TSTP Solution File: GEO185+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO185+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 20:35:24 EDT 2022
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO185+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 06:46:20 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(incident_point_and_line_type, type, (
% 0.21/0.40 incident_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_V_0_type, type, (
% 0.21/0.40 tptp_fun_V_0: $i)).
% 0.21/0.40 tff(tptp_fun_X_3_type, type, (
% 0.21/0.40 tptp_fun_X_3: $i)).
% 0.21/0.40 tff(apart_point_and_line_type, type, (
% 0.21/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.40 tff(distinct_points_type, type, (
% 0.21/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.21/0.40 tff(intersection_point_type, type, (
% 0.21/0.40 intersection_point: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_U_1_type, type, (
% 0.21/0.40 tptp_fun_U_1: $i)).
% 0.21/0.40 tff(equal_points_type, type, (
% 0.21/0.40 equal_points: ( $i * $i ) > $o)).
% 0.21/0.40 tff(convergent_lines_type, type, (
% 0.21/0.40 convergent_lines: ( $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.21/0.40 tptp_fun_Y_2: $i)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 (^[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))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(4,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.40 tff(6,plain,(
% 0.21/0.40 ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[5])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(X!3, V!0) <=> (~apart_point_and_line(X!3, V!0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (incident_point_and_line(X!3, V!0) <=> (~apart_point_and_line(X!3, V!0))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (^[X: $i, Y: $i] : refl((equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> (equal_points(X, Y) <=> (~distinct_points(X, Y))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(13,axiom,(![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax1')).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.40 tff(15,plain,(
% 0.21/0.40 ![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[14])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))) | (equal_points(X!3, intersection_point(U!1, V!0)) <=> (~distinct_points(X!3, intersection_point(U!1, V!0))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (equal_points(X!3, intersection_point(U!1, V!0)) <=> (~distinct_points(X!3, intersection_point(U!1, V!0)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & equal_points(X, intersection_point(U, V)))) | (incident_point_and_line(X, U) & incident_point_and_line(X, V)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & equal_points(X, intersection_point(U, V)))) | (incident_point_and_line(X, U) & incident_point_and_line(X, V))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & equal_points(X, intersection_point(U, V))) => (incident_point_and_line(X, U) & incident_point_and_line(X, V)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & equal_points(X, intersection_point(U, V)))) | (incident_point_and_line(X, U) & incident_point_and_line(X, V))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(21,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & equal_points(X, intersection_point(U, V))) => (incident_point_and_line(X, U) & incident_point_and_line(X, V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & equal_points(X, intersection_point(U, V)))) | (incident_point_and_line(X, U) & incident_point_and_line(X, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & equal_points(X, intersection_point(U, V)))) | (incident_point_and_line(X, U) & incident_point_and_line(X, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & equal_points(X, intersection_point(U, V)))) | (incident_point_and_line(X, U) & incident_point_and_line(X, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & equal_points(X, intersection_point(U, V)))) | (incident_point_and_line(X, U) & incident_point_and_line(X, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & equal_points(X, intersection_point(U, V)))) | (incident_point_and_line(X, U) & incident_point_and_line(X, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & equal_points(X, intersection_point(U, V)))) | (incident_point_and_line(X, U) & incident_point_and_line(X, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & equal_points(X, intersection_point(U, V)))) | (incident_point_and_line(X, U) & incident_point_and_line(X, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.21/0.41 tff(29,plain,(
% 0.21/0.41 ~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & equal_points(X!3, intersection_point(U!1, V!0)))) | (incident_point_and_line(X!3, U!1) & incident_point_and_line(X!3, V!0)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[28])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & equal_points(X!3, intersection_point(U!1, V!0))),
% 0.21/0.41 inference(or_elim,[status(thm)],[29])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (equal_points(X!3, intersection_point(U!1, V!0))),
% 0.21/0.41 inference(and_elim,[status(thm)],[30])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 ((~(equal_points(X!3, intersection_point(U!1, V!0)) <=> (~distinct_points(X!3, intersection_point(U!1, V!0))))) | (~equal_points(X!3, intersection_point(U!1, V!0))) | (~distinct_points(X!3, intersection_point(U!1, V!0)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 ((~(equal_points(X!3, intersection_point(U!1, V!0)) <=> (~distinct_points(X!3, intersection_point(U!1, V!0))))) | (~distinct_points(X!3, intersection_point(U!1, V!0)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (~distinct_points(X!3, intersection_point(U!1, V!0))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[33, 18])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (convergent_lines(U!1, V!0)),
