TSTP Solution File: GEO189+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO189+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 20:35:27 EDT 2022
% Result : Theorem 0.14s 0.34s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GEO189+3 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.29 % Computer : n004.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Wed Aug 31 06:47:19 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.29 Usage: tptp [options] [-file:]file
% 0.08/0.29 -h, -? prints this message.
% 0.08/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.29 -m, -model generate model.
% 0.08/0.29 -p, -proof generate proof.
% 0.08/0.29 -c, -core generate unsat core of named formulas.
% 0.08/0.29 -st, -statistics display statistics.
% 0.08/0.29 -t:timeout set timeout (in second).
% 0.08/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.29 -<param>:<value> configuration parameter and value.
% 0.08/0.29 -o:<output-file> file to place output in.
% 0.14/0.34 % SZS status Theorem
% 0.14/0.34 % SZS output start Proof
% 0.14/0.34 tff(distinct_lines_type, type, (
% 0.14/0.34 distinct_lines: ( $i * $i ) > $o)).
% 0.14/0.34 tff(line_connecting_type, type, (
% 0.14/0.34 line_connecting: ( $i * $i ) > $i)).
% 0.14/0.34 tff(tptp_fun_Y_1_type, type, (
% 0.14/0.34 tptp_fun_Y_1: $i)).
% 0.14/0.34 tff(tptp_fun_X_2_type, type, (
% 0.14/0.34 tptp_fun_X_2: $i)).
% 0.14/0.34 tff(tptp_fun_Z_0_type, type, (
% 0.14/0.34 tptp_fun_Z_0: $i)).
% 0.14/0.34 tff(apart_point_and_line_type, type, (
% 0.14/0.34 apart_point_and_line: ( $i * $i ) > $o)).
% 0.14/0.34 tff(incident_point_and_line_type, type, (
% 0.14/0.34 incident_point_and_line: ( $i * $i ) > $o)).
% 0.14/0.34 tff(distinct_points_type, type, (
% 0.14/0.34 distinct_points: ( $i * $i ) > $o)).
% 0.14/0.34 tff(1,plain,
% 0.14/0.34 (^[X: $i, Y: $i] : refl((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(2,plain,
% 0.14/0.34 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.34 tff(3,plain,
% 0.14/0.34 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(4,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.14/0.34 tff(5,plain,
% 0.14/0.34 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.34 tff(6,plain,(
% 0.14/0.34 ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.14/0.34 inference(skolemize,[status(sab)],[5])).
% 0.14/0.34 tff(7,plain,
% 0.14/0.34 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.34 tff(8,plain,
% 0.14/0.34 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(9,plain,
% 0.14/0.34 (incident_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.34 tff(10,plain,
% 0.14/0.34 ((~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Y, line_connecting(X, Z)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Y, line_connecting(X, Z))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(11,plain,
% 0.14/0.34 ((~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & incident_point_and_line(Z, line_connecting(X, Y))) => incident_point_and_line(Y, line_connecting(X, Z)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Y, line_connecting(X, Z))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(12,axiom,(~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & incident_point_and_line(Z, line_connecting(X, Y))) => incident_point_and_line(Y, line_connecting(X, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.14/0.34 tff(13,plain,
% 0.14/0.34 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Y, line_connecting(X, Z)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.14/0.34 tff(14,plain,
% 0.14/0.34 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Y, line_connecting(X, Z)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.14/0.34 tff(15,plain,
% 0.14/0.34 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Y, line_connecting(X, Z)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.14/0.34 tff(16,plain,
% 0.14/0.34 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Y, line_connecting(X, Z)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.14/0.34 tff(17,plain,
% 0.14/0.34 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Y, line_connecting(X, Z)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.14/0.34 tff(18,plain,
% 0.14/0.34 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Y, line_connecting(X, Z)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.14/0.34 tff(19,plain,
% 0.14/0.34 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Y, line_connecting(X, Z)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.14/0.34 tff(20,plain,(
% 0.14/0.34 ~((~(distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & incident_point_and_line(Z!0, line_connecting(X!2, Y!1)))) | incident_point_and_line(Y!1, line_connecting(X!2, Z!0)))),
% 0.14/0.34 inference(skolemize,[status(sab)],[19])).
