TSTP Solution File: GEO199+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO199+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO199+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 06:50:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(distinct_points_type, type, (
% 0.20/0.46 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.46 tff(intersection_point_type, type, (
% 0.20/0.46 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.46 tptp_fun_Y_1: $i)).
% 0.20/0.46 tff(tptp_fun_X_2_type, type, (
% 0.20/0.46 tptp_fun_X_2: $i)).
% 0.20/0.46 tff(apart_point_and_line_type, type, (
% 0.20/0.46 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.46 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.46 tptp_fun_Z_0: $i)).
% 0.20/0.46 tff(incident_point_and_line_type, type, (
% 0.20/0.46 incident_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.46 tff(convergent_lines_type, type, (
% 0.20/0.46 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.46 tff(distinct_lines_type, type, (
% 0.20/0.46 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.46 tff(parallel_through_point_type, type, (
% 0.20/0.46 parallel_through_point: ( $i * $i ) > $i)).
% 0.20/0.46 tff(unorthogonal_lines_type, type, (
% 0.20/0.46 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.46 tff(orthogonal_through_point_type, type, (
% 0.20/0.46 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 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')).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.46 tff(6,plain,(
% 0.20/0.46 ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[5])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(Y!1, X!2), Z!0) <=> (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (incident_point_and_line(intersection_point(Y!1, X!2), Z!0) <=> (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 ((~![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(Y, X), Z))) <=> (~![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(Y, X), Z)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 ((~![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(Y, X), Z))) <=> (~![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(Y, X), Z)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 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(Y, X), Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (~![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(Y, X), Z))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (~![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(Y, X), Z))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (~![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(Y, X), Z))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (~![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(Y, X), Z))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (~![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(Y, X), Z))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (~![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(Y, X), Z))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (~![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(Y, X), Z))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.20/0.46 tff(20,plain,(
% 0.20/0.46 ~((~(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(Y!1, X!2), Z!0))),
% 0.20/0.46 inference(skolemize,[status(sab)],[19])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (~incident_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.20/0.46 inference(or_elim,[status(thm)],[20])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 ((~(incident_point_and_line(intersection_point(Y!1, X!2), Z!0) <=> (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)))) | incident_point_and_line(intersection_point(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 ((~(incident_point_and_line(intersection_point(Y!1, X!2), Z!0) <=> (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)))) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (apart_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[23, 9])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 ((~![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)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 (incident_point_and_line(intersection_point(X!2, Y!1), Z!0) <=> (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[25, 7])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (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)),
% 0.20/0.46 inference(or_elim,[status(thm)],[20])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (incident_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.20/0.46 inference(and_elim,[status(thm)],[27])).
% 0.20/0.46 tff(29,plain,
% 0.20/0.46 ((~(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))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 ((~(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))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[30, 26])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(33,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(35,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(36,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.46 tff(37,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')).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.46 tff(40,plain,(
% 0.20/0.46 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[39])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 (((~![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), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | distinct_points(intersection_point(Y!1, X!2), 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), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 ((distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (((~![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(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!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(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (((~![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(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!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(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 ((~![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(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 ((~![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), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 (distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[47, 41, 31, 24])).
% 0.20/0.46 tff(49,assumption,(convergent_lines(X!2, X!2)), introduced(assumption)).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(53,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.46 tff(55,plain,(
% 0.20/0.46 ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(skolemize,[status(sab)],[54])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!2, X!2))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[57, 56, 49])).
% 0.20/0.46 tff(59,plain,(~convergent_lines(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(60,assumption,(~distinct_lines(Y!1, X!2)), introduced(assumption)).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (convergent_lines(X!2, Y!1)),
% 0.20/0.47 inference(and_elim,[status(thm)],[27])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.47 tff(67,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')).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.20/0.47 tff(70,plain,(
% 0.20/0.47 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[69])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, 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, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 ((distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[73])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.47 inference(transitivity,[status(thm)],[74, 72])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[77, 71, 61, 60, 59])).
% 0.20/0.47 tff(79,plain,(distinct_lines(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.47 tff(85,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.47 tff(88,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.47 inference(skolemize,[status(sab)],[87])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(Y!1, X!2)) | convergent_lines(Y!1, X!2))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(Y!1, X!2)) | convergent_lines(Y!1, X!2))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(Y!1, X!2)) | convergent_lines(Y!1, X!2))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(Y!1, X!2)) | convergent_lines(Y!1, X!2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (convergent_lines(Y!1, X!2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[92, 89, 79])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.47 tff(99,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')).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.47 tff(102,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[101])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[107, 93])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(112,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.47 tff(114,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.20/0.47 inference(skolemize,[status(sab)],[113])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (~convergent_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1)) | convergent_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1)) | convergent_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1)) | convergent_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1)) | convergent_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (~distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[120, 89, 117])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(125,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.47 tff(127,plain,(
% 0.20/0.47 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.47 inference(skolemize,[status(sab)],[126])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 (~unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (^[L: $i, M: $i, N: $i] : refl((unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.47 tff(138,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.20/0.47 tff(141,plain,(
% 0.20/0.47 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[140])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | ((~convergent_lines(Y!1, Y!1)) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(Y!1, Y!1)) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 ((unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~convergent_lines(Y!1, Y!1))) <=> ((~convergent_lines(Y!1, Y!1)) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~convergent_lines(Y!1, Y!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | ((~convergent_lines(Y!1, Y!1)) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[145])).
