%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO195+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 : Sat Jun 21 05:05:52 AM UTC 2025
% Result : Theorem 185.03s 185.25s
% Output : Proof 185.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO195+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:40:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 185.03/185.25 % SZS status Theorem
% 185.03/185.25 % SZS output start Proof
% 185.03/185.25 tff(convergent_lines_type, type, (
% 185.03/185.25 convergent_lines: ( $i * $i ) > $o)).
% 185.03/185.25 tff(line_connecting_type, type, (
% 185.03/185.25 line_connecting: ( $i * $i ) > $i)).
% 185.03/185.25 tff(intersection_point_type, type, (
% 185.03/185.25 intersection_point: ( $i * $i ) > $i)).
% 185.03/185.25 tff(tptp_fun_Y_1_type, type, (
% 185.03/185.25 tptp_fun_Y_1: $i)).
% 185.03/185.25 tff(tptp_fun_X_2_type, type, (
% 185.03/185.25 tptp_fun_X_2: $i)).
% 185.03/185.25 tff(tptp_fun_Z_0_type, type, (
% 185.03/185.25 tptp_fun_Z_0: $i)).
% 185.03/185.25 tff(distinct_lines_type, type, (
% 185.03/185.25 distinct_lines: ( $i * $i ) > $o)).
% 185.03/185.25 tff(apart_point_and_line_type, type, (
% 185.03/185.25 apart_point_and_line: ( $i * $i ) > $o)).
% 185.03/185.25 tff(distinct_points_type, type, (
% 185.03/185.25 distinct_points: ( $i * $i ) > $o)).
% 185.03/185.25 tff(1,assumption,(convergent_lines(X!2, X!2)), introduced(assumption)).
% 185.03/185.25 tff(2,plain,
% 185.03/185.25 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 185.03/185.25 inference(bind,[status(th)],[])).
% 185.03/185.25 tff(3,plain,
% 185.03/185.25 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 185.03/185.25 inference(quant_intro,[status(thm)],[2])).
% 185.03/185.25 tff(4,plain,
% 185.03/185.25 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 185.03/185.25 inference(rewrite,[status(thm)],[])).
% 185.03/185.25 tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 185.03/185.25 tff(6,plain,
% 185.03/185.25 (![X: $i] : (~convergent_lines(X, X))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[5, 4])).
% 185.03/185.25 tff(7,plain,(
% 185.03/185.25 ![X: $i] : (~convergent_lines(X, X))),
% 185.03/185.25 inference(skolemize,[status(sab)],[6])).
% 185.03/185.25 tff(8,plain,
% 185.03/185.25 (![X: $i] : (~convergent_lines(X, X))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[7, 3])).
% 185.03/185.25 tff(9,plain,
% 185.03/185.25 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!2, X!2))),
% 185.03/185.25 inference(quant_inst,[status(thm)],[])).
% 185.03/185.25 tff(10,plain,
% 185.03/185.25 ($false),
% 185.03/185.25 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 185.03/185.25 tff(11,plain,(~convergent_lines(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 185.03/185.25 tff(12,assumption,(distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), introduced(assumption)).
% 185.03/185.25 tff(13,plain,
% 185.03/185.25 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 185.03/185.25 inference(bind,[status(th)],[])).
% 185.03/185.25 tff(14,plain,
% 185.03/185.25 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 185.03/185.25 inference(quant_intro,[status(thm)],[13])).
% 185.03/185.25 tff(15,plain,
% 185.03/185.25 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 185.03/185.25 inference(rewrite,[status(thm)],[])).
% 185.03/185.25 tff(16,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart1')).
% 185.03/185.25 tff(17,plain,
% 185.03/185.25 (![X: $i] : (~distinct_points(X, X))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[16, 15])).
% 185.03/185.25 tff(18,plain,(
% 185.03/185.25 ![X: $i] : (~distinct_points(X, X))),
% 185.03/185.25 inference(skolemize,[status(sab)],[17])).
% 185.03/185.25 tff(19,plain,
% 185.03/185.25 (![X: $i] : (~distinct_points(X, X))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[18, 14])).
% 185.03/185.25 tff(20,plain,
% 185.03/185.25 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)))),
% 185.03/185.25 inference(quant_inst,[status(thm)],[])).
% 185.03/185.25 tff(21,plain,
% 185.03/185.25 ($false),
% 185.03/185.25 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 185.03/185.25 tff(22,plain,(~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 185.03/185.25 tff(23,plain,
% 185.03/185.25 ((~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~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(Y!1, X!2), Z!0) | (~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)))))),
% 185.03/185.25 inference(rewrite,[status(thm)],[])).
% 185.03/185.25 tff(24,plain,
% 185.03/185.25 ((~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~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(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 185.03/185.25 inference(rewrite,[status(thm)],[])).
% 185.03/185.25 tff(25,plain,
% 185.03/185.25 ((~![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(Y, X), Z)))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 185.03/185.25 inference(rewrite,[status(thm)],[])).
% 185.03/185.25 tff(26,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(Y, X), Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 185.03/185.25 tff(27,plain,
% 185.03/185.25 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[26, 25])).
% 185.03/185.25 tff(28,plain,
% 185.03/185.25 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[27, 24])).
% 185.03/185.25 tff(29,plain,
% 185.03/185.25 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[28, 24])).
% 185.03/185.25 tff(30,plain,
% 185.03/185.25 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[29, 24])).
% 185.03/185.25 tff(31,plain,(
% 185.03/185.25 ~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~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))))),
% 185.03/185.25 inference(skolemize,[status(sab)],[30])).
% 185.03/185.25 tff(32,plain,
% 185.03/185.25 (~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~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))))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[31, 23])).
% 185.03/185.25 tff(33,plain,
% 185.03/185.25 (convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0)),
% 185.03/185.25 inference(or_elim,[status(thm)],[32])).
% 185.03/185.25 tff(34,plain,
% 185.03/185.25 (convergent_lines(X!2, Z!0)),
% 185.03/185.25 inference(and_elim,[status(thm)],[33])).
% 185.03/185.25 tff(35,plain,
% 185.03/185.25 (^[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))))),
% 185.03/185.25 inference(bind,[status(th)],[])).
% 185.03/185.25 tff(36,plain,
% 185.03/185.25 (![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)))),
% 185.03/185.25 inference(quant_intro,[status(thm)],[35])).
% 185.03/185.25 tff(37,plain,
% 185.03/185.25 (![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)))),
% 185.03/185.25 inference(rewrite,[status(thm)],[])).
% 185.03/185.25 tff(38,plain,
% 185.03/185.25 (^[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))))),
% 185.03/185.25 inference(bind,[status(th)],[])).
% 185.03/185.25 tff(39,plain,
% 185.03/185.25 (![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)))),
% 185.03/185.25 inference(quant_intro,[status(thm)],[38])).
% 185.03/185.25 tff(40,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 185.03/185.25 tff(41,plain,
% 185.03/185.25 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[40, 39])).
% 185.03/185.25 tff(42,plain,
% 185.03/185.25 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[41, 37])).
% 185.03/185.25 tff(43,plain,(
% 185.03/185.25 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 185.03/185.25 inference(skolemize,[status(sab)],[42])).
% 185.03/185.25 tff(44,plain,
% 185.03/185.25 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[43, 36])).
% 185.03/185.25 tff(45,plain,
% 185.03/185.25 (((~![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)))),
% 185.03/185.25 inference(rewrite,[status(thm)],[])).
% 185.03/185.25 tff(46,plain,
% 185.03/185.25 ((~![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)))),
% 185.03/185.25 inference(quant_inst,[status(thm)],[])).
% 185.03/185.25 tff(47,plain,
% 185.03/185.25 ((~![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))),
% 185.03/185.25 inference(modus_ponens,[status(thm)],[46, 45])).
% 185.03/185.25 tff(48,plain,
% 185.03/185.25 (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)),
% 185.03/185.25 inference(unit_resolution,[status(thm)],[47, 44, 34])).
% 185.03/185.25 tff(49,plain,
% 185.03/185.25 (apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 185.03/185.25 inference(or_elim,[status(thm)],[32])).
% 185.03/185.25 tff(50,plain,
% 185.03/185.25 (^[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))))),
% 185.03/185.25 inference(bind,[status(th)],[])).
% 185.03/185.25 tff(51,plain,
% 185.03/185.25 (![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)))),
% 185.03/185.25 inference(quant_intro,[status(thm)],[50])).
% 185.03/185.25 tff(52,plain,
% 185.03/185.25 (![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)))),
% 185.03/185.25 inference(rewrite,[status(thm)],[])).
% 185.03/185.25 tff(53,plain,
% 185.03/185.25 (^[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)))))),
% 185.03/185.25 inference(bind,[status(th)],[])).
% 185.03/185.25 tff(54,plain,
% 185.03/185.25 (![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)))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[53])).
% 185.03/185.26 tff(55,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 185.03/185.26 tff(56,plain,
% 185.03/185.26 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[55, 54])).
% 185.03/185.26 tff(57,plain,
% 185.03/185.26 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[56, 52])).
% 185.03/185.26 tff(58,plain,(
% 185.03/185.26 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 185.03/185.26 inference(skolemize,[status(sab)],[57])).
% 185.03/185.26 tff(59,plain,
% 185.03/185.26 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[58, 51])).
% 185.03/185.26 tff(60,plain,
% 185.03/185.26 (((~![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)))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(61,plain,
% 185.03/185.26 ((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)))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(62,plain,
% 185.03/185.26 (((~![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))))),
% 185.03/185.26 inference(monotonicity,[status(thm)],[61])).
% 185.03/185.26 tff(63,plain,
% 185.03/185.26 (((~![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)))),
% 185.03/185.26 inference(transitivity,[status(thm)],[62, 60])).
