TSTP Solution File: GEO194+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO194+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 20:35:30 EDT 2022
% Result : Theorem 0.98s 0.85s
% Output : Proof 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO194+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:51:09 EDT 2022
% 0.13/0.34 % 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.
% 0.98/0.85 % SZS status Theorem
% 0.98/0.85 % SZS output start Proof
% 0.98/0.85 tff(convergent_lines_type, type, (
% 0.98/0.85 convergent_lines: ( $i * $i ) > $o)).
% 0.98/0.85 tff(tptp_fun_X_2_type, type, (
% 0.98/0.85 tptp_fun_X_2: $i)).
% 0.98/0.85 tff(line_connecting_type, type, (
% 0.98/0.85 line_connecting: ( $i * $i ) > $i)).
% 0.98/0.85 tff(intersection_point_type, type, (
% 0.98/0.85 intersection_point: ( $i * $i ) > $i)).
% 0.98/0.85 tff(tptp_fun_Z_0_type, type, (
% 0.98/0.85 tptp_fun_Z_0: $i)).
% 0.98/0.85 tff(tptp_fun_Y_1_type, type, (
% 0.98/0.85 tptp_fun_Y_1: $i)).
% 0.98/0.85 tff(distinct_lines_type, type, (
% 0.98/0.85 distinct_lines: ( $i * $i ) > $o)).
% 0.98/0.85 tff(apart_point_and_line_type, type, (
% 0.98/0.85 apart_point_and_line: ( $i * $i ) > $o)).
% 0.98/0.85 tff(distinct_points_type, type, (
% 0.98/0.85 distinct_points: ( $i * $i ) > $o)).
% 0.98/0.85 tff(1,assumption,(convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))), introduced(assumption)).
% 0.98/0.85 tff(2,plain,
% 0.98/0.85 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(3,plain,
% 0.98/0.85 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[2])).
% 0.98/0.85 tff(4,plain,
% 0.98/0.85 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.98/0.85 tff(6,plain,
% 0.98/0.85 (![X: $i] : (~convergent_lines(X, X))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.98/0.85 tff(7,plain,(
% 0.98/0.85 ![X: $i] : (~convergent_lines(X, X))),
% 0.98/0.85 inference(skolemize,[status(sab)],[6])).
% 0.98/0.85 tff(8,plain,
% 0.98/0.85 (![X: $i] : (~convergent_lines(X, X))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.98/0.85 tff(9,plain,
% 0.98/0.85 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(10,plain,
% 0.98/0.85 ($false),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.98/0.85 tff(11,plain,(~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))), inference(lemma,lemma(discharge,[]))).
% 0.98/0.85 tff(12,assumption,(~convergent_lines(Z!0, X!2)), introduced(assumption)).
% 0.98/0.85 tff(13,plain,
% 0.98/0.85 ((~(apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))) <=> (~(apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0)))))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(14,plain,
% 0.98/0.85 ((~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(15,plain,
% 0.98/0.85 ((~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) => (apart_point_and_line(intersection_point(X, Y), Z) => apart_point_and_line(intersection_point(X, Z), Y)))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(16,axiom,(~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) => (apart_point_and_line(intersection_point(X, Y), Z) => apart_point_and_line(intersection_point(X, Z), Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.98/0.85 tff(17,plain,
% 0.98/0.85 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.98/0.85 tff(18,plain,
% 0.98/0.85 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.98/0.85 tff(19,plain,
% 0.98/0.85 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.98/0.85 tff(20,plain,
% 0.98/0.85 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.98/0.85 tff(21,plain,
% 0.98/0.85 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.98/0.85 tff(22,plain,
% 0.98/0.85 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.98/0.85 tff(23,plain,
% 0.98/0.85 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.98/0.85 tff(24,plain,(
% 0.98/0.85 ~(apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))),
% 0.98/0.85 inference(skolemize,[status(sab)],[23])).