% 0.20/0.48 tff(147,plain,
% 0.20/0.48 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~convergent_lines(Y!1, Y!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(Y!1, Y!1)) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1))),
% 0.20/0.48 inference(transitivity,[status(thm)],[146, 144])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~convergent_lines(Y!1, Y!1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (~convergent_lines(Y!1, Y!1)) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 (~convergent_lines(Y!1, Y!1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[149, 143, 130])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Y!1, Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 ((distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))))) <=> (convergent_lines(Y!1, Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[152])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Y!1, Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[153, 151])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Y!1, Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (~convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[156, 71, 150, 121])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 ((~![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)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 ((~![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))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[160, 103, 61])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 (^[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))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 (^[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)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.48 tff(167,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')).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.20/0.48 tff(170,plain,(
% 0.20/0.48 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[169])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 (((~![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(intersection_point(X!2, Y!1), Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))) <=> ((~![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(intersection_point(X!2, Y!1), Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 ((distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))) <=> ((~![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(intersection_point(X!2, Y!1), Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))) <=> ((~![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(intersection_point(X!2, Y!1), Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[174, 172])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 ((~![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(intersection_point(X!2, Y!1), Y!1) | distinct_lines(parallel_through_point(Y!1, intersection_point(Y!1, X!2)), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[177, 171, 161, 121])).
% 0.20/0.49 tff(179,plain,
% 0.20/0.49 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(180,plain,
% 0.20/0.49 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[179])).
% 0.20/0.49 tff(181,plain,
% 0.20/0.49 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(182,plain,
% 0.20/0.49 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) <=> (apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> ((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)))), rewrite(((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))))), rewrite((distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(183,plain,
% 0.20/0.49 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[182])).
% 0.20/0.49 tff(184,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.20/0.49 tff(187,plain,(
% 0.20/0.49 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[186])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | (~distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | (~distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 ((convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | (~distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | (~distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[190])).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | (~distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[191, 189])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | convergent_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | (~distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 (~distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[194, 188, 161, 178, 157])).
% 0.20/0.49 tff(196,plain,
% 0.20/0.49 (^[X: $i, Y: $i] : refl((~apart_point_and_line(X, parallel_through_point(Y, X))) <=> (~apart_point_and_line(X, parallel_through_point(Y, X))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[196])).
% 0.20/0.49 tff(198,plain,
% 0.20/0.49 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(199,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.20/0.49 tff(200,plain,
% 0.20/0.49 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.20/0.49 tff(201,plain,(
% 0.20/0.49 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[200])).
% 0.20/0.49 tff(202,plain,
% 0.20/0.49 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.20/0.49 tff(203,plain,
% 0.20/0.49 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(204,plain,
% 0.20/0.49 (~apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.20/0.49 tff(205,plain,
% 0.20/0.49 (((~![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(intersection_point(Y!1, X!2), Y!1)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))))) <=> ((~![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(intersection_point(Y!1, X!2), Y!1)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(206,plain,
% 0.20/0.49 ((distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1))) <=> ((~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(207,plain,
% 0.20/0.49 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | (~apart_point_and_line(intersection_point(Y!1, 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(intersection_point(Y!1, X!2), Y!1)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[206])).
% 0.20/0.49 tff(208,plain,
% 0.20/0.49 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | (~apart_point_and_line(intersection_point(Y!1, 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(intersection_point(Y!1, X!2), Y!1)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[207, 205])).
% 0.20/0.49 tff(209,plain,
% 0.20/0.49 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(210,plain,
% 0.20/0.49 ((~![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(intersection_point(Y!1, X!2), Y!1)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Y!1, intersection_point(Y!1, X!2))) | distinct_lines(Y!1, parallel_through_point(Y!1, intersection_point(Y!1, X!2)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.20/0.49 tff(211,plain,
% 0.20/0.49 (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[210, 171, 204, 195])).
% 0.20/0.49 tff(212,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(213,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[212])).
% 0.20/0.49 tff(214,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(215,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(216,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[215])).
% 0.20/0.49 tff(217,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')).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.20/0.49 tff(220,plain,(
% 0.20/0.49 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[219])).
% 0.20/0.49 tff(221,plain,
% 0.20/0.49 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 ((~![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)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 ((~![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))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[224, 221, 61])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[226])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 (^[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)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[228])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 (![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))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 (^[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))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(232,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[231])).
% 0.20/0.50 tff(233,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')).
% 0.20/0.50 tff(234,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.20/0.50 tff(235,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.20/0.50 tff(236,plain,(
% 0.20/0.50 ![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))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[235])).
% 0.20/0.50 tff(237,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[236, 229])).
% 0.20/0.50 tff(238,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[237, 227])).
% 0.20/0.50 tff(239,plain,
% 0.20/0.50 (((~![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), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), 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), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(240,plain,
% 0.20/0.50 ((apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), 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, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(241,plain,
% 0.20/0.50 (((~![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), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), 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), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[240])).
% 0.20/0.50 tff(242,plain,
% 0.20/0.50 (((~![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), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), 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), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[241, 239])).
% 0.20/0.50 tff(243,plain,
% 0.20/0.50 ((~![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), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(244,plain,
% 0.20/0.50 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.20/0.50 tff(245,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[244, 238, 161, 225, 211, 108, 79, 48])).
% 0.20/0.50 % SZS output end Proof
%------------------------------------------------------------------------------