% 185.03/185.26 tff(64,plain,
% 185.03/185.26 ((~![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)))),
% 185.03/185.26 inference(quant_inst,[status(thm)],[])).
% 185.03/185.26 tff(65,plain,
% 185.03/185.26 ((~![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))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[64, 63])).
% 185.03/185.26 tff(66,plain,
% 185.03/185.26 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 185.03/185.26 inference(unit_resolution,[status(thm)],[65, 59, 49, 48])).
% 185.03/185.26 tff(67,plain,
% 185.03/185.26 (^[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))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(68,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[67])).
% 185.03/185.26 tff(69,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(70,plain,
% 185.03/185.26 (^[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)))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(71,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[70])).
% 185.03/185.26 tff(72,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart4')).
% 185.03/185.26 tff(73,plain,
% 185.03/185.26 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[72, 71])).
% 185.03/185.26 tff(74,plain,
% 185.03/185.26 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[73, 69])).
% 185.03/185.26 tff(75,plain,(
% 185.03/185.26 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 185.03/185.26 inference(skolemize,[status(sab)],[74])).
% 185.03/185.26 tff(76,plain,
% 185.03/185.26 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[75, 68])).
% 185.03/185.26 tff(77,plain,
% 185.03/185.26 (((~![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(X!2, Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> ((~![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(X!2, Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(78,plain,
% 185.03/185.26 ((distinct_points(intersection_point(X!2, Z!0), 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(X!2, Z!0)))) <=> (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(79,plain,
% 185.03/185.26 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(X!2, Z!0), 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(X!2, Z!0))))) <=> ((~![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(X!2, Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.26 inference(monotonicity,[status(thm)],[78])).
% 185.03/185.26 tff(80,plain,
% 185.03/185.26 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(X!2, Z!0), 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(X!2, Z!0))))) <=> ((~![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(X!2, Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.26 inference(transitivity,[status(thm)],[79, 77])).
% 185.03/185.26 tff(81,plain,
% 185.03/185.26 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(X!2, Z!0), 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(X!2, Z!0))))),
% 185.03/185.26 inference(quant_inst,[status(thm)],[])).
% 185.03/185.26 tff(82,plain,
% 185.03/185.26 ((~![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(X!2, Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[81, 80])).
% 185.03/185.26 tff(83,plain,
% 185.03/185.26 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))),
% 185.03/185.26 inference(unit_resolution,[status(thm)],[82, 76, 66])).
% 185.03/185.26 tff(84,plain,
% 185.03/185.26 (distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))),
% 185.03/185.26 inference(unit_resolution,[status(thm)],[83, 22])).
% 185.03/185.26 tff(85,plain,
% 185.03/185.26 (^[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)))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(86,plain,
% 185.03/185.26 (![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))))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[85])).
% 185.03/185.26 tff(87,plain,
% 185.03/185.26 (![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))))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(88,plain,
% 185.03/185.26 (^[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)))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(89,plain,
% 185.03/185.26 (![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))))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[88])).
% 185.03/185.26 tff(90,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci1')).
% 185.03/185.26 tff(91,plain,
% 185.03/185.26 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[90, 89])).
% 185.03/185.26 tff(92,plain,
% 185.03/185.26 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[91, 87])).
% 185.03/185.26 tff(93,plain,(
% 185.03/185.26 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 185.03/185.26 inference(skolemize,[status(sab)],[92])).
% 185.03/185.26 tff(94,plain,
% 185.03/185.26 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[93, 86])).
% 185.03/185.26 tff(95,plain,
% 185.03/185.26 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(96,plain,
% 185.03/185.26 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))),
% 185.03/185.26 inference(quant_inst,[status(thm)],[])).
% 185.03/185.26 tff(97,plain,
% 185.03/185.26 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[96, 95])).
% 185.03/185.26 tff(98,plain,
% 185.03/185.26 (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))),
% 185.03/185.26 inference(unit_resolution,[status(thm)],[97, 94, 84])).
% 185.03/185.26 tff(99,plain,
% 185.03/185.26 (^[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)))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(100,plain,
% 185.03/185.26 (![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))))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[99])).
% 185.03/185.26 tff(101,plain,
% 185.03/185.26 (![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))))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(102,plain,
% 185.03/185.26 (^[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)))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(103,plain,
% 185.03/185.26 (![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))))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[102])).
% 185.03/185.26 tff(104,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci2')).
% 185.03/185.26 tff(105,plain,
% 185.03/185.26 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[104, 103])).
% 185.03/185.26 tff(106,plain,
% 185.03/185.26 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[105, 101])).
% 185.03/185.26 tff(107,plain,(
% 185.03/185.26 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 185.03/185.26 inference(skolemize,[status(sab)],[106])).
% 185.03/185.26 tff(108,plain,
% 185.03/185.26 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[107, 100])).
% 185.03/185.26 tff(109,plain,
% 185.03/185.26 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(110,plain,
% 185.03/185.26 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))),
% 185.03/185.26 inference(quant_inst,[status(thm)],[])).
% 185.03/185.26 tff(111,plain,
% 185.03/185.26 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[110, 109])).
% 185.03/185.26 tff(112,plain,
% 185.03/185.26 (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))),
% 185.03/185.26 inference(unit_resolution,[status(thm)],[111, 108, 84])).
% 185.03/185.26 tff(113,plain,
% 185.03/185.26 (^[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))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(114,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[113])).
% 185.03/185.26 tff(115,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(116,plain,
% 185.03/185.26 (^[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))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(117,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[116])).
% 185.03/185.26 tff(118,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 185.03/185.26 tff(119,plain,
% 185.03/185.26 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[118, 117])).
% 185.03/185.26 tff(120,plain,
% 185.03/185.26 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[119, 115])).
% 185.03/185.26 tff(121,plain,(
% 185.03/185.26 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 185.03/185.26 inference(skolemize,[status(sab)],[120])).
% 185.03/185.26 tff(122,plain,
% 185.03/185.26 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[121, 114])).
% 185.03/185.26 tff(123,plain,
% 185.03/185.26 (((~![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)))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(124,plain,
% 185.03/185.26 ((~![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)))),
% 185.03/185.26 inference(quant_inst,[status(thm)],[])).
% 185.03/185.26 tff(125,plain,
% 185.03/185.26 ((~![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))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[124, 123])).
% 185.03/185.26 tff(126,plain,
% 185.03/185.26 (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)),
% 185.03/185.26 inference(unit_resolution,[status(thm)],[125, 122, 34])).
% 185.03/185.26 tff(127,plain,
% 185.03/185.26 (convergent_lines(X!2, Y!1)),
% 185.03/185.26 inference(and_elim,[status(thm)],[33])).
% 185.03/185.26 tff(128,plain,
% 185.03/185.26 (((~![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)))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(129,plain,
% 185.03/185.26 ((~![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)))),
% 185.03/185.26 inference(quant_inst,[status(thm)],[])).
% 185.03/185.26 tff(130,plain,
% 185.03/185.26 ((~![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))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[129, 128])).
% 185.03/185.26 tff(131,plain,
% 185.03/185.26 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 185.03/185.26 inference(unit_resolution,[status(thm)],[130, 122, 127])).
% 185.03/185.26 tff(132,plain,
% 185.03/185.26 (^[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))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(133,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[132])).
% 185.03/185.26 tff(134,plain,
% 185.03/185.26 (^[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)))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(135,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[134])).
% 185.03/185.26 tff(136,plain,
% 185.03/185.26 (![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))))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(137,plain,
% 185.03/185.26 (^[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))))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(138,plain,
% 185.03/185.26 (![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))))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[137])).
% 185.03/185.26 tff(139,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','cu1')).
% 185.03/185.26 tff(140,plain,
% 185.03/185.26 (![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))))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[139, 138])).
% 185.03/185.26 tff(141,plain,
% 185.03/185.26 (![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))))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[140, 136])).
% 185.03/185.26 tff(142,plain,(
% 185.03/185.26 ![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))))),
% 185.03/185.26 inference(skolemize,[status(sab)],[141])).
% 185.03/185.26 tff(143,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[142, 135])).
% 185.03/185.26 tff(144,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[143, 133])).
% 185.03/185.26 tff(145,plain,
% 185.03/185.26 (((~![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(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, 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, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2)))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(146,plain,
% 185.03/185.26 ((apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2))) <=> (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, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2)))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(147,plain,
% 185.03/185.26 (((~![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(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, 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, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2))))),
% 185.03/185.26 inference(monotonicity,[status(thm)],[146])).
% 185.03/185.26 tff(148,plain,
% 185.03/185.26 (((~![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(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, 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, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2)))),
% 185.03/185.26 inference(transitivity,[status(thm)],[147, 145])).
% 185.03/185.26 tff(149,plain,
% 185.03/185.26 ((~![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(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2)))),
% 185.03/185.26 inference(quant_inst,[status(thm)],[])).
% 185.03/185.26 tff(150,plain,
% 185.03/185.26 ((~![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(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[149, 148])).
% 185.03/185.26 tff(151,plain,
% 185.03/185.26 (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2)),
% 185.03/185.26 inference(unit_resolution,[status(thm)],[150, 144, 131, 126, 84, 112, 98])).
% 185.03/185.26 tff(152,plain,
% 185.03/185.26 (^[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))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(153,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[152])).
% 185.03/185.26 tff(154,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(155,plain,
% 185.03/185.26 (^[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)))))),
% 185.03/185.26 inference(bind,[status(th)],[])).
% 185.03/185.26 tff(156,plain,
% 185.03/185.26 (![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)))),
% 185.03/185.26 inference(quant_intro,[status(thm)],[155])).
% 185.03/185.26 tff(157,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 185.03/185.26 tff(158,plain,
% 185.03/185.26 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[157, 156])).
