TSTP Solution File: GEO178+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO178+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:35:19 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO178+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 06:58:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(apart_point_and_line_type, type, (
% 0.21/0.41 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.41 tff(line_connecting_type, type, (
% 0.21/0.41 line_connecting: ( $i * $i ) > $i)).
% 0.21/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.41 tptp_fun_Y_1: $i)).
% 0.21/0.41 tff(tptp_fun_X_2_type, type, (
% 0.21/0.41 tptp_fun_X_2: $i)).
% 0.21/0.41 tff(distinct_points_type, type, (
% 0.21/0.41 distinct_points: ( $i * $i ) > $o)).
% 0.21/0.41 tff(tptp_fun_Z_0_type, type, (
% 0.21/0.41 tptp_fun_Z_0: $i)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : ((distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y))) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(3,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/theBenchmark.p','con')).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.41 tff(11,plain,(
% 0.21/0.41 ~((~(distinct_points(X!2, Y!1) & apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) | (distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[10])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (distinct_points(X!2, Y!1) & apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.21/0.41 inference(or_elim,[status(thm)],[11])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (distinct_points(X!2, Y!1)),
% 0.21/0.41 inference(and_elim,[status(thm)],[12])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.41 tff(19,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.21/0.41 tff(22,plain,(
% 0.21/0.41 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[21])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.41 tff(33,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.21/0.42 tff(36,plain,(
% 0.21/0.42 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[35])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[40, 37, 13])).
% 0.21/0.42 tff(42,assumption,(~distinct_points(Z!0, Y!1)), introduced(assumption)).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.21/0.42 inference(and_elim,[status(thm)],[12])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | apart_point_and_line(Z, Y)) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))))), rewrite((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.42 tff(49,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.42 tff(52,plain,(
% 0.21/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[51])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(Z!0, Y!1) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(Z!0, Y!1) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(Z!0, Y!1) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(Z!0, Y!1) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[56, 53, 43, 42, 41])).
% 0.21/0.42 tff(58,plain,(distinct_points(Z!0, Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 ((~(~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))))) <=> ((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 ((distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1)) <=> (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 ((~(distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1))) <=> (~(~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[60])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 ((~(distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1))) <=> ((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[61, 59])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 (~(distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1))),
% 0.21/0.42 inference(or_elim,[status(thm)],[11])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 ((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.42 tff(65,plain,
% 0.21/0.42 (~distinct_points(Z!0, X!2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[64, 58])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(Z!0, X!2) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(Z!0, X!2) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(Z!0, X!2) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(Z!0, X!2) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[68, 53, 43, 65, 27])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------