% 0.98/0.85 tff(25,plain,
% 0.98/0.85 (~(apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[24, 13])).
% 0.98/0.85 tff(26,plain,
% 0.98/0.85 (convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0)),
% 0.98/0.85 inference(or_elim,[status(thm)],[25])).
% 0.98/0.85 tff(27,plain,
% 0.98/0.85 (convergent_lines(X!2, Z!0)),
% 0.98/0.85 inference(and_elim,[status(thm)],[26])).
% 0.98/0.85 tff(28,plain,
% 0.98/0.85 (^[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))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(29,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[28])).
% 0.98/0.85 tff(30,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(31,plain,
% 0.98/0.85 (^[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))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(32,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[31])).
% 0.98/0.85 tff(33,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.98/0.85 tff(34,plain,
% 0.98/0.85 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.98/0.85 tff(35,plain,
% 0.98/0.85 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.98/0.85 tff(36,plain,(
% 0.98/0.85 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.98/0.85 inference(skolemize,[status(sab)],[35])).
% 0.98/0.85 tff(37,plain,
% 0.98/0.85 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.98/0.85 tff(38,plain,
% 0.98/0.85 (((~![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)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(39,plain,
% 0.98/0.85 ((~![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)))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(40,plain,
% 0.98/0.85 ((~![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))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.98/0.85 tff(41,plain,
% 0.98/0.85 (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 0.98/0.85 tff(42,plain,
% 0.98/0.85 (apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.98/0.85 inference(or_elim,[status(thm)],[25])).
% 0.98/0.85 tff(43,plain,
% 0.98/0.85 (^[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))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(44,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[43])).
% 0.98/0.85 tff(45,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(46,plain,
% 0.98/0.85 (^[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)))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(47,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[46])).
% 0.98/0.85 tff(48,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.98/0.85 tff(49,plain,
% 0.98/0.85 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.98/0.85 tff(50,plain,
% 0.98/0.85 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.98/0.85 tff(51,plain,(
% 0.98/0.85 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.98/0.85 inference(skolemize,[status(sab)],[50])).
% 0.98/0.85 tff(52,plain,
% 0.98/0.85 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.98/0.85 tff(53,plain,
% 0.98/0.85 (((~![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(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(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(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(54,plain,
% 0.98/0.85 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), 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)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(55,plain,
% 0.98/0.85 (((~![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, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), 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(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.98/0.85 inference(monotonicity,[status(thm)],[54])).
% 0.98/0.85 tff(56,plain,
% 0.98/0.85 (((~![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, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), 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(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.98/0.85 inference(transitivity,[status(thm)],[55, 53])).
% 0.98/0.85 tff(57,plain,
% 0.98/0.85 ((~![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, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(58,plain,
% 0.98/0.85 ((~![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(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.98/0.85 tff(59,plain,
% 0.98/0.85 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[58, 52, 42, 41])).
% 0.98/0.85 tff(60,plain,
% 0.98/0.85 (^[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))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(61,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[60])).
% 0.98/0.85 tff(62,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(63,plain,
% 0.98/0.85 (^[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))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(64,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[63])).
% 0.98/0.85 tff(65,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.98/0.85 tff(66,plain,
% 0.98/0.85 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.98/0.85 tff(67,plain,
% 0.98/0.85 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.98/0.85 tff(68,plain,(
% 0.98/0.85 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.98/0.85 inference(skolemize,[status(sab)],[67])).
% 0.98/0.85 tff(69,plain,
% 0.98/0.85 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.98/0.85 tff(70,plain,
% 0.98/0.85 (((~![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)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(71,plain,
% 0.98/0.85 ((~![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)))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(72,plain,
% 0.98/0.85 ((~![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))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.98/0.85 tff(73,plain,
% 0.98/0.85 (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[72, 69, 27])).
% 0.98/0.85 tff(74,plain,
% 0.98/0.85 (convergent_lines(X!2, Y!1)),
% 0.98/0.85 inference(and_elim,[status(thm)],[26])).