% 185.03/185.26 tff(159,plain,
% 185.03/185.26 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[158, 154])).
% 185.03/185.26 tff(160,plain,(
% 185.03/185.26 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 185.03/185.26 inference(skolemize,[status(sab)],[159])).
% 185.03/185.26 tff(161,plain,
% 185.03/185.26 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 185.03/185.26 inference(modus_ponens,[status(thm)],[160, 153])).
% 185.03/185.26 tff(162,plain,
% 185.03/185.26 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | convergent_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | convergent_lines(X!2, X!2))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(163,plain,
% 185.03/185.26 ((distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))) <=> (distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | convergent_lines(X!2, X!2))),
% 185.03/185.26 inference(rewrite,[status(thm)],[])).
% 185.03/185.26 tff(164,plain,
% 185.03/185.26 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | convergent_lines(X!2, X!2)))),
% 185.03/185.26 inference(monotonicity,[status(thm)],[163])).
% 185.03/185.26 tff(165,plain,
% 185.03/185.26 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | convergent_lines(X!2, X!2))),
% 185.03/185.26 inference(transitivity,[status(thm)],[164, 162])).
% 185.03/185.27 tff(166,plain,
% 185.03/185.27 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))),
% 185.03/185.27 inference(quant_inst,[status(thm)],[])).
% 185.03/185.27 tff(167,plain,
% 185.03/185.27 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), X!2) | (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | convergent_lines(X!2, X!2)),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[166, 165])).
% 185.03/185.27 tff(168,plain,
% 185.03/185.27 (~convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[167, 161, 151, 11])).
% 185.03/185.27 tff(169,assumption,(~convergent_lines(X!2, X!2)), introduced(assumption)).
% 185.03/185.27 tff(170,assumption,(~convergent_lines(Y!1, X!2)), introduced(assumption)).
% 185.03/185.27 tff(171,plain,
% 185.03/185.27 (^[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))))),
% 185.03/185.27 inference(bind,[status(th)],[])).
% 185.03/185.27 tff(172,plain,
% 185.03/185.27 (![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)))),
% 185.03/185.27 inference(quant_intro,[status(thm)],[171])).
% 185.03/185.27 tff(173,plain,
% 185.03/185.27 (![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)))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(174,plain,
% 185.03/185.27 (^[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)))))),
% 185.03/185.27 inference(bind,[status(th)],[])).
% 185.03/185.27 tff(175,plain,
% 185.03/185.27 (![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)))),
% 185.03/185.27 inference(quant_intro,[status(thm)],[174])).
% 185.03/185.27 tff(176,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ax6')).
% 185.03/185.27 tff(177,plain,
% 185.03/185.27 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[176, 175])).
% 185.03/185.27 tff(178,plain,
% 185.03/185.27 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[177, 173])).
% 185.03/185.27 tff(179,plain,(
% 185.03/185.27 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 185.03/185.27 inference(skolemize,[status(sab)],[178])).
% 185.03/185.27 tff(180,plain,
% 185.03/185.27 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[179, 172])).
% 185.03/185.27 tff(181,plain,
% 185.03/185.27 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(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, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(182,plain,
% 185.03/185.27 ((convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(183,plain,
% 185.03/185.27 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2)))),
% 185.03/185.27 inference(monotonicity,[status(thm)],[182])).
% 185.03/185.27 tff(184,plain,
% 185.03/185.27 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 185.03/185.27 inference(transitivity,[status(thm)],[183, 181])).
% 185.03/185.27 tff(185,plain,
% 185.03/185.27 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))),
% 185.03/185.27 inference(quant_inst,[status(thm)],[])).
% 185.03/185.27 tff(186,plain,
% 185.03/185.27 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[185, 184])).
% 185.03/185.27 tff(187,plain,
% 185.03/185.27 ($false),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[186, 180, 127, 170, 169])).
% 185.03/185.27 tff(188,plain,(convergent_lines(X!2, X!2) | convergent_lines(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 185.03/185.27 tff(189,plain,
% 185.03/185.27 (convergent_lines(Y!1, X!2)),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[188, 11])).
% 185.03/185.27 tff(190,plain,
% 185.03/185.27 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(191,plain,
% 185.03/185.27 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)))),
% 185.03/185.27 inference(quant_inst,[status(thm)],[])).
% 185.03/185.27 tff(192,plain,
% 185.03/185.27 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1))),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[191, 190])).
% 185.03/185.27 tff(193,plain,
% 185.03/185.27 ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1))),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[192, 122])).
% 185.03/185.27 tff(194,plain,
% 185.03/185.27 (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[193, 189])).
% 185.03/185.27 tff(195,assumption,(distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1)), introduced(assumption)).
% 185.03/185.27 tff(196,plain,
% 185.03/185.27 (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 185.03/185.27 inference(or_elim,[status(thm)],[32])).
% 185.03/185.27 tff(197,plain,
% 185.03/185.27 (((~![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(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, 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(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(198,plain,
% 185.03/185.27 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))) <=> (apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(199,plain,
% 185.03/185.27 (((~![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(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, 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(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))))),
% 185.03/185.27 inference(monotonicity,[status(thm)],[198])).
% 185.03/185.27 tff(200,plain,
% 185.03/185.27 (((~![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(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, 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(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)))),
% 185.03/185.27 inference(transitivity,[status(thm)],[199, 197])).
% 185.03/185.27 tff(201,plain,
% 185.03/185.27 ((~![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(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 185.03/185.27 inference(quant_inst,[status(thm)],[])).
% 185.03/185.27 tff(202,plain,
% 185.03/185.27 ((~![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(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[201, 200])).
% 185.03/185.27 tff(203,plain,
% 185.03/185.27 (distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[202, 59, 196, 49])).
% 185.03/185.27 tff(204,plain,
% 185.03/185.27 (((~![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(Y!1, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, 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(Y!1, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(205,plain,
% 185.03/185.27 ((distinct_points(intersection_point(Y!1, 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(Y!1, X!2)))) <=> (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(206,plain,
% 185.03/185.27 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Y!1, 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(Y!1, 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(Y!1, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)))))),
% 185.03/185.27 inference(monotonicity,[status(thm)],[205])).
% 185.03/185.27 tff(207,plain,
% 185.03/185.27 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Y!1, 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(Y!1, 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(Y!1, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))))),
% 185.03/185.27 inference(transitivity,[status(thm)],[206, 204])).
% 185.03/185.27 tff(208,plain,
% 185.03/185.27 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Y!1, 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(Y!1, X!2))))),
% 185.03/185.27 inference(quant_inst,[status(thm)],[])).
% 185.03/185.27 tff(209,plain,
% 185.03/185.27 ((~![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(Y!1, X!2), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)))),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[208, 207])).
% 185.03/185.27 tff(210,plain,
% 185.03/185.27 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[209, 76, 203])).
% 185.03/185.27 tff(211,plain,
% 185.03/185.27 (distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[210, 22])).
% 185.03/185.27 tff(212,plain,
% 185.03/185.27 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(213,plain,
% 185.03/185.27 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.03/185.27 inference(quant_inst,[status(thm)],[])).
% 185.03/185.27 tff(214,plain,
% 185.03/185.27 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[213, 212])).
% 185.03/185.27 tff(215,plain,
% 185.03/185.27 (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[214, 94, 211])).
% 185.03/185.27 tff(216,plain,
% 185.03/185.27 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(217,plain,
% 185.03/185.27 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.03/185.27 inference(quant_inst,[status(thm)],[])).
% 185.03/185.27 tff(218,plain,
% 185.03/185.27 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[217, 216])).
% 185.03/185.27 tff(219,plain,
% 185.03/185.27 (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[218, 108, 211])).
% 185.03/185.27 tff(220,assumption,(~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)), introduced(assumption)).
% 185.03/185.27 tff(221,plain,
% 185.03/185.27 (((~![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)))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(222,plain,
% 185.03/185.27 ((~![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)))),
% 185.03/185.27 inference(quant_inst,[status(thm)],[])).
% 185.03/185.27 tff(223,plain,
% 185.03/185.27 ((~![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))),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[222, 221])).
% 185.03/185.27 tff(224,plain,
% 185.03/185.27 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[223, 44, 127])).
% 185.03/185.27 tff(225,plain,
% 185.03/185.27 (((~![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(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1)))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(226,plain,
% 185.03/185.27 ((apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1)))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(227,plain,
% 185.03/185.27 (((~![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(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1))))),
% 185.03/185.27 inference(monotonicity,[status(thm)],[226])).
% 185.03/185.27 tff(228,plain,
% 185.03/185.27 (((~![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(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1)))),
% 185.03/185.27 inference(transitivity,[status(thm)],[227, 225])).
% 185.03/185.27 tff(229,plain,
% 185.03/185.27 ((~![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(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1)))),
% 185.03/185.27 inference(quant_inst,[status(thm)],[])).
% 185.03/185.27 tff(230,plain,
% 185.03/185.27 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1))),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[229, 228])).
% 185.03/185.27 tff(231,plain,
% 185.03/185.27 ($false),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[230, 144, 224, 220, 211, 219, 215, 195])).
% 185.03/185.27 tff(232,plain,(apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1))), inference(lemma,lemma(discharge,[]))).
% 185.03/185.27 tff(233,plain,
% 185.03/185.27 (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1)),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[232, 194])).
% 185.03/185.27 tff(234,assumption,(distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1)), introduced(assumption)).
% 185.03/185.27 tff(235,assumption,(convergent_lines(Y!1, X!2)), introduced(assumption)).
% 185.03/185.27 tff(236,plain,
% 185.03/185.27 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(237,plain,
% 185.03/185.27 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)))),
% 185.03/185.27 inference(quant_inst,[status(thm)],[])).
