skolemize,[status(sab)],[105])).
% 0.16/0.39 tff(107,plain,
% 0.16/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.16/0.39 tff(108,plain,
% 0.16/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, 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)))) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(109,plain,
% 0.16/0.39 ((distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1)))) <=> ((~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(110,plain,
% 0.16/0.39 (((~![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(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(X!2, 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)))) | ((~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[109])).
% 0.16/0.39 tff(111,plain,
% 0.16/0.39 (((~![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(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(X!2, 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)))) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.16/0.39 inference(transitivity,[status(thm)],[110, 108])).
% 0.16/0.39 tff(112,plain,
% 0.16/0.39 ((~![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(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(113,plain,
% 0.16/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.16/0.39 tff(114,plain,
% 0.16/0.39 (distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[113, 107, 97])).
% 0.16/0.39 tff(115,plain,
% 0.16/0.39 (distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[114, 96])).
% 0.16/0.39 tff(116,plain,
% 0.16/0.39 (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.16/0.39 inference(and_elim,[status(thm)],[26])).
% 0.16/0.39 tff(117,plain,
% 0.16/0.39 (^[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))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(118,plain,
% 0.16/0.39 (![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)))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[117])).
% 0.16/0.39 tff(119,plain,
% 0.16/0.39 (^[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)))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(120,plain,
% 0.16/0.39 (![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)))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[119])).
% 0.16/0.39 tff(121,plain,
% 0.16/0.39 (![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))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(122,plain,
% 0.16/0.39 (^[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))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(123,plain,
% 0.16/0.39 (![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))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[122])).
% 0.16/0.39 tff(124,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')).
% 0.16/0.39 tff(125,plain,
% 0.16/0.39 (![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))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.16/0.39 tff(126,plain,
% 0.16/0.39 (![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))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.16/0.39 tff(127,plain,(
% 0.16/0.39 ![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))))),
% 0.16/0.39 inference(skolemize,[status(sab)],[126])).
% 0.16/0.39 tff(128,plain,
% 0.16/0.39 (![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)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.16/0.39 tff(129,plain,
% 0.16/0.39 (![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)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[128, 118])).
% 0.16/0.39 tff(130,plain,
% 0.16/0.39 (((~![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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(131,plain,
% 0.16/0.39 ((apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)))) <=> (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(132,plain,
% 0.16/0.39 (((~![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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0))))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[131])).
% 0.16/0.39 tff(133,plain,
% 0.16/0.39 (((~![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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)))),
% 0.16/0.39 inference(transitivity,[status(thm)],[132, 130])).
% 0.16/0.39 tff(134,plain,
% 0.16/0.39 ((~![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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(135,plain,
% 0.16/0.39 ((~![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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.16/0.39 tff(136,plain,
% 0.16/0.39 (apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[135, 129, 54, 116, 115])).
% 0.16/0.39 tff(137,plain,
% 0.16/0.39 (apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[136, 81, 49])).
% 0.16/0.39 tff(138,plain,
% 0.16/0.39 (((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~distinct_points(Z!0, Y!1)) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~distinct_points(Z!0, Y!1)) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1)))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(139,plain,
% 0.16/0.39 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~distinct_points(Z!0, Y!1)) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1)))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(140,plain,
% 0.16/0.39 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Z, line_connecting(X, Y))) | (~distinct_points(X, Y)) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~distinct_points(Z!0, Y!1)) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.16/0.39 tff(141,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[140, 40, 69, 137, 48])).
% 0.16/0.40 tff(142,plain,(distinct_points(Y!1, Y!1) | distinct_points(Z!0, Z!0) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.40 tff(143,plain,
% 0.16/0.40 (distinct_points(Z!0, Z!0) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[142, 11])).
% 0.16/0.40 tff(144,plain,
% 0.16/0.40 (distinct_points(Z!0, Z!0)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[143, 45])).
% 0.16/0.40 tff(145,plain,
% 0.16/0.40 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Z!0, Z!0))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(146,plain,
% 0.16/0.40 ($false),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[145, 8, 144])).
% 0.16/0.40 % SZS output end Proof
%------------------------------------------------------------------------------