TSTP Solution File: GEO198+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO198+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 20:35:34 EDT 2022
% Result : Theorem 0.10s 0.42s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GEO198+3 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.06 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.06/0.25 % Computer : n009.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Wed Aug 31 06:49:35 EDT 2022
% 0.06/0.25 % CPUTime :
% 0.06/0.25 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.06/0.25 Usage: tptp [options] [-file:]file
% 0.06/0.25 -h, -? prints this message.
% 0.06/0.25 -smt2 print SMT-LIB2 benchmark.
% 0.06/0.25 -m, -model generate model.
% 0.06/0.25 -p, -proof generate proof.
% 0.06/0.25 -c, -core generate unsat core of named formulas.
% 0.06/0.25 -st, -statistics display statistics.
% 0.06/0.25 -t:timeout set timeout (in second).
% 0.06/0.25 -smt2status display status in smt2 format instead of SZS.
% 0.06/0.25 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.06/0.25 -<param>:<value> configuration parameter and value.
% 0.06/0.25 -o:<output-file> file to place output in.
% 0.10/0.42 % SZS status Theorem
% 0.10/0.42 % SZS output start Proof
% 0.10/0.42 tff(convergent_lines_type, type, (
% 0.10/0.42 convergent_lines: ( $i * $i ) > $o)).
% 0.10/0.42 tff(tptp_fun_X_2_type, type, (
% 0.10/0.42 tptp_fun_X_2: $i)).
% 0.10/0.42 tff(distinct_lines_type, type, (
% 0.10/0.42 distinct_lines: ( $i * $i ) > $o)).
% 0.10/0.42 tff(tptp_fun_Z_0_type, type, (
% 0.10/0.42 tptp_fun_Z_0: $i)).
% 0.10/0.42 tff(distinct_points_type, type, (
% 0.10/0.42 distinct_points: ( $i * $i ) > $o)).
% 0.10/0.42 tff(intersection_point_type, type, (
% 0.10/0.42 intersection_point: ( $i * $i ) > $i)).
% 0.10/0.42 tff(tptp_fun_Y_1_type, type, (
% 0.10/0.42 tptp_fun_Y_1: $i)).
% 0.10/0.42 tff(apart_point_and_line_type, type, (
% 0.10/0.42 apart_point_and_line: ( $i * $i ) > $o)).
% 0.10/0.42 tff(incident_point_and_line_type, type, (
% 0.10/0.42 incident_point_and_line: ( $i * $i ) > $o)).
% 0.10/0.42 tff(1,plain,
% 0.10/0.42 (^[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))))),
% 0.10/0.42 inference(bind,[status(th)],[])).
% 0.10/0.42 tff(2,plain,
% 0.10/0.42 (![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)))),
% 0.10/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.10/0.42 tff(3,plain,
% 0.10/0.42 (![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)))),
% 0.10/0.42 inference(rewrite,[status(thm)],[])).
% 0.10/0.42 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')).
% 0.10/0.42 tff(5,plain,
% 0.10/0.42 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.10/0.42 tff(6,plain,(
% 0.10/0.42 ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.10/0.42 inference(skolemize,[status(sab)],[5])).
% 0.10/0.42 tff(7,plain,
% 0.10/0.42 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.10/0.42 tff(8,plain,
% 0.10/0.42 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(X!2, Z!0), Y!1) <=> (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))),
% 0.10/0.42 inference(quant_inst,[status(thm)],[])).
% 0.10/0.42 tff(9,plain,
% 0.10/0.42 (incident_point_and_line(intersection_point(X!2, Z!0), Y!1) <=> (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1))),
% 0.10/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.10/0.42 tff(10,plain,
% 0.10/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(X, Z), Y))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(X, Z), Y)))),
% 0.10/0.42 inference(rewrite,[status(thm)],[])).
% 0.10/0.42 tff(11,plain,
% 0.10/0.42 ((~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & incident_point_and_line(intersection_point(X, Y), Z)) => incident_point_and_line(intersection_point(X, Z), Y))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(X, Z), Y)))),
% 0.10/0.42 inference(rewrite,[status(thm)],[])).