% 185.03/185.27 tff(238,plain,
% 185.03/185.27 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2))),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[237, 236])).
% 185.03/185.27 tff(239,plain,
% 185.03/185.27 ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2))),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[238, 44])).
% 185.03/185.27 tff(240,plain,
% 185.03/185.27 (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[239, 235])).
% 185.03/185.27 tff(241,assumption,(~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))), introduced(assumption)).
% 185.03/185.27 tff(242,assumption,(~convergent_lines(Z!0, X!2)), introduced(assumption)).
% 185.03/185.27 tff(243,assumption,(~distinct_lines(Y!1, X!2)), introduced(assumption)).
% 185.03/185.27 tff(244,plain,
% 185.03/185.27 (convergent_lines(Z!0, Y!1)),
% 185.03/185.27 inference(and_elim,[status(thm)],[33])).
% 185.03/185.27 tff(245,plain,
% 185.03/185.27 (((~![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))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(246,plain,
% 185.03/185.27 ((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))),
% 185.03/185.27 inference(rewrite,[status(thm)],[])).
% 185.03/185.27 tff(247,plain,
% 185.03/185.27 (((~![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)))),
% 185.03/185.27 inference(monotonicity,[status(thm)],[246])).
% 185.03/185.27 tff(248,plain,
% 185.03/185.27 (((~![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))),
% 185.03/185.27 inference(transitivity,[status(thm)],[247, 245])).
% 185.03/185.27 tff(249,plain,
% 185.03/185.27 ((~![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)))),
% 185.03/185.27 inference(quant_inst,[status(thm)],[])).
% 185.03/185.27 tff(250,plain,
% 185.03/185.27 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(Z!0, X!2)),
% 185.03/185.27 inference(modus_ponens,[status(thm)],[249, 248])).
% 185.03/185.27 tff(251,plain,
% 185.03/185.27 ($false),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[250, 161, 244, 243, 242])).
% 185.03/185.27 tff(252,plain,(distinct_lines(Y!1, X!2) | convergent_lines(Z!0, X!2)), inference(lemma,lemma(discharge,[]))).
% 185.03/185.27 tff(253,plain,
% 185.03/185.27 (distinct_lines(Y!1, X!2)),
% 185.03/185.27 inference(unit_resolution,[status(thm)],[252, 242])).
% 185.03/185.28 tff(254,plain,
% 185.03/185.28 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(Z!0, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(Z!0, X!2))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(255,plain,
% 185.03/185.28 ((convergent_lines(Y!1, X!2) | convergent_lines(Z!0, X!2) | (~convergent_lines(Z!0, Y!1))) <=> ((~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(Z!0, X!2))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(256,plain,
% 185.03/185.28 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(Z!0, X!2) | (~convergent_lines(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(Z!0, X!2)))),
% 185.03/185.28 inference(monotonicity,[status(thm)],[255])).
% 185.03/185.28 tff(257,plain,
% 185.03/185.28 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(Z!0, X!2) | (~convergent_lines(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(Z!0, X!2))),
% 185.03/185.28 inference(transitivity,[status(thm)],[256, 254])).
% 185.03/185.28 tff(258,plain,
% 185.03/185.28 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(Z!0, X!2) | (~convergent_lines(Z!0, Y!1)))),
% 185.03/185.28 inference(quant_inst,[status(thm)],[])).
% 185.03/185.28 tff(259,plain,
% 185.03/185.28 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(Z!0, X!2)),
% 185.03/185.28 inference(modus_ponens,[status(thm)],[258, 257])).
% 185.03/185.28 tff(260,plain,
% 185.03/185.28 ($false),
% 185.03/185.28 inference(unit_resolution,[status(thm)],[259, 180, 244, 170, 242])).
% 185.03/185.28 tff(261,plain,(convergent_lines(Y!1, X!2) | convergent_lines(Z!0, X!2)), inference(lemma,lemma(discharge,[]))).
% 185.03/185.28 tff(262,plain,
% 185.03/185.28 (convergent_lines(Y!1, X!2)),
% 185.03/185.28 inference(unit_resolution,[status(thm)],[261, 242])).
% 185.03/185.28 tff(263,plain,
% 185.03/185.28 (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)),
% 185.03/185.28 inference(unit_resolution,[status(thm)],[239, 262])).
% 185.03/185.28 tff(264,plain,
% 185.03/185.28 (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)),
% 185.03/185.28 inference(unit_resolution,[status(thm)],[193, 262])).
% 185.03/185.28 tff(265,plain,
% 185.03/185.28 (((~![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(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(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, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(266,plain,
% 185.03/185.28 ((apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), 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(Y!1, X!2))) | (~distinct_lines(Y!1, X!2))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(267,plain,
% 185.03/185.28 (((~![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(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), 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(Y!1, X!2))) | (~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, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)))))),
% 185.03/185.28 inference(monotonicity,[status(thm)],[266])).
% 185.03/185.28 tff(268,plain,
% 185.03/185.28 (((~![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(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), 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(Y!1, X!2))) | (~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, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))))),
% 185.03/185.28 inference(transitivity,[status(thm)],[267, 265])).
% 185.03/185.28 tff(269,plain,
% 185.03/185.28 ((~![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(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), 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(Y!1, X!2))) | (~distinct_lines(Y!1, X!2)))),
% 185.03/185.28 inference(quant_inst,[status(thm)],[])).
% 185.03/185.28 tff(270,plain,
% 185.03/185.28 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)))),
% 185.03/185.28 inference(modus_ponens,[status(thm)],[269, 268])).
% 185.03/185.28 tff(271,plain,
% 185.03/185.28 ($false),
% 185.03/185.28 inference(unit_resolution,[status(thm)],[270, 144, 224, 131, 264, 263, 253, 203])).
% 185.03/185.28 tff(272,plain,(convergent_lines(Z!0, X!2)), inference(lemma,lemma(discharge,[]))).
% 185.03/185.28 tff(273,plain,
% 185.03/185.28 (((~![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(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))) <=> ((~![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(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(274,plain,
% 185.03/185.28 ((~![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(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.28 inference(quant_inst,[status(thm)],[])).
% 185.03/185.28 tff(275,plain,
% 185.03/185.28 ((~![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(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.28 inference(modus_ponens,[status(thm)],[274, 273])).
% 185.03/185.28 tff(276,plain,
% 185.03/185.28 (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 185.03/185.28 inference(unit_resolution,[status(thm)],[275, 94, 66])).
% 185.03/185.28 tff(277,plain,
% 185.03/185.28 (((~![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(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))) <=> ((~![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(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(278,plain,
% 185.03/185.28 ((~![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(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.28 inference(quant_inst,[status(thm)],[])).
% 185.03/185.28 tff(279,plain,
% 185.03/185.28 ((~![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(X!2, Z!0))) | (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.28 inference(modus_ponens,[status(thm)],[278, 277])).
% 185.03/185.28 tff(280,plain,
% 185.03/185.28 (~apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 185.03/185.28 inference(unit_resolution,[status(thm)],[279, 108, 66])).
% 185.03/185.28 tff(281,plain,
% 185.03/185.28 (((~![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(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(282,plain,
% 185.03/185.28 ((apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> (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))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(283,plain,
% 185.03/185.28 (((~![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), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))))),
% 185.03/185.28 inference(monotonicity,[status(thm)],[282])).
% 185.03/185.28 tff(284,plain,
% 185.03/185.28 (((~![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), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.28 inference(transitivity,[status(thm)],[283, 281])).
% 185.03/185.28 tff(285,plain,
% 185.03/185.28 ((~![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), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.28 inference(quant_inst,[status(thm)],[])).
% 185.03/185.28 tff(286,plain,
% 185.03/185.28 ((~![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(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.28 inference(modus_ponens,[status(thm)],[285, 284])).
% 185.03/185.28 tff(287,plain,
% 185.03/185.28 (~distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 185.03/185.28 inference(unit_resolution,[status(thm)],[286, 144, 131, 126, 66, 280, 276])).
% 185.03/185.28 tff(288,plain,
% 185.03/185.28 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(Z!0, X!2)) | distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, X!2)) | distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(289,plain,
% 185.03/185.28 ((distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~convergent_lines(Z!0, X!2))) <=> ((~convergent_lines(Z!0, X!2)) | distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(290,plain,
% 185.03/185.28 (((~![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(X!2, Z!0))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~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, X!2)) | distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.28 inference(monotonicity,[status(thm)],[289])).
% 185.03/185.28 tff(291,plain,
% 185.03/185.28 (((~![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(X!2, Z!0))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~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, X!2)) | distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.28 inference(transitivity,[status(thm)],[290, 288])).
% 185.03/185.28 tff(292,plain,
% 185.03/185.28 ((~![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(X!2, Z!0))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~convergent_lines(Z!0, X!2)))),
% 185.03/185.28 inference(quant_inst,[status(thm)],[])).
% 185.03/185.28 tff(293,plain,
% 185.03/185.28 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, X!2)) | distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 185.03/185.28 inference(modus_ponens,[status(thm)],[292, 291])).
% 185.03/185.28 tff(294,plain,
% 185.03/185.28 ($false),
% 185.03/185.28 inference(unit_resolution,[status(thm)],[293, 161, 287, 272, 241])).
% 185.03/185.28 tff(295,plain,(convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))), inference(lemma,lemma(discharge,[]))).
% 185.03/185.28 tff(296,plain,
% 185.03/185.28 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(297,plain,
% 185.03/185.28 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.28 inference(quant_inst,[status(thm)],[])).
% 185.03/185.28 tff(298,plain,
% 185.03/185.28 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.28 inference(modus_ponens,[status(thm)],[297, 296])).