% 0.14/0.34 tff(21,plain,
% 0.14/0.34 (distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & incident_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.14/0.34 inference(or_elim,[status(thm)],[20])).
% 0.14/0.34 tff(22,plain,
% 0.14/0.34 (incident_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.14/0.34 inference(and_elim,[status(thm)],[21])).
% 0.14/0.34 tff(23,plain,
% 0.14/0.34 ((~(incident_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) | (~incident_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(24,plain,
% 0.14/0.34 ((~(incident_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.14/0.34 tff(25,plain,
% 0.14/0.34 (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[24, 9])).
% 0.14/0.34 tff(26,plain,
% 0.14/0.34 (distinct_points(X!2, Z!0)),
% 0.14/0.34 inference(and_elim,[status(thm)],[21])).
% 0.14/0.34 tff(27,plain,
% 0.14/0.34 (^[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)))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(28,plain,
% 0.14/0.34 (![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))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[27])).
% 0.14/0.34 tff(29,plain,
% 0.14/0.34 (![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))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(30,plain,
% 0.14/0.34 (^[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)))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(31,plain,
% 0.14/0.34 (![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))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[30])).
% 0.14/0.34 tff(32,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.14/0.34 tff(33,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.14/0.34 tff(34,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.14/0.34 tff(35,plain,(
% 0.14/0.34 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.34 inference(skolemize,[status(sab)],[34])).
% 0.14/0.34 tff(36,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.14/0.34 tff(37,plain,
% 0.14/0.34 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(38,plain,
% 0.14/0.34 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(39,plain,
% 0.14/0.34 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.14/0.34 tff(40,plain,
% 0.14/0.34 (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[39, 36, 26])).
% 0.14/0.34 tff(41,plain,
% 0.14/0.34 (^[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)))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(42,plain,
% 0.14/0.34 (![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))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[41])).
% 0.14/0.34 tff(43,plain,
% 0.14/0.34 (![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))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(44,plain,
% 0.14/0.34 (^[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)))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(45,plain,
% 0.14/0.34 (![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))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[44])).
% 0.14/0.34 tff(46,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.14/0.34 tff(47,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.14/0.34 tff(48,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.14/0.34 tff(49,plain,(
% 0.14/0.34 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.34 inference(skolemize,[status(sab)],[48])).
% 0.14/0.34 tff(50,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.14/0.34 tff(51,plain,
% 0.14/0.34 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(52,plain,
% 0.14/0.34 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(53,plain,
% 0.14/0.34 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.14/0.34 tff(54,plain,
% 0.14/0.34 (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[53, 50, 26])).
% 0.14/0.34 tff(55,plain,
% 0.14/0.34 (distinct_points(X!2, Y!1)),
% 0.14/0.34 inference(and_elim,[status(thm)],[21])).
% 0.14/0.34 tff(56,plain,
% 0.14/0.34 (((~![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))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(57,plain,
% 0.14/0.34 ((~![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))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(58,plain,
% 0.14/0.34 ((~![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)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.14/0.34 tff(59,plain,
% 0.14/0.34 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[58, 36, 55])).
% 0.14/0.34 tff(60,plain,
% 0.14/0.34 (^[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_lines(U, V)) | (~distinct_points(X, Y))) <=> (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_lines(U, V)) | (~distinct_points(X, Y))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(61,plain,
% 0.14/0.34 (![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_lines(U, V)) | (~distinct_points(X, Y))) <=> ![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[60])).
% 0.14/0.34 tff(62,plain,
% 0.14/0.34 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))))), rewrite((~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((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_lines(U, V)) | (~distinct_points(X, Y)))))), 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_lines(U, V)) | (~distinct_points(X, Y)))) <=> (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_lines(U, V)) | (~distinct_points(X, Y)))), ((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_lines(U, V)) | (~distinct_points(X, Y)))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(63,plain,
% 0.14/0.34 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[62])).
% 0.14/0.34 tff(64,plain,
% 0.14/0.34 (![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))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(65,plain,
% 0.14/0.34 (^[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))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(66,plain,
% 0.14/0.35 (![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))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[65])).
% 0.14/0.35 tff(67,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/GEO006+0.ax','cu1')).