% 0.10/0.42 tff(12,axiom,(~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & incident_point_and_line(intersection_point(X, Y), Z)) => incident_point_and_line(intersection_point(X, Z), Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.10/0.42 tff(13,plain,
% 0.10/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(X, Z), Y))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.10/0.42 tff(14,plain,
% 0.10/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(X, Z), Y))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.10/0.42 tff(15,plain,
% 0.10/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(X, Z), Y))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.10/0.42 tff(16,plain,
% 0.10/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(X, Z), Y))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.10/0.42 tff(17,plain,
% 0.10/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(X, Z), Y))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.10/0.42 tff(18,plain,
% 0.10/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(X, Z), Y))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.10/0.42 tff(19,plain,
% 0.10/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(X, Z), Y))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.10/0.42 tff(20,plain,(
% 0.10/0.42 ~((~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & incident_point_and_line(intersection_point(X!2, Y!1), Z!0))) | incident_point_and_line(intersection_point(X!2, Z!0), Y!1))),
% 0.10/0.42 inference(skolemize,[status(sab)],[19])).
% 0.10/0.42 tff(21,plain,
% 0.10/0.42 (~incident_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.10/0.42 inference(or_elim,[status(thm)],[20])).
% 0.10/0.42 tff(22,plain,
% 0.10/0.42 ((~(incident_point_and_line(intersection_point(X!2, Z!0), Y!1) <=> (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))) | incident_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.10/0.42 inference(tautology,[status(thm)],[])).
% 0.10/0.42 tff(23,plain,
% 0.10/0.42 ((~(incident_point_and_line(intersection_point(X!2, Z!0), Y!1) <=> (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.10/0.42 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.10/0.42 tff(24,plain,
% 0.10/0.42 (apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.10/0.42 inference(unit_resolution,[status(thm)],[23, 9])).
% 0.10/0.42 tff(25,plain,
% 0.10/0.42 (convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & incident_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.10/0.42 inference(or_elim,[status(thm)],[20])).
% 0.10/0.42 tff(26,plain,
% 0.10/0.42 (convergent_lines(X!2, Y!1)),
% 0.10/0.42 inference(and_elim,[status(thm)],[25])).
% 0.10/0.42 tff(27,plain,
% 0.10/0.42 (^[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))))),
% 0.10/0.42 inference(bind,[status(th)],[])).
% 0.10/0.42 tff(28,plain,
% 0.10/0.42 (![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)))),
% 0.10/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.10/0.42 tff(29,plain,
% 0.10/0.42 (![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)))),
% 0.10/0.42 inference(rewrite,[status(thm)],[])).
% 0.10/0.42 tff(30,plain,
% 0.10/0.42 (^[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))))),
% 0.10/0.42 inference(bind,[status(th)],[])).
% 0.10/0.42 tff(31,plain,
% 0.10/0.42 (![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)))),
% 0.10/0.42 inference(quant_intro,[status(thm)],[30])).
% 0.10/0.42 tff(32,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.10/0.42 tff(33,plain,
% 0.10/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.10/0.42 tff(34,plain,
% 0.10/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.10/0.42 tff(35,plain,(
% 0.10/0.42 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.10/0.42 inference(skolemize,[status(sab)],[34])).
% 0.10/0.42 tff(36,plain,
% 0.10/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.10/0.42 tff(37,plain,
% 0.10/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.10/0.42 inference(rewrite,[status(thm)],[])).
% 0.10/0.42 tff(38,plain,
% 0.10/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.10/0.42 inference(quant_inst,[status(thm)],[])).
% 0.10/0.42 tff(39,plain,
% 0.10/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.10/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.10/0.42 tff(40,plain,
% 0.10/0.42 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.10/0.42 inference(unit_resolution,[status(thm)],[39, 36, 26])).
% 0.10/0.42 tff(41,plain,
% 0.10/0.42 (^[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))))),
% 0.10/0.42 inference(bind,[status(th)],[])).