% 185.03/185.28 tff(299,plain,
% 185.03/185.28 (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 185.03/185.28 inference(unit_resolution,[status(thm)],[298, 44, 295])).
% 185.03/185.28 tff(300,plain,
% 185.03/185.28 (^[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))))),
% 185.03/185.28 inference(bind,[status(th)],[])).
% 185.03/185.28 tff(301,plain,
% 185.03/185.28 (![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)))),
% 185.03/185.28 inference(quant_intro,[status(thm)],[300])).
% 185.03/185.28 tff(302,plain,
% 185.03/185.28 (![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)))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(303,plain,
% 185.03/185.28 (^[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)))))),
% 185.03/185.28 inference(bind,[status(th)],[])).
% 185.03/185.28 tff(304,plain,
% 185.03/185.28 (![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)))),
% 185.03/185.28 inference(quant_intro,[status(thm)],[303])).
% 185.03/185.28 tff(305,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 185.03/185.28 tff(306,plain,
% 185.03/185.28 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 185.03/185.28 inference(modus_ponens,[status(thm)],[305, 304])).
% 185.03/185.28 tff(307,plain,
% 185.03/185.28 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 185.03/185.28 inference(modus_ponens,[status(thm)],[306, 302])).
% 185.03/185.28 tff(308,plain,(
% 185.03/185.28 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 185.03/185.28 inference(skolemize,[status(sab)],[307])).
% 185.03/185.28 tff(309,plain,
% 185.03/185.28 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 185.03/185.28 inference(modus_ponens,[status(thm)],[308, 301])).
% 185.03/185.28 tff(310,plain,
% 185.03/185.28 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2)))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(311,plain,
% 185.03/185.28 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2)))),
% 185.03/185.28 inference(quant_inst,[status(thm)],[])).
% 185.03/185.28 tff(312,plain,
% 185.03/185.28 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(X!2, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2))),
% 185.03/185.28 inference(modus_ponens,[status(thm)],[311, 310])).
% 185.03/185.28 tff(313,plain,
% 185.03/185.28 (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2)),
% 185.03/185.28 inference(unit_resolution,[status(thm)],[312, 309, 287, 299])).
% 185.03/185.28 tff(314,plain,
% 185.03/185.28 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0)))),
% 185.03/185.28 inference(rewrite,[status(thm)],[])).
% 185.03/185.28 tff(315,plain,
% 185.03/185.28 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0)))),
% 185.03/185.28 inference(quant_inst,[status(thm)],[])).
% 185.03/185.28 tff(316,plain,
% 185.03/185.28 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0))),
% 185.03/185.29 inference(modus_ponens,[status(thm)],[315, 314])).
% 185.03/185.29 tff(317,plain,
% 185.03/185.29 (~apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0)),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[316, 122, 295])).
% 185.03/185.29 tff(318,plain,
% 185.03/185.29 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(Z!0, Z!0))),
% 185.03/185.29 inference(quant_inst,[status(thm)],[])).
% 185.03/185.29 tff(319,plain,
% 185.03/185.29 (~convergent_lines(Z!0, Z!0)),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[318, 8])).
% 185.03/185.29 tff(320,assumption,(~distinct_lines(X!2, Z!0)), introduced(assumption)).
% 185.03/185.29 tff(321,plain,
% 185.03/185.29 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!2, Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(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, Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, X!2)))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(322,plain,
% 185.03/185.29 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!2, Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, X!2)))),
% 185.03/185.29 inference(quant_inst,[status(thm)],[])).
% 185.03/185.29 tff(323,plain,
% 185.03/185.29 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(X!2, Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, X!2))),
% 185.03/185.29 inference(modus_ponens,[status(thm)],[322, 321])).
% 185.03/185.29 tff(324,plain,
% 185.03/185.29 (~convergent_lines(Z!0, X!2)),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[323, 161, 320, 319])).
% 185.03/185.29 tff(325,plain,
% 185.03/185.29 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(326,plain,
% 185.03/185.29 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))),
% 185.03/185.29 inference(quant_inst,[status(thm)],[])).
% 185.03/185.29 tff(327,plain,
% 185.03/185.29 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0))),
% 185.03/185.29 inference(modus_ponens,[status(thm)],[326, 325])).
% 185.03/185.29 tff(328,plain,
% 185.03/185.29 (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[327, 122, 244])).
% 185.03/185.29 tff(329,plain,
% 185.03/185.29 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_lines(X!2, Z!0) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_lines(X!2, Z!0) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(330,plain,
% 185.03/185.29 ((distinct_lines(X!2, Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2))) <=> (apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_lines(X!2, Z!0) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(331,plain,
% 185.03/185.29 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(X!2, Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_lines(X!2, Z!0) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2))))),
% 185.03/185.29 inference(monotonicity,[status(thm)],[330])).
% 185.03/185.29 tff(332,plain,
% 185.03/185.29 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(X!2, Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_lines(X!2, Z!0) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))),
% 185.03/185.29 inference(transitivity,[status(thm)],[331, 329])).
% 185.03/185.29 tff(333,plain,
% 185.03/185.29 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(X!2, Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))),
% 185.03/185.29 inference(quant_inst,[status(thm)],[])).
% 185.03/185.29 tff(334,plain,
% 185.03/185.29 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_lines(X!2, Z!0) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2))),
% 185.03/185.29 inference(modus_ponens,[status(thm)],[333, 332])).
% 185.03/185.29 tff(335,plain,
% 185.03/185.29 (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[334, 309, 328, 320])).
% 185.03/185.29 tff(336,plain,
% 185.03/185.29 (((~![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, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(337,plain,
% 185.03/185.29 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))) <=> ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(338,plain,
% 185.03/185.29 (((~![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, Y!1)) | apart_point_and_line(intersection_point(Z!0, Y!1), 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, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 185.03/185.29 inference(monotonicity,[status(thm)],[337])).
% 185.03/185.29 tff(339,plain,
% 185.03/185.29 (((~![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, Y!1)) | apart_point_and_line(intersection_point(Z!0, Y!1), 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, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 185.03/185.29 inference(transitivity,[status(thm)],[338, 336])).
% 185.03/185.29 tff(340,plain,
% 185.03/185.29 ((~![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, Y!1)) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 185.03/185.29 inference(quant_inst,[status(thm)],[])).
% 185.03/185.29 tff(341,plain,
% 185.03/185.29 ((~![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, Y!1), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))),
% 185.03/185.29 inference(modus_ponens,[status(thm)],[340, 339])).
% 185.03/185.29 tff(342,plain,
% 185.03/185.29 (distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[341, 59, 49, 328])).
% 185.03/185.29 tff(343,plain,
% 185.03/185.29 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(344,plain,
% 185.03/185.29 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))),
% 185.03/185.29 inference(quant_inst,[status(thm)],[])).
% 185.03/185.29 tff(345,plain,
% 185.03/185.29 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1))),
% 185.03/185.29 inference(modus_ponens,[status(thm)],[344, 343])).
% 185.03/185.29 tff(346,plain,
% 185.03/185.29 (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[345, 44, 244])).
% 185.03/185.29 tff(347,plain,
% 185.03/185.29 (((~![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(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | (~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, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | (~distinct_lines(Y!1, X!2)))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(348,plain,
% 185.03/185.29 ((apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), 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(Z!0, Y!1))) | (~distinct_lines(Y!1, X!2))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | (~distinct_lines(Y!1, X!2)))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(349,plain,
% 185.03/185.29 (((~![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, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), 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(Z!0, Y!1))) | (~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, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | (~distinct_lines(Y!1, X!2))))),
% 185.03/185.29 inference(monotonicity,[status(thm)],[348])).
% 185.03/185.29 tff(350,plain,
% 185.03/185.29 (((~![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, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), 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(Z!0, Y!1))) | (~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, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | (~distinct_lines(Y!1, X!2)))),
% 185.03/185.29 inference(transitivity,[status(thm)],[349, 347])).
% 185.03/185.29 tff(351,plain,
% 185.03/185.29 ((~![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, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), 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(Z!0, Y!1))) | (~distinct_lines(Y!1, X!2)))),
% 185.03/185.29 inference(quant_inst,[status(thm)],[])).
% 185.03/185.29 tff(352,plain,
% 185.03/185.29 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | (~distinct_lines(Y!1, X!2))),
% 185.03/185.29 inference(modus_ponens,[status(thm)],[351, 350])).
% 185.03/185.29 tff(353,plain,
% 185.03/185.29 (~distinct_lines(Y!1, X!2)),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[352, 144, 224, 131, 346, 342, 335])).
% 185.03/185.29 tff(354,plain,
% 185.03/185.29 ($false),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[250, 161, 244, 353, 324])).
% 185.03/185.29 tff(355,plain,(distinct_lines(X!2, Z!0)), inference(lemma,lemma(discharge,[]))).
% 185.03/185.29 tff(356,plain,
% 185.03/185.29 (((~![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(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(X!2, Z!0)) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(X!2, Z!0)) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(357,plain,
% 185.03/185.29 ((apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) | (~distinct_lines(X!2, Z!0))) <=> (apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(X!2, Z!0)) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(358,plain,
% 185.03/185.29 (((~![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, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) | (~distinct_lines(X!2, Z!0)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(X!2, Z!0)) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))))),
% 185.03/185.29 inference(monotonicity,[status(thm)],[357])).
% 185.03/185.29 tff(359,plain,
% 185.03/185.29 (((~![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, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) | (~distinct_lines(X!2, Z!0)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(X!2, Z!0)) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))))),
% 185.03/185.29 inference(transitivity,[status(thm)],[358, 356])).
% 185.03/185.29 tff(360,plain,
% 185.03/185.29 ((~![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, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) | (~distinct_lines(X!2, Z!0)))),
% 185.03/185.29 inference(quant_inst,[status(thm)],[])).