% 0.98/0.85 tff(75,plain,
% 0.98/0.85 (((~![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)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(76,plain,
% 0.98/0.85 ((~![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)))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(77,plain,
% 0.98/0.85 ((~![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))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.98/0.85 tff(78,plain,
% 0.98/0.85 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[77, 69, 74])).
% 0.98/0.85 tff(79,plain,
% 0.98/0.85 (((~![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)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(80,plain,
% 0.98/0.85 ((~![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)))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(81,plain,
% 0.98/0.85 ((~![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))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.98/0.85 tff(82,plain,
% 0.98/0.85 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[81, 37, 74])).
% 0.98/0.85 tff(83,plain,
% 0.98/0.85 (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.98/0.85 inference(or_elim,[status(thm)],[25])).
% 0.98/0.85 tff(84,plain,
% 0.98/0.85 (^[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_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_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(85,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[84])).
% 0.98/0.85 tff(86,plain,
% 0.98/0.85 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, 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) | (~(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_points(X, Y)) | (~distinct_lines(U, V)))))), 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_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_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_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_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(87,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[86])).
% 0.98/0.85 tff(88,plain,
% 0.98/0.85 (![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))))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(89,plain,
% 0.98/0.85 (^[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))))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(90,plain,
% 0.98/0.85 (![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))))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[89])).
% 0.98/0.85 tff(91,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/sandbox/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.98/0.85 tff(92,plain,
% 0.98/0.85 (![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))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.98/0.85 tff(93,plain,
% 0.98/0.85 (![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))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.98/0.85 tff(94,plain,(
% 0.98/0.85 ![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))))),
% 0.98/0.85 inference(skolemize,[status(sab)],[93])).
% 0.98/0.85 tff(95,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.98/0.85 tff(96,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.98/0.85 tff(97,plain,
% 0.98/0.85 (((~![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)))) | (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, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2)))) <=> ((~![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)))) | 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, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(98,plain,
% 0.98/0.85 ((apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2))) <=> (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, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(99,plain,
% 0.98/0.85 (((~![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)))) | (apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2)))) <=> ((~![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)))) | (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, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2))))),
% 0.98/0.85 inference(monotonicity,[status(thm)],[98])).
% 0.98/0.85 tff(100,plain,
% 0.98/0.85 (((~![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)))) | (apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2)))) <=> ((~![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)))) | 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, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2)))),
% 0.98/0.85 inference(transitivity,[status(thm)],[99, 97])).
% 0.98/0.85 tff(101,plain,
% 0.98/0.85 ((~![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)))) | (apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2)))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(102,plain,
% 0.98/0.85 ((~![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)))) | 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, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.98/0.85 tff(103,plain,
% 0.98/0.85 ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[102, 96, 83, 82, 78, 73])).
% 0.98/0.85 tff(104,plain,
% 0.98/0.85 (~distinct_lines(Y!1, X!2)),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[103, 59])).
% 0.98/0.85 tff(105,plain,
% 0.98/0.85 (convergent_lines(Z!0, Y!1)),
% 0.98/0.85 inference(and_elim,[status(thm)],[26])).
% 0.98/0.85 tff(106,plain,
% 0.98/0.85 (^[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))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(107,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[106])).
% 0.98/0.85 tff(108,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(109,plain,
% 0.98/0.85 (^[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)))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(110,plain,
% 0.98/0.85 (![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)))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[109])).
% 0.98/0.85 tff(111,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.98/0.85 tff(112,plain,
% 0.98/0.85 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.98/0.85 tff(113,plain,
% 0.98/0.85 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.98/0.85 tff(114,plain,(
% 0.98/0.85 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.98/0.85 inference(skolemize,[status(sab)],[113])).