% 0.21/0.41 inference(and_elim,[status(thm)],[30])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.41 tff(41,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.21/0.41 tff(44,plain,(
% 0.21/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[43])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[48, 45, 35])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.41 tff(55,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')).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.21/0.41 tff(58,plain,(
% 0.21/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[57])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, V!0)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 ((distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(X!3, V!0))) <=> (apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, V!0)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(X!3, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, V!0))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(X!3, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, V!0)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[62, 60])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(X!3, V!0)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, V!0))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (~apart_point_and_line(X!3, V!0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[65, 59, 49, 34])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 ((~(incident_point_and_line(X!3, V!0) <=> (~apart_point_and_line(X!3, V!0)))) | incident_point_and_line(X!3, V!0) | apart_point_and_line(X!3, V!0)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 ((~(incident_point_and_line(X!3, V!0) <=> (~apart_point_and_line(X!3, V!0)))) | incident_point_and_line(X!3, V!0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (incident_point_and_line(X!3, V!0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[68, 9])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(X!3, U!1) <=> (~apart_point_and_line(X!3, U!1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (incident_point_and_line(X!3, U!1) <=> (~apart_point_and_line(X!3, U!1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[70, 7])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.41 tff(77,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.21/0.41 tff(80,plain,(
% 0.21/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[79])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (~apart_point_and_line(intersection_point(U!1, V!0), U!1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[84, 81, 35])).
% 0.21/0.42 tff(86,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)))) | (apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, U!1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 ((distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(X!3, U!1))) <=> (apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, U!1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(88,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(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(X!3, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, U!1))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[87])).
% 0.21/0.42 tff(89,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(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(X!3, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, U!1)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[88, 86])).
% 0.21/0.42 tff(90,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(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(X!3, U!1)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(91,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)))) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~apart_point_and_line(X!3, U!1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (~apart_point_and_line(X!3, U!1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[91, 59, 85, 34])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 ((~(incident_point_and_line(X!3, U!1) <=> (~apart_point_and_line(X!3, U!1)))) | incident_point_and_line(X!3, U!1) | apart_point_and_line(X!3, U!1)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 ((~(incident_point_and_line(X!3, U!1) <=> (~apart_point_and_line(X!3, U!1)))) | incident_point_and_line(X!3, U!1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (incident_point_and_line(X!3, U!1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[94, 71])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 ((~(~((~incident_point_and_line(X!3, U!1)) | (~incident_point_and_line(X!3, V!0))))) <=> ((~incident_point_and_line(X!3, U!1)) | (~incident_point_and_line(X!3, V!0)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 ((incident_point_and_line(X!3, U!1) & incident_point_and_line(X!3, V!0)) <=> (~((~incident_point_and_line(X!3, U!1)) | (~incident_point_and_line(X!3, V!0))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 ((~(incident_point_and_line(X!3, U!1) & incident_point_and_line(X!3, V!0))) <=> (~(~((~incident_point_and_line(X!3, U!1)) | (~incident_point_and_line(X!3, V!0)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((~(incident_point_and_line(X!3, U!1) & incident_point_and_line(X!3, V!0))) <=> ((~incident_point_and_line(X!3, U!1)) | (~incident_point_and_line(X!3, V!0)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[98, 96])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (~(incident_point_and_line(X!3, U!1) & incident_point_and_line(X!3, V!0))),
% 0.21/0.42 inference(or_elim,[status(thm)],[29])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 ((~incident_point_and_line(X!3, U!1)) | (~incident_point_and_line(X!3, V!0))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[101, 95, 69])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------