% 185.03/185.29 tff(361,plain,
% 185.03/185.29 ((~![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(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(X!2, Z!0)) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), Z!0) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.29 inference(modus_ponens,[status(thm)],[360, 359])).
% 185.03/185.29 tff(362,plain,
% 185.03/185.29 (apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[361, 144, 196, 355, 317, 313])).
% 185.03/185.29 tff(363,plain,
% 185.03/185.29 (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[362, 240])).
% 185.03/185.29 tff(364,assumption,(~distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))), introduced(assumption)).
% 185.03/185.29 tff(365,assumption,(apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))), introduced(assumption)).
% 185.03/185.29 tff(366,plain,
% 185.03/185.29 (((~![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(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(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(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(367,plain,
% 185.03/185.29 ((distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> ((~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.29 inference(rewrite,[status(thm)],[])).
% 185.03/185.29 tff(368,plain,
% 185.03/185.29 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(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(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))))),
% 185.03/185.29 inference(monotonicity,[status(thm)],[367])).
% 185.03/185.29 tff(369,plain,
% 185.03/185.29 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(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(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.29 inference(transitivity,[status(thm)],[368, 366])).
% 185.03/185.29 tff(370,plain,
% 185.03/185.29 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.03/185.29 inference(quant_inst,[status(thm)],[])).
% 185.03/185.29 tff(371,plain,
% 185.03/185.29 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | apart_point_and_line(intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.03/185.29 inference(modus_ponens,[status(thm)],[370, 369])).
% 185.03/185.29 tff(372,plain,
% 185.03/185.29 ($false),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[371, 59, 365, 299, 364])).
% 185.03/185.29 tff(373,plain,(distinct_points(intersection_point(Y!1, X!2), intersection_point(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) | (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))), inference(lemma,lemma(discharge,[]))).
% 185.03/185.29 tff(374,plain,
% 185.03/185.29 (~apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[373, 363])).
% 185.03/185.29 tff(375,plain,
% 185.03/185.29 (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)),
% 185.03/185.29 inference(unit_resolution,[status(thm)],[193, 235])).
% 185.03/185.29 tff(376,plain,
% 185.03/185.29 (((~![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(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, 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(X!2, Z!0))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, 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(X!2, Z!0))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1)))),
% 185.03/185.30 inference(rewrite,[status(thm)],[])).
% 185.03/185.30 tff(377,plain,
% 185.03/185.30 ((apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), 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(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, 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(X!2, Z!0))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1)))),
% 185.03/185.30 inference(rewrite,[status(thm)],[])).
% 185.03/185.30 tff(378,plain,
% 185.03/185.30 (((~![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(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, 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(X!2, Z!0))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1))))),
% 185.03/185.30 inference(monotonicity,[status(thm)],[377])).
% 185.03/185.30 tff(379,plain,
% 185.03/185.30 (((~![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(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, 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(X!2, Z!0))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1)))),
% 185.03/185.30 inference(transitivity,[status(thm)],[378, 376])).
% 185.12/185.30 tff(380,plain,
% 185.12/185.30 ((~![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(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1)))),
% 185.12/185.30 inference(quant_inst,[status(thm)],[])).
% 185.12/185.30 tff(381,plain,
% 185.12/185.30 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(Y!1, X!2), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1))),
% 185.12/185.30 inference(modus_ponens,[status(thm)],[380, 379])).
% 185.12/185.30 tff(382,plain,
% 185.12/185.30 ($false),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[381, 144, 224, 375, 276, 374, 234, 211])).
% 185.12/185.30 tff(383,plain,((~convergent_lines(Y!1, X!2)) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1))), inference(lemma,lemma(discharge,[]))).
% 185.12/185.30 tff(384,plain,
% 185.12/185.30 (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1)),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[383, 189])).
% 185.12/185.30 tff(385,plain,
% 185.12/185.30 (((~![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(X!2, Y!1), intersection_point(Z!0, Y!1))) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))) <=> ((~![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(X!2, Y!1), intersection_point(Z!0, Y!1))) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.30 inference(rewrite,[status(thm)],[])).
% 185.12/185.30 tff(386,plain,
% 185.12/185.30 ((distinct_points(intersection_point(Z!0, Y!1), 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, 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, Y!1))) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.30 inference(rewrite,[status(thm)],[])).
% 185.12/185.30 tff(387,plain,
% 185.12/185.30 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Z!0, Y!1), 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, Y!1))))) <=> ((~![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(X!2, Y!1), intersection_point(Z!0, Y!1))) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 185.12/185.30 inference(monotonicity,[status(thm)],[386])).
% 185.12/185.30 tff(388,plain,
% 185.12/185.30 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Z!0, Y!1), 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, Y!1))))) <=> ((~![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(X!2, Y!1), intersection_point(Z!0, Y!1))) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.30 inference(transitivity,[status(thm)],[387, 385])).
% 185.12/185.30 tff(389,plain,
% 185.12/185.30 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Z!0, Y!1), 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, Y!1))))),
% 185.12/185.30 inference(quant_inst,[status(thm)],[])).
% 185.12/185.30 tff(390,plain,
% 185.12/185.30 ((~![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(X!2, Y!1), intersection_point(Z!0, Y!1))) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))),
% 185.12/185.30 inference(modus_ponens,[status(thm)],[389, 388])).
% 185.12/185.30 tff(391,plain,
% 185.12/185.30 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[390, 76, 342])).
% 185.12/185.30 tff(392,plain,
% 185.12/185.30 (distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[391, 22])).
% 185.12/185.30 tff(393,plain,
% 185.12/185.30 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.30 inference(rewrite,[status(thm)],[])).
% 185.12/185.30 tff(394,plain,
% 185.12/185.30 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.30 inference(quant_inst,[status(thm)],[])).
% 185.12/185.30 tff(395,plain,
% 185.12/185.30 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 185.12/185.30 inference(modus_ponens,[status(thm)],[394, 393])).
% 185.12/185.30 tff(396,plain,
% 185.12/185.30 (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[395, 94, 392])).
% 185.12/185.30 tff(397,plain,
% 185.12/185.30 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.30 inference(rewrite,[status(thm)],[])).
% 185.12/185.30 tff(398,plain,
% 185.12/185.30 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.30 inference(quant_inst,[status(thm)],[])).
% 185.12/185.30 tff(399,plain,
% 185.12/185.30 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 185.12/185.30 inference(modus_ponens,[status(thm)],[398, 397])).
% 185.12/185.30 tff(400,plain,
% 185.12/185.30 (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[399, 108, 392])).
% 185.12/185.30 tff(401,plain,
% 185.12/185.30 (((~![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, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.30 inference(rewrite,[status(thm)],[])).
% 185.12/185.30 tff(402,plain,
% 185.12/185.30 ((apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.30 inference(rewrite,[status(thm)],[])).
% 185.12/185.30 tff(403,plain,
% 185.12/185.30 (((~![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, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))))),
% 185.12/185.30 inference(monotonicity,[status(thm)],[402])).
% 185.12/185.30 tff(404,plain,
% 185.12/185.30 (((~![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, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.30 inference(transitivity,[status(thm)],[403, 401])).
% 185.12/185.30 tff(405,plain,
% 185.12/185.30 ((~![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, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.30 inference(quant_inst,[status(thm)],[])).
% 185.12/185.30 tff(406,plain,
% 185.12/185.30 ((~![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, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 185.12/185.30 inference(modus_ponens,[status(thm)],[405, 404])).
% 185.12/185.30 tff(407,plain,
% 185.12/185.30 (~distinct_lines(Y!1, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[406, 144, 224, 346, 342, 400, 396])).
% 185.12/185.30 tff(408,assumption,(distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))), introduced(assumption)).
% 185.12/185.30 tff(409,plain,
% 185.12/185.30 ((~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[395, 94])).
% 185.12/185.30 tff(410,plain,
% 185.12/185.30 (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[409, 408])).
% 185.12/185.30 tff(411,assumption,(distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))), introduced(assumption)).
% 185.12/185.30 tff(412,plain,
% 185.12/185.30 ((~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[399, 108])).
% 185.12/185.30 tff(413,plain,
% 185.12/185.30 (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[412, 408])).
% 185.12/185.30 tff(414,plain,
% 185.12/185.30 (((~![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, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))) <=> ((~![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, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))),
% 185.12/185.30 inference(rewrite,[status(thm)],[])).
% 185.12/185.30 tff(415,plain,
% 185.12/185.30 ((~![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, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))),
% 185.12/185.30 inference(quant_inst,[status(thm)],[])).
% 185.12/185.30 tff(416,plain,
% 185.12/185.30 ((~![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, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 185.12/185.30 inference(modus_ponens,[status(thm)],[415, 414])).
% 185.12/185.30 tff(417,plain,
% 185.12/185.30 (~apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[416, 94, 342])).
% 185.12/185.30 tff(418,plain,
% 185.12/185.30 (((~![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, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))) <=> ((~![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, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))),
% 185.12/185.30 inference(rewrite,[status(thm)],[])).
% 185.12/185.30 tff(419,plain,
% 185.12/185.30 ((~![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, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))),
% 185.12/185.30 inference(quant_inst,[status(thm)],[])).
% 185.12/185.30 tff(420,plain,
% 185.12/185.30 ((~![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, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 185.12/185.30 inference(modus_ponens,[status(thm)],[419, 418])).
% 185.12/185.30 tff(421,plain,
% 185.12/185.30 (~apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 185.12/185.30 inference(unit_resolution,[status(thm)],[420, 108, 342])).
% 185.12/185.30 tff(422,plain,
% 185.12/185.30 (((~![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)))) | ((~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.30 inference(rewrite,[status(thm)],[])).