% 0.10/0.42 tff(42,plain,
% 0.10/0.42 (![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)))),
% 0.10/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.10/0.42 tff(43,plain,
% 0.10/0.42 (![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)))),
% 0.10/0.42 inference(rewrite,[status(thm)],[])).
% 0.10/0.42 tff(44,plain,
% 0.10/0.42 (^[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)))))),
% 0.10/0.42 inference(bind,[status(th)],[])).
% 0.10/0.42 tff(45,plain,
% 0.10/0.42 (![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)))),
% 0.10/0.43 inference(quant_intro,[status(thm)],[44])).
% 0.10/0.43 tff(46,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/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.10/0.43 tff(47,plain,
% 0.10/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.10/0.43 tff(48,plain,
% 0.10/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.10/0.43 tff(49,plain,(
% 0.10/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.10/0.43 inference(skolemize,[status(sab)],[48])).
% 0.10/0.43 tff(50,plain,
% 0.10/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.10/0.43 tff(51,plain,
% 0.10/0.43 (((~![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(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(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)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(52,plain,
% 0.10/0.43 ((distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(53,plain,
% 0.10/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!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(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))),
% 0.10/0.43 inference(monotonicity,[status(thm)],[52])).
% 0.10/0.43 tff(54,plain,
% 0.10/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!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(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))),
% 0.10/0.43 inference(transitivity,[status(thm)],[53, 51])).
% 0.10/0.43 tff(55,plain,
% 0.10/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))),
% 0.10/0.43 inference(quant_inst,[status(thm)],[])).
% 0.10/0.43 tff(56,plain,
% 0.10/0.43 ((~![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(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.10/0.43 tff(57,plain,
% 0.10/0.43 (distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))),
% 0.10/0.43 inference(unit_resolution,[status(thm)],[56, 50, 40, 24])).
% 0.10/0.43 tff(58,plain,
% 0.10/0.43 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(X!2, Y!1), Z!0) <=> (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.10/0.43 inference(quant_inst,[status(thm)],[])).
% 0.10/0.43 tff(59,plain,
% 0.10/0.43 (incident_point_and_line(intersection_point(X!2, Y!1), Z!0) <=> (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))),
% 0.10/0.43 inference(unit_resolution,[status(thm)],[58, 7])).
% 0.10/0.43 tff(60,plain,
% 0.10/0.43 (incident_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.10/0.43 inference(and_elim,[status(thm)],[25])).
% 0.10/0.43 tff(61,plain,
% 0.10/0.43 ((~(incident_point_and_line(intersection_point(X!2, Y!1), Z!0) <=> (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) | (~incident_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))),
% 0.10/0.43 inference(tautology,[status(thm)],[])).
% 0.10/0.43 tff(62,plain,
% 0.10/0.43 ((~(incident_point_and_line(intersection_point(X!2, Y!1), Z!0) <=> (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))),
% 0.10/0.43 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.10/0.43 tff(63,plain,
% 0.10/0.43 (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.10/0.43 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.10/0.43 tff(64,plain,
% 0.10/0.43 (convergent_lines(X!2, Z!0)),
% 0.10/0.43 inference(and_elim,[status(thm)],[25])).
% 0.10/0.43 tff(65,plain,
% 0.10/0.43 (^[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))))),
% 0.10/0.43 inference(bind,[status(th)],[])).
% 0.10/0.43 tff(66,plain,
% 0.10/0.43 (![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)))),
% 0.10/0.43 inference(quant_intro,[status(thm)],[65])).
% 0.10/0.43 tff(67,plain,
% 0.10/0.43 (![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)))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(68,plain,
% 0.10/0.43 (^[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))))),
% 0.10/0.43 inference(bind,[status(th)],[])).
% 0.10/0.43 tff(69,plain,
% 0.10/0.43 (![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)))),
% 0.10/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.10/0.43 tff(70,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.10/0.43 tff(71,plain,
% 0.10/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.10/0.43 tff(72,plain,
% 0.10/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.10/0.43 tff(73,plain,(
% 0.10/0.43 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.10/0.43 inference(skolemize,[status(sab)],[72])).