% 0.98/0.85 tff(115,plain,
% 0.98/0.85 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.98/0.85 tff(116,plain,
% 0.98/0.85 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(Z!0, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(Z!0, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(Z!0, X!2))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(117,plain,
% 0.98/0.85 ((distinct_lines(Y!1, X!2) | convergent_lines(Z!0, X!2) | (~convergent_lines(Z!0, Y!1))) <=> ((~convergent_lines(Z!0, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(Z!0, X!2))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(118,plain,
% 0.98/0.85 (((~![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(Z!0, X!2) | (~convergent_lines(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(Z!0, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(Z!0, X!2)))),
% 0.98/0.85 inference(monotonicity,[status(thm)],[117])).
% 0.98/0.85 tff(119,plain,
% 0.98/0.85 (((~![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(Z!0, X!2) | (~convergent_lines(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(Z!0, X!2))),
% 0.98/0.86 inference(transitivity,[status(thm)],[118, 116])).
% 0.98/0.86 tff(120,plain,
% 0.98/0.86 ((~![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(Z!0, X!2) | (~convergent_lines(Z!0, Y!1)))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(121,plain,
% 0.98/0.86 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(Z!0, X!2)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.98/0.86 tff(122,plain,
% 0.98/0.86 ($false),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[121, 115, 105, 104, 12])).
% 0.98/0.86 tff(123,plain,(convergent_lines(Z!0, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.86 tff(124,plain,
% 0.98/0.86 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, X!2)) | (~apart_point_and_line(intersection_point(Z!0, X!2), Z!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, X!2)) | (~apart_point_and_line(intersection_point(Z!0, X!2), Z!0)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(125,plain,
% 0.98/0.86 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, X!2)) | (~apart_point_and_line(intersection_point(Z!0, X!2), Z!0)))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(126,plain,
% 0.98/0.86 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, X!2)) | (~apart_point_and_line(intersection_point(Z!0, X!2), Z!0))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.98/0.86 tff(127,plain,
% 0.98/0.86 (~apart_point_and_line(intersection_point(Z!0, X!2), Z!0)),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[126, 69, 123])).
% 0.98/0.86 tff(128,plain,
% 0.98/0.86 (((~![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(Z!0, X!2), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) <=> ((~![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(Z!0, X!2), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(129,plain,
% 0.98/0.86 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)) | apart_point_and_line(intersection_point(Z!0, X!2), 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)) | apart_point_and_line(intersection_point(Z!0, X!2), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(130,plain,
% 0.98/0.86 (((~![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, Y!1), intersection_point(Z!0, X!2)) | apart_point_and_line(intersection_point(Z!0, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), 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(Z!0, X!2), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(monotonicity,[status(thm)],[129])).
% 0.98/0.86 tff(131,plain,
% 0.98/0.86 (((~![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, Y!1), intersection_point(Z!0, X!2)) | apart_point_and_line(intersection_point(Z!0, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), 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(Z!0, X!2), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.86 inference(transitivity,[status(thm)],[130, 128])).
% 0.98/0.86 tff(132,plain,
% 0.98/0.86 ((~![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, Y!1), intersection_point(Z!0, X!2)) | apart_point_and_line(intersection_point(Z!0, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(133,plain,
% 0.98/0.86 ((~![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(Z!0, X!2), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.98/0.86 tff(134,plain,
% 0.98/0.86 (apart_point_and_line(intersection_point(Z!0, X!2), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[133, 52, 42])).
% 0.98/0.86 tff(135,plain,
% 0.98/0.86 (distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[134, 127])).
% 0.98/0.86 tff(136,plain,
% 0.98/0.86 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(137,plain,
% 0.98/0.86 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[136])).
% 0.98/0.86 tff(138,plain,
% 0.98/0.86 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(139,plain,
% 0.98/0.86 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(140,plain,
% 0.98/0.86 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[139])).
% 0.98/0.86 tff(141,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.98/0.86 tff(142,plain,
% 0.98/0.86 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.98/0.86 tff(143,plain,
% 0.98/0.86 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.98/0.86 tff(144,plain,(
% 0.98/0.86 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.98/0.86 inference(skolemize,[status(sab)],[143])).