% 185.12/185.30 tff(423,plain,
% 185.12/185.30 ((apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), 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, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))) <=> ((~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.30 inference(rewrite,[status(thm)],[])).
% 185.12/185.30 tff(424,plain,
% 185.12/185.30 (((~![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(Z!0, Y!1), 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, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))))),
% 185.12/185.31 inference(monotonicity,[status(thm)],[423])).
% 185.12/185.31 tff(425,plain,
% 185.12/185.31 (((~![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(Z!0, Y!1), 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, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.31 inference(transitivity,[status(thm)],[424, 422])).
% 185.12/185.31 tff(426,plain,
% 185.12/185.31 ((~![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(Z!0, Y!1), 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, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.31 inference(quant_inst,[status(thm)],[])).
% 185.12/185.31 tff(427,plain,
% 185.12/185.31 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 185.12/185.31 inference(modus_ponens,[status(thm)],[426, 425])).
% 185.12/185.31 tff(428,plain,
% 185.12/185.31 ($false),
% 185.12/185.31 inference(unit_resolution,[status(thm)],[427, 144, 408, 421, 417, 413, 411, 410])).
% 185.12/185.31 tff(429,plain,((~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))), inference(lemma,lemma(discharge,[]))).
% 185.12/185.31 tff(430,plain,
% 185.12/185.31 (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.31 inference(unit_resolution,[status(thm)],[429, 392])).
% 185.12/185.31 tff(431,assumption,(~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))), introduced(assumption)).
% 185.12/185.31 tff(432,plain,
% 185.12/185.31 (((~![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, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))),
% 185.12/185.31 inference(rewrite,[status(thm)],[])).
% 185.12/185.31 tff(433,plain,
% 185.12/185.31 ((apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))),
% 185.12/185.31 inference(rewrite,[status(thm)],[])).
% 185.12/185.31 tff(434,plain,
% 185.12/185.31 (((~![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, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))))),
% 185.12/185.31 inference(monotonicity,[status(thm)],[433])).
% 185.12/185.31 tff(435,plain,
% 185.12/185.31 (((~![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, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))),
% 185.12/185.31 inference(transitivity,[status(thm)],[434, 432])).
% 185.12/185.31 tff(436,plain,
% 185.12/185.31 ((~![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, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))),
% 185.12/185.31 inference(quant_inst,[status(thm)],[])).
% 185.12/185.31 tff(437,plain,
% 185.12/185.31 ((~![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, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 185.12/185.31 inference(modus_ponens,[status(thm)],[436, 435])).
% 185.12/185.31 tff(438,plain,
% 185.12/185.31 (~distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 185.12/185.31 inference(unit_resolution,[status(thm)],[437, 144, 224, 346, 342, 421, 417])).
% 185.12/185.31 tff(439,plain,
% 185.12/185.31 (((~![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, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(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, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 185.12/185.31 inference(rewrite,[status(thm)],[])).
% 185.12/185.31 tff(440,plain,
% 185.12/185.31 ((distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~convergent_lines(Z!0, Y!1))) <=> ((~convergent_lines(Z!0, Y!1)) | distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 185.12/185.31 inference(rewrite,[status(thm)],[])).
% 185.12/185.31 tff(441,plain,
% 185.12/185.31 (((~![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, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~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, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))),
% 185.12/185.31 inference(monotonicity,[status(thm)],[440])).
% 185.12/185.31 tff(442,plain,
% 185.12/185.31 (((~![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, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~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, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 185.12/185.31 inference(transitivity,[status(thm)],[441, 439])).
% 185.12/185.31 tff(443,plain,
% 185.12/185.31 ((~![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, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~convergent_lines(Z!0, Y!1)))),
% 185.12/185.31 inference(quant_inst,[status(thm)],[])).
% 185.12/185.31 tff(444,plain,
% 185.12/185.31 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, Y!1)) | distinct_lines(Y!1, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 185.12/185.31 inference(modus_ponens,[status(thm)],[443, 442])).
% 185.12/185.31 tff(445,plain,
% 185.12/185.31 ($false),
% 185.12/185.31 inference(unit_resolution,[status(thm)],[444, 161, 244, 438, 431])).
% 185.12/185.31 tff(446,plain,(convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))), inference(lemma,lemma(discharge,[]))).
% 185.12/185.31 tff(447,plain,
% 185.12/185.31 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 185.12/185.31 inference(rewrite,[status(thm)],[])).
% 185.12/185.31 tff(448,plain,
% 185.12/185.31 ((distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))) <=> ((~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 185.12/185.31 inference(rewrite,[status(thm)],[])).
% 185.12/185.31 tff(449,plain,
% 185.12/185.31 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(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, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.31 inference(monotonicity,[status(thm)],[448])).
% 185.12/185.31 tff(450,plain,
% 185.12/185.31 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(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, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 185.12/185.31 inference(transitivity,[status(thm)],[449, 447])).
% 185.12/185.31 tff(451,plain,
% 185.12/185.31 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))),
% 185.12/185.31 inference(quant_inst,[status(thm)],[])).
% 185.12/185.31 tff(452,plain,
% 185.12/185.31 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.31 inference(modus_ponens,[status(thm)],[451, 450])).
% 185.12/185.31 tff(453,plain,
% 185.12/185.31 (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.31 inference(unit_resolution,[status(thm)],[452, 161, 446])).
% 185.12/185.31 tff(454,plain,
% 185.12/185.31 (convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.31 inference(unit_resolution,[status(thm)],[453, 430])).
% 185.12/185.31 tff(455,plain,
% 185.12/185.31 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))) | convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))) | convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))),
% 185.12/185.31 inference(rewrite,[status(thm)],[])).
% 185.12/185.31 tff(456,plain,
% 185.12/185.31 ((convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))) <=> (convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))) | convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))),
% 185.12/185.31 inference(rewrite,[status(thm)],[])).
% 185.12/185.31 tff(457,plain,
% 185.12/185.31 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))) | convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)))),
% 185.12/185.31 inference(monotonicity,[status(thm)],[456])).
% 185.12/185.31 tff(458,plain,
% 185.12/185.31 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))) | convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))),
% 185.12/185.31 inference(transitivity,[status(thm)],[457, 455])).
% 185.12/185.31 tff(459,plain,
% 185.12/185.31 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.31 inference(quant_inst,[status(thm)],[])).
% 185.12/185.31 tff(460,plain,
% 185.12/185.31 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))) | convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)),
% 185.12/185.31 inference(modus_ponens,[status(thm)],[459, 458])).
% 185.12/185.31 tff(461,plain,
% 185.12/185.31 ((~convergent_lines(Z!0, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))) | convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)),
% 185.12/185.31 inference(unit_resolution,[status(thm)],[460, 180, 319])).
% 185.12/185.31 tff(462,plain,
% 185.12/185.31 (convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)),
% 185.12/185.31 inference(unit_resolution,[status(thm)],[461, 454])).
% 185.12/185.31 tff(463,plain,
% 185.12/185.31 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.31 inference(rewrite,[status(thm)],[])).
% 185.12/185.31 tff(464,plain,
% 185.12/185.31 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 185.12/185.31 inference(quant_inst,[status(thm)],[])).
% 185.12/185.31 tff(465,plain,
% 185.12/185.31 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 185.12/185.31 inference(modus_ponens,[status(thm)],[464, 463])).
% 185.12/185.31 tff(466,plain,
% 185.12/185.31 (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[465, 122, 462])).
% 185.12/185.32 tff(467,plain,
% 185.12/185.32 (((~![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, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), 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, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1)))),
% 185.12/185.32 inference(rewrite,[status(thm)],[])).
% 185.12/185.32 tff(468,plain,
% 185.12/185.32 ((~![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, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1)))),
% 185.12/185.32 inference(quant_inst,[status(thm)],[])).
% 185.12/185.32 tff(469,plain,
% 185.12/185.32 ((~![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, line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1))),
% 185.12/185.32 inference(modus_ponens,[status(thm)],[468, 467])).
% 185.12/185.32 tff(470,plain,
% 185.12/185.32 (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1)),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[469, 309, 466, 407])).
% 185.12/185.32 tff(471,assumption,(apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))), introduced(assumption)).
% 185.12/185.32 tff(472,assumption,(~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1)), introduced(assumption)).
% 185.12/185.32 tff(473,plain,
% 185.12/185.32 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.12/185.32 inference(rewrite,[status(thm)],[])).
% 185.12/185.32 tff(474,plain,
% 185.12/185.32 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.12/185.32 inference(quant_inst,[status(thm)],[])).
% 185.12/185.32 tff(475,plain,
% 185.12/185.32 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.12/185.32 inference(modus_ponens,[status(thm)],[474, 473])).
% 185.12/185.32 tff(476,plain,
% 185.12/185.32 ($false),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[475, 309, 472, 471, 470])).
% 185.12/185.32 tff(477,plain,(distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Y!1) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))), inference(lemma,lemma(discharge,[]))).
% 185.12/185.32 tff(478,plain,
% 185.12/185.32 (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[477, 384])).
% 185.12/185.32 tff(479,plain,
% 185.12/185.32 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Z!0, Z!0) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Z!0, Z!0) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.12/185.32 inference(rewrite,[status(thm)],[])).
% 185.12/185.32 tff(480,plain,
% 185.12/185.32 ((distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> (convergent_lines(Z!0, Z!0) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.12/185.32 inference(rewrite,[status(thm)],[])).
% 185.12/185.32 tff(481,plain,
% 185.12/185.32 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Z!0, Z!0) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))))),
% 185.12/185.32 inference(monotonicity,[status(thm)],[480])).