% 0.10/0.43 tff(74,plain,
% 0.10/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.10/0.43 tff(75,plain,
% 0.10/0.43 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(76,plain,
% 0.10/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))),
% 0.10/0.43 inference(quant_inst,[status(thm)],[])).
% 0.10/0.43 tff(77,plain,
% 0.10/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.10/0.43 tff(78,plain,
% 0.10/0.43 (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)),
% 0.10/0.43 inference(unit_resolution,[status(thm)],[77, 74, 64])).
% 0.10/0.43 tff(79,plain,
% 0.10/0.43 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(80,plain,
% 0.10/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.10/0.43 inference(quant_inst,[status(thm)],[])).
% 0.10/0.43 tff(81,plain,
% 0.10/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.10/0.43 tff(82,plain,
% 0.10/0.43 (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)),
% 0.10/0.43 inference(unit_resolution,[status(thm)],[81, 36, 64])).
% 0.10/0.43 tff(83,plain,
% 0.10/0.43 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(84,plain,
% 0.10/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.10/0.43 inference(quant_inst,[status(thm)],[])).
% 0.10/0.43 tff(85,plain,
% 0.10/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.10/0.43 tff(86,plain,
% 0.10/0.43 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.10/0.43 inference(unit_resolution,[status(thm)],[85, 74, 26])).
% 0.10/0.43 tff(87,plain,
% 0.10/0.43 (^[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))))),
% 0.10/0.43 inference(bind,[status(th)],[])).
% 0.10/0.43 tff(88,plain,
% 0.10/0.43 (![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)))),
% 0.10/0.43 inference(quant_intro,[status(thm)],[87])).
% 0.10/0.43 tff(89,plain,
% 0.10/0.43 (^[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)))))),
% 0.10/0.43 inference(bind,[status(th)],[])).
% 0.10/0.43 tff(90,plain,
% 0.10/0.43 (![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)))),
% 0.10/0.43 inference(quant_intro,[status(thm)],[89])).
% 0.10/0.43 tff(91,plain,
% 0.10/0.43 (![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))))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(92,plain,
% 0.10/0.43 (^[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))))))),
% 0.10/0.43 inference(bind,[status(th)],[])).
% 0.10/0.43 tff(93,plain,
% 0.10/0.43 (![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))))),
% 0.10/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.10/0.43 tff(94,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')).
% 0.10/0.43 tff(95,plain,
% 0.10/0.43 (![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))))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.10/0.43 tff(96,plain,
% 0.10/0.43 (![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))))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.10/0.43 tff(97,plain,(
% 0.10/0.43 ![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))))),
% 0.10/0.43 inference(skolemize,[status(sab)],[96])).
% 0.10/0.43 tff(98,plain,
% 0.10/0.43 (![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)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.10/0.43 tff(99,plain,
% 0.10/0.43 (![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)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.10/0.43 tff(100,plain,
% 0.10/0.43 (((~![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(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, X!2)) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(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(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, X!2)) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(101,plain,
% 0.10/0.43 ((apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~distinct_lines(Z!0, X!2)) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, X!2)) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(102,plain,
% 0.10/0.43 (((~![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(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~distinct_lines(Z!0, X!2)) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(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(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, X!2)) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))),
% 0.10/0.43 inference(monotonicity,[status(thm)],[101])).
% 0.10/0.43 tff(103,plain,
% 0.10/0.43 (((~![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(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~distinct_lines(Z!0, X!2)) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(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(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, X!2)) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))),
% 0.10/0.43 inference(transitivity,[status(thm)],[102, 100])).
% 0.10/0.43 tff(104,plain,
% 0.10/0.43 ((~![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(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~distinct_lines(Z!0, X!2)) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))),
% 0.10/0.43 inference(quant_inst,[status(thm)],[])).
% 0.10/0.43 tff(105,plain,
% 0.10/0.43 ((~![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(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, X!2)) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.10/0.43 tff(106,plain,
% 0.10/0.43 ((~distinct_lines(Z!0, X!2)) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))),
% 0.10/0.43 inference(unit_resolution,[status(thm)],[105, 99, 86, 82, 78, 63])).