% 0.98/0.86 tff(145,plain,
% 0.98/0.86 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.98/0.86 tff(146,plain,
% 0.98/0.86 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(147,plain,
% 0.98/0.86 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(148,plain,
% 0.98/0.86 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.98/0.86 tff(149,plain,
% 0.98/0.86 (~apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[148, 145, 135])).
% 0.98/0.86 tff(150,plain,
% 0.98/0.86 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Z!0, X!2)) | (~apart_point_and_line(intersection_point(Z!0, X!2), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Z!0, X!2)) | (~apart_point_and_line(intersection_point(Z!0, X!2), X!2)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(151,plain,
% 0.98/0.86 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Z!0, X!2)) | (~apart_point_and_line(intersection_point(Z!0, X!2), X!2)))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(152,plain,
% 0.98/0.86 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Z!0, X!2)) | (~apart_point_and_line(intersection_point(Z!0, X!2), X!2))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.98/0.86 tff(153,plain,
% 0.98/0.86 (~apart_point_and_line(intersection_point(Z!0, X!2), X!2)),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[152, 37, 123])).
% 0.98/0.86 tff(154,plain,
% 0.98/0.86 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(155,plain,
% 0.98/0.86 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[154])).
% 0.98/0.86 tff(156,plain,
% 0.98/0.86 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(157,plain,
% 0.98/0.86 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(158,plain,
% 0.98/0.86 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[157])).
% 0.98/0.86 tff(159,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.98/0.86 tff(160,plain,
% 0.98/0.86 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.98/0.86 tff(161,plain,
% 0.98/0.86 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.98/0.86 tff(162,plain,(
% 0.98/0.86 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.98/0.86 inference(skolemize,[status(sab)],[161])).
% 0.98/0.86 tff(163,plain,
% 0.98/0.86 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.98/0.86 tff(164,plain,
% 0.98/0.86 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(165,plain,
% 0.98/0.86 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(166,plain,
% 0.98/0.86 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.98/0.86 tff(167,plain,
% 0.98/0.86 (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[166, 163, 135])).
% 0.98/0.86 tff(168,assumption,(distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), introduced(assumption)).
% 0.98/0.86 tff(169,plain,
% 0.98/0.86 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(170,plain,
% 0.98/0.86 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[169])).
% 0.98/0.86 tff(171,plain,
% 0.98/0.86 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(172,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart1')).
% 0.98/0.86 tff(173,plain,
% 0.98/0.86 (![X: $i] : (~distinct_points(X, X))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.98/0.86 tff(174,plain,(
% 0.98/0.86 ![X: $i] : (~distinct_points(X, X))),
% 0.98/0.86 inference(skolemize,[status(sab)],[173])).
% 0.98/0.86 tff(175,plain,
% 0.98/0.86 (![X: $i] : (~distinct_points(X, X))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.98/0.86 tff(176,plain,
% 0.98/0.86 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(177,plain,
% 0.98/0.86 ($false),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[176, 175, 168])).
% 0.98/0.86 tff(178,plain,(~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.98/0.86 tff(179,plain,
% 0.98/0.86 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(180,plain,
% 0.98/0.86 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[179])).
% 0.98/0.86 tff(181,plain,
% 0.98/0.86 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(182,plain,
% 0.98/0.86 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | distinct_points(Y, Z)) <=> (distinct_points(Y, Z) | distinct_points(X, Z))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))))), rewrite((distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(183,plain,
% 0.98/0.86 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[182])).
% 0.98/0.86 tff(184,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart4')).
% 0.98/0.86 tff(185,plain,
% 0.98/0.86 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.98/0.86 tff(186,plain,
% 0.98/0.86 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.98/0.86 tff(187,plain,(
% 0.98/0.86 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.98/0.86 inference(skolemize,[status(sab)],[186])).