% 0.14/0.35 tff(68,plain,
% 0.14/0.35 (![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))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.14/0.35 tff(69,plain,
% 0.14/0.35 (![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))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.14/0.35 tff(70,plain,(
% 0.14/0.35 ![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))))),
% 0.14/0.35 inference(skolemize,[status(sab)],[69])).
% 0.14/0.35 tff(71,plain,
% 0.14/0.35 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.14/0.35 tff(72,plain,
% 0.14/0.35 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.14/0.35 tff(73,plain,
% 0.14/0.35 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), 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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(74,plain,
% 0.14/0.35 ((apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Z!0))) <=> (apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(75,plain,
% 0.14/0.35 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, 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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))))),
% 0.14/0.35 inference(monotonicity,[status(thm)],[74])).
% 0.14/0.35 tff(76,plain,
% 0.14/0.35 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, 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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.14/0.35 inference(transitivity,[status(thm)],[75, 73])).
% 0.14/0.35 tff(77,plain,
% 0.14/0.35 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Z!0)))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(78,plain,
% 0.14/0.35 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.14/0.35 tff(79,plain,
% 0.14/0.35 (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[78, 72, 26, 59, 54, 40, 25])).
% 0.14/0.35 tff(80,plain,
% 0.14/0.35 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(Y!1, line_connecting(X!2, Z!0)) <=> (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(81,plain,
% 0.14/0.35 (incident_point_and_line(Y!1, line_connecting(X!2, Z!0)) <=> (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0)))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[80, 7])).
% 0.14/0.35 tff(82,plain,
% 0.14/0.35 (~incident_point_and_line(Y!1, line_connecting(X!2, Z!0))),
% 0.14/0.35 inference(or_elim,[status(thm)],[20])).
% 0.14/0.35 tff(83,plain,
% 0.14/0.35 ((~(incident_point_and_line(Y!1, line_connecting(X!2, Z!0)) <=> (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))) | incident_point_and_line(Y!1, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(84,plain,
% 0.14/0.35 ((~(incident_point_and_line(Y!1, line_connecting(X!2, Z!0)) <=> (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.14/0.35 tff(85,plain,
% 0.14/0.35 (apart_point_and_line(Y!1, line_connecting(X!2, Z!0))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[84, 81])).
% 0.14/0.35 tff(86,plain,
% 0.14/0.35 (((~![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))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(87,plain,
% 0.14/0.35 ((~![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))))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(88,plain,
% 0.14/0.35 ((~![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)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.14/0.35 tff(89,plain,
% 0.14/0.35 (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[88, 50, 55])).
% 0.14/0.35 tff(90,plain,
% 0.14/0.35 (^[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))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(91,plain,
% 0.14/0.35 (![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)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[90])).
% 0.14/0.35 tff(92,plain,
% 0.14/0.35 (![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)))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(93,plain,
% 0.14/0.35 (^[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)))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(94,plain,
% 0.14/0.35 (![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)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[93])).
% 0.14/0.35 tff(95,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/GEO006+0.ax','ceq2')).
% 0.14/0.35 tff(96,plain,
% 0.14/0.35 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.14/0.35 tff(97,plain,
% 0.14/0.35 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.14/0.35 tff(98,plain,(
% 0.14/0.35 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.14/0.35 inference(skolemize,[status(sab)],[97])).
% 0.14/0.35 tff(99,plain,
% 0.14/0.35 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.14/0.35 tff(100,plain,
% 0.14/0.35 (((~![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(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(101,plain,
% 0.14/0.35 ((distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0)))) <=> (apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(102,plain,
% 0.14/0.35 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))) <=> ((~![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(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.14/0.35 inference(monotonicity,[status(thm)],[101])).
% 0.14/0.35 tff(103,plain,
% 0.14/0.35 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))) <=> ((~![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(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))),
% 0.14/0.35 inference(transitivity,[status(thm)],[102, 100])).
% 0.14/0.35 tff(104,plain,
% 0.14/0.35 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(105,plain,
% 0.14/0.35 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.14/0.35 tff(106,plain,
% 0.14/0.35 ($false),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[105, 99, 89, 85, 79])).
% 0.14/0.36 % SZS output end Proof
%------------------------------------------------------------------------------