% 0.10/0.43 tff(107,plain,
% 0.10/0.43 (~distinct_lines(Z!0, X!2)),
% 0.10/0.43 inference(unit_resolution,[status(thm)],[106, 57])).
% 0.10/0.43 tff(108,plain,
% 0.10/0.43 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.10/0.43 inference(bind,[status(th)],[])).
% 0.10/0.43 tff(109,plain,
% 0.10/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.43 inference(quant_intro,[status(thm)],[108])).
% 0.10/0.43 tff(110,plain,
% 0.10/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.43 inference(rewrite,[status(thm)],[])).
% 0.10/0.43 tff(111,plain,
% 0.10/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.10/0.43 inference(bind,[status(th)],[])).
% 0.10/0.43 tff(112,plain,
% 0.10/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.43 inference(quant_intro,[status(thm)],[111])).
% 0.10/0.43 tff(113,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.10/0.43 tff(114,plain,
% 0.10/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.10/0.43 tff(115,plain,
% 0.10/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.10/0.43 tff(116,plain,(
% 0.10/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.43 inference(skolemize,[status(sab)],[115])).
% 0.10/0.43 tff(117,plain,
% 0.10/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.10/0.43 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.10/0.43 tff(118,plain,
% 0.10/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Z!0)) | distinct_lines(Z!0, X!2) | convergent_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Z!0)) | distinct_lines(Z!0, X!2) | convergent_lines(X!2, X!2))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(119,plain,
% 0.10/0.44 ((distinct_lines(Z!0, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Z!0))) <=> ((~convergent_lines(X!2, Z!0)) | distinct_lines(Z!0, X!2) | convergent_lines(X!2, X!2))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(120,plain,
% 0.10/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Z!0, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Z!0)) | distinct_lines(Z!0, X!2) | convergent_lines(X!2, X!2)))),
% 0.10/0.44 inference(monotonicity,[status(thm)],[119])).
% 0.10/0.44 tff(121,plain,
% 0.10/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Z!0, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Z!0)) | distinct_lines(Z!0, X!2) | convergent_lines(X!2, X!2))),
% 0.10/0.44 inference(transitivity,[status(thm)],[120, 118])).
% 0.10/0.44 tff(122,plain,
% 0.10/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Z!0, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Z!0)))),
% 0.10/0.44 inference(quant_inst,[status(thm)],[])).
% 0.10/0.44 tff(123,plain,
% 0.10/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Z!0)) | distinct_lines(Z!0, X!2) | convergent_lines(X!2, X!2)),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.10/0.44 tff(124,plain,
% 0.10/0.44 (convergent_lines(X!2, X!2)),
% 0.10/0.44 inference(unit_resolution,[status(thm)],[123, 117, 64, 107])).
% 0.10/0.44 tff(125,plain,
% 0.10/0.44 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.10/0.44 inference(bind,[status(th)],[])).
% 0.10/0.44 tff(126,plain,
% 0.10/0.44 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.10/0.44 inference(quant_intro,[status(thm)],[125])).
% 0.10/0.44 tff(127,plain,
% 0.10/0.44 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.10/0.44 inference(rewrite,[status(thm)],[])).
% 0.10/0.44 tff(128,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.10/0.44 tff(129,plain,
% 0.10/0.44 (![X: $i] : (~convergent_lines(X, X))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.10/0.44 tff(130,plain,(
% 0.10/0.44 ![X: $i] : (~convergent_lines(X, X))),
% 0.10/0.44 inference(skolemize,[status(sab)],[129])).
% 0.10/0.44 tff(131,plain,
% 0.10/0.44 (![X: $i] : (~convergent_lines(X, X))),
% 0.10/0.44 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.10/0.44 tff(132,plain,
% 0.10/0.44 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!2, X!2))),
% 0.10/0.44 inference(quant_inst,[status(thm)],[])).
% 0.10/0.44 tff(133,plain,
% 0.10/0.44 ($false),
% 0.10/0.44 inference(unit_resolution,[status(thm)],[132, 131, 124])).
% 0.10/0.44 % SZS output end Proof
%------------------------------------------------------------------------------