% 0.98/0.86 tff(188,plain,
% 0.98/0.86 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.98/0.86 tff(189,plain,
% 0.98/0.86 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(190,plain,
% 0.98/0.86 ((distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) <=> (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(191,plain,
% 0.98/0.86 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.86 inference(monotonicity,[status(thm)],[190])).
% 0.98/0.86 tff(192,plain,
% 0.98/0.86 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(transitivity,[status(thm)],[191, 189])).
% 0.98/0.86 tff(193,plain,
% 0.98/0.86 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(194,plain,
% 0.98/0.86 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.98/0.86 tff(195,plain,
% 0.98/0.86 (distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[194, 188, 178])).
% 0.98/0.86 tff(196,plain,
% 0.98/0.86 (distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1))),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[195, 135])).
% 0.98/0.86 tff(197,plain,
% 0.98/0.86 (((~![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)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | (~distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))) <=> ((~![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)))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | (~distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(198,plain,
% 0.98/0.86 ((apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | (~distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | (~distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(199,plain,
% 0.98/0.86 (((~![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)))) | (apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | (~distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))) <=> ((~![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)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | (~distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.86 inference(monotonicity,[status(thm)],[198])).
% 0.98/0.86 tff(200,plain,
% 0.98/0.86 (((~![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)))) | (apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | (~distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))) <=> ((~![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)))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | (~distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(transitivity,[status(thm)],[199, 197])).
% 0.98/0.86 tff(201,plain,
% 0.98/0.86 ((~![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)))) | (apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | (~distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(202,plain,
% 0.98/0.86 ((~![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)))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | (~distinct_points(intersection_point(Z!0, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.98/0.86 tff(203,plain,
% 0.98/0.86 (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[202, 96, 78, 196, 167, 153, 149])).
% 0.98/0.86 tff(204,plain,
% 0.98/0.86 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(205,plain,
% 0.98/0.86 ((distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2))) <=> (distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(206,plain,
% 0.98/0.86 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.87 inference(monotonicity,[status(thm)],[205])).
% 0.98/0.87 tff(207,plain,
% 0.98/0.87 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.87 inference(transitivity,[status(thm)],[206, 204])).
% 0.98/0.87 tff(208,plain,
% 0.98/0.87 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(209,plain,
% 0.98/0.87 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.98/0.87 tff(210,plain,
% 0.98/0.87 ((~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[209, 115, 203])).
% 0.98/0.87 tff(211,plain,
% 0.98/0.87 (~convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[210, 11])).
% 0.98/0.87 tff(212,plain,
% 0.98/0.87 (^[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))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(213,plain,
% 0.98/0.87 (![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)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[212])).
% 0.98/0.87 tff(214,plain,
% 0.98/0.87 (![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)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(215,plain,
% 0.98/0.87 (^[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)))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(216,plain,
% 0.98/0.87 (![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)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[215])).
% 0.98/0.87 tff(217,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/sandbox/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.98/0.87 tff(218,plain,
% 0.98/0.87 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.98/0.87 tff(219,plain,
% 0.98/0.87 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.98/0.87 tff(220,plain,(
% 0.98/0.87 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.98/0.87 inference(skolemize,[status(sab)],[219])).
% 0.98/0.87 tff(221,plain,
% 0.98/0.87 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.98/0.87 tff(222,plain,
% 0.98/0.87 (((~![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, X!2) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | (~apart_point_and_line(intersection_point(Z!0, 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)))) | distinct_lines(Y!1, X!2) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | (~apart_point_and_line(intersection_point(Z!0, X!2), Y!1)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(223,plain,
% 0.98/0.87 ((~![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, X!2) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | (~apart_point_and_line(intersection_point(Z!0, X!2), Y!1)))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(224,plain,
% 0.98/0.87 ((~![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, X!2) | apart_point_and_line(intersection_point(Z!0, X!2), X!2) | (~apart_point_and_line(intersection_point(Z!0, X!2), Y!1))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.98/0.87 tff(225,plain,
% 0.98/0.87 (~apart_point_and_line(intersection_point(Z!0, X!2), Y!1)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[224, 221, 104, 153])).
% 0.98/0.87 tff(226,plain,
% 0.98/0.87 (((~![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)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))) <=> ((~![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)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(227,plain,
% 0.98/0.87 ((apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(Z!0, X!2), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(228,plain,
% 0.98/0.87 (((~![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)))) | (apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(Z!0, X!2), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))) <=> ((~![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)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.87 inference(monotonicity,[status(thm)],[227])).
% 0.98/0.87 tff(229,plain,
% 0.98/0.87 (((~![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)))) | (apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(Z!0, X!2), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))) <=> ((~![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)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.87 inference(transitivity,[status(thm)],[228, 226])).
% 0.98/0.87 tff(230,plain,
% 0.98/0.87 ((~![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)))) | (apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(Z!0, X!2), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(231,plain,
% 0.98/0.87 ((~![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)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), Y!1) | apart_point_and_line(intersection_point(Z!0, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.98/0.87 tff(232,plain,
% 0.98/0.87 (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[231, 96, 82, 135, 167, 225, 149])).
% 0.98/0.87 tff(233,plain,
% 0.98/0.87 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, 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)) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(234,plain,
% 0.98/0.87 ((distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(235,plain,
% 0.98/0.87 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, 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)) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.87 inference(monotonicity,[status(thm)],[234])).
% 0.98/0.87 tff(236,plain,
% 0.98/0.87 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, 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)) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))),
% 0.98/0.87 inference(transitivity,[status(thm)],[235, 233])).
% 0.98/0.87 tff(237,plain,
% 0.98/0.87 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | (~convergent_lines(X!2, Y!1)))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(238,plain,
% 0.98/0.87 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.98/0.87 tff(239,plain,
% 0.98/0.87 (convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))) | distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[238, 115, 74])).
% 0.98/0.87 tff(240,plain,
% 0.98/0.87 (convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[239, 232])).
% 0.98/0.87 tff(241,plain,
% 0.98/0.87 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(242,plain,
% 0.98/0.87 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[241])).
% 0.98/0.87 tff(243,plain,
% 0.98/0.87 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(244,plain,
% 0.98/0.87 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(245,plain,
% 0.98/0.87 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[244])).
% 0.98/0.87 tff(246,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.98/0.87 tff(247,plain,
% 0.98/0.87 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.98/0.87 tff(248,plain,
% 0.98/0.87 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.98/0.87 tff(249,plain,(
% 0.98/0.87 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.98/0.87 inference(skolemize,[status(sab)],[248])).
% 0.98/0.87 tff(250,plain,
% 0.98/0.87 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.98/0.87 tff(251,plain,
% 0.98/0.87 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(252,plain,
% 0.98/0.87 ((convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2))))) <=> (convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(253,plain,
% 0.98/0.87 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)))),
% 0.98/0.87 inference(monotonicity,[status(thm)],[252])).
% 0.98/0.87 tff(254,plain,
% 0.98/0.87 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2))),
% 0.98/0.87 inference(transitivity,[status(thm)],[253, 251])).
% 0.98/0.87 tff(255,plain,
% 0.98/0.87 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(256,plain,
% 0.98/0.87 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)))) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.98/0.87 tff(257,plain,
% 0.98/0.87 (convergent_lines(X!2, X!2) | convergent_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, X!2)), X!2)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[256, 250, 240])).
% 0.98/0.87 tff(258,plain,
% 0.98/0.87 (convergent_lines(X!2, X!2)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[257, 211])).
% 0.98/0.87 tff(259,plain,
% 0.98/0.87 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!2, X!2))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(260,plain,
% 0.98/0.87 ($false),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[259, 8, 258])).
% 0.98/0.87 % SZS output end Proof
%------------------------------------------------------------------------------