% 185.12/185.32 tff(482,plain,
% 185.12/185.32 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Z!0, Z!0) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.12/185.32 inference(transitivity,[status(thm)],[481, 479])).
% 185.12/185.32 tff(483,plain,
% 185.12/185.32 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 185.12/185.32 inference(quant_inst,[status(thm)],[])).
% 185.12/185.32 tff(484,plain,
% 185.12/185.32 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Z!0, Z!0) | distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.12/185.32 inference(modus_ponens,[status(thm)],[483, 482])).
% 185.12/185.32 tff(485,plain,
% 185.12/185.32 (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0) | (~convergent_lines(Z!0, line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[484, 161, 319])).
% 185.12/185.32 tff(486,plain,
% 185.12/185.32 (distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0)),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[485, 295])).
% 185.12/185.32 tff(487,plain,
% 185.12/185.32 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0)))),
% 185.12/185.32 inference(rewrite,[status(thm)],[])).
% 185.12/185.32 tff(488,plain,
% 185.12/185.32 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0)))),
% 185.12/185.32 inference(quant_inst,[status(thm)],[])).
% 185.12/185.32 tff(489,plain,
% 185.12/185.32 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0))),
% 185.12/185.32 inference(modus_ponens,[status(thm)],[488, 487])).
% 185.12/185.32 tff(490,plain,
% 185.12/185.32 (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0)),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[489, 44, 462])).
% 185.12/185.32 tff(491,plain,
% 185.12/185.32 (((~![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), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0))))),
% 185.12/185.32 inference(rewrite,[status(thm)],[])).
% 185.12/185.32 tff(492,plain,
% 185.12/185.32 ((apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0))) <=> (apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0))))),
% 185.12/185.32 inference(rewrite,[status(thm)],[])).
% 185.12/185.32 tff(493,plain,
% 185.12/185.32 (((~![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), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)))))),
% 185.12/185.32 inference(monotonicity,[status(thm)],[492])).
% 185.12/185.32 tff(494,plain,
% 185.12/185.32 (((~![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), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0))))),
% 185.12/185.32 inference(transitivity,[status(thm)],[493, 491])).
% 185.12/185.32 tff(495,plain,
% 185.12/185.32 ((~![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), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0)))),
% 185.12/185.32 inference(quant_inst,[status(thm)],[])).
% 185.12/185.32 tff(496,plain,
% 185.12/185.32 ((~![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), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)))),
% 185.12/185.32 inference(modus_ponens,[status(thm)],[495, 494])).
% 185.12/185.32 tff(497,plain,
% 185.12/185.32 ((~distinct_lines(line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)), Z!0)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)))),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[496, 144, 48, 280, 490])).
% 185.12/185.32 tff(498,plain,
% 185.12/185.32 (apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)))),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[497, 486])).
% 185.12/185.32 tff(499,plain,
% 185.12/185.32 (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0))),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[498, 478])).
% 185.12/185.32 tff(500,assumption,(~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0))), introduced(assumption)).
% 185.12/185.32 tff(501,assumption,(apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))), introduced(assumption)).
% 185.12/185.32 tff(502,plain,
% 185.12/185.32 (((~![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, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))),
% 185.12/185.32 inference(rewrite,[status(thm)],[])).
% 185.12/185.32 tff(503,plain,
% 185.12/185.32 ((distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))) <=> (apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))),
% 185.12/185.32 inference(rewrite,[status(thm)],[])).
% 185.12/185.32 tff(504,plain,
% 185.12/185.32 (((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))))),
% 185.12/185.32 inference(monotonicity,[status(thm)],[503])).
% 185.12/185.32 tff(505,plain,
% 185.12/185.32 (((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))),
% 185.12/185.32 inference(transitivity,[status(thm)],[504, 502])).
% 185.12/185.32 tff(506,plain,
% 185.12/185.32 ((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))),
% 185.12/185.32 inference(quant_inst,[status(thm)],[])).
% 185.12/185.32 tff(507,plain,
% 185.12/185.32 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(X!2, Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))),
% 185.12/185.32 inference(modus_ponens,[status(thm)],[506, 505])).
% 185.12/185.32 tff(508,plain,
% 185.12/185.32 ($false),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[507, 59, 98, 501, 500])).
% 185.12/185.32 tff(509,plain,(distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Z!0)) | (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))), inference(lemma,lemma(discharge,[]))).
% 185.12/185.32 tff(510,plain,
% 185.12/185.32 (~apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))),
% 185.12/185.32 inference(unit_resolution,[status(thm)],[509, 499])).
% 185.12/185.32 tff(511,plain,
% 185.12/185.32 (((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), 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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)))),
% 185.12/185.32 inference(rewrite,[status(thm)],[])).
% 185.12/185.32 tff(512,plain,
% 185.12/185.32 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), 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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)))),
% 185.12/185.32 inference(rewrite,[status(thm)],[])).
% 185.12/185.32 tff(513,plain,
% 185.12/185.32 (((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), 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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))))),
% 185.12/185.33 inference(monotonicity,[status(thm)],[512])).
% 185.12/185.33 tff(514,plain,
% 185.12/185.33 (((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), 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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)))),
% 185.12/185.33 inference(transitivity,[status(thm)],[513, 511])).
% 185.12/185.33 tff(515,plain,
% 185.12/185.33 ((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 185.12/185.33 inference(quant_inst,[status(thm)],[])).
% 185.12/185.33 tff(516,plain,
% 185.12/185.33 ((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))),
% 185.12/185.33 inference(modus_ponens,[status(thm)],[515, 514])).
% 185.12/185.33 tff(517,plain,
% 185.12/185.33 (distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))),
% 185.12/185.33 inference(unit_resolution,[status(thm)],[516, 59, 49, 490])).
% 185.12/185.33 tff(518,assumption,(~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))), introduced(assumption)).
% 185.12/185.33 tff(519,plain,
% 185.12/185.33 (((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))))) <=> ((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))))),
% 185.12/185.33 inference(rewrite,[status(thm)],[])).
% 185.12/185.33 tff(520,plain,
% 185.12/185.33 ((distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), 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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)))) <=> (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))))),
% 185.12/185.33 inference(rewrite,[status(thm)],[])).
% 185.12/185.33 tff(521,plain,
% 185.12/185.33 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), 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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))))) <=> ((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)))))),
% 185.12/185.33 inference(monotonicity,[status(thm)],[520])).
% 185.12/185.33 tff(522,plain,
% 185.12/185.33 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), 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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))))) <=> ((~![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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))))),
% 185.12/185.33 inference(transitivity,[status(thm)],[521, 519])).
% 185.12/185.33 tff(523,plain,
% 185.12/185.33 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), 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(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0))))),
% 185.12/185.33 inference(quant_inst,[status(thm)],[])).
% 185.12/185.33 tff(524,plain,
% 185.12/185.33 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0)))),
% 185.12/185.33 inference(modus_ponens,[status(thm)],[523, 522])).
% 185.12/185.33 tff(525,plain,
% 185.12/185.33 ($false),
% 185.12/185.33 inference(unit_resolution,[status(thm)],[524, 76, 22, 518, 517])).
% 185.12/185.33 tff(526,plain,(distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 185.12/185.33 tff(527,plain,
% 185.12/185.33 (((~![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) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1))),
% 185.12/185.33 inference(rewrite,[status(thm)],[])).
% 185.12/185.33 tff(528,plain,
% 185.12/185.33 ((apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1))),
% 185.12/185.33 inference(rewrite,[status(thm)],[])).
% 185.12/185.33 tff(529,plain,
% 185.12/185.33 (((~![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(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1)))),
% 185.12/185.33 inference(monotonicity,[status(thm)],[528])).
% 185.12/185.33 tff(530,plain,
% 185.12/185.33 (((~![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(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1))),
% 185.12/185.33 inference(transitivity,[status(thm)],[529, 527])).
% 185.12/185.33 tff(531,plain,
% 185.12/185.33 ((~![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(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1)))),
% 185.12/185.33 inference(quant_inst,[status(thm)],[])).
% 185.12/185.33 tff(532,plain,
% 185.12/185.33 ((~![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) | (~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1)) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), Y!1)),
% 185.12/185.33 inference(modus_ponens,[status(thm)],[531, 530])).
% 185.12/185.33 tff(533,plain,
% 185.12/185.33 ((~distinct_points(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1))),
% 185.12/185.33 inference(unit_resolution,[status(thm)],[532, 144, 224, 112, 470])).
% 185.12/185.33 tff(534,plain,
% 185.12/185.33 (apart_point_and_line(intersection_point(line_connecting(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)), Z!0), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1))),
% 185.12/185.33 inference(unit_resolution,[status(thm)],[533, 526])).
% 185.12/185.33 tff(535,plain,
% 185.12/185.33 (~distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1)),
% 185.12/185.33 inference(unit_resolution,[status(thm)],[534, 510])).
% 185.12/185.33 tff(536,plain,
% 185.12/185.33 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 185.12/185.33 inference(bind,[status(th)],[])).
% 185.12/185.33 tff(537,plain,
% 185.12/185.33 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 185.12/185.33 inference(quant_intro,[status(thm)],[536])).
% 185.12/185.33 tff(538,plain,
% 185.12/185.33 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 185.12/185.33 inference(rewrite,[status(thm)],[])).
% 185.12/185.33 tff(539,plain,
% 185.12/185.33 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 185.12/185.33 inference(bind,[status(th)],[])).
% 185.12/185.33 tff(540,plain,
% 185.12/185.33 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 185.12/185.33 inference(quant_intro,[status(thm)],[539])).
% 185.12/185.33 tff(541,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart5')).
% 185.12/185.33 tff(542,plain,
% 185.12/185.33 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 185.12/185.33 inference(modus_ponens,[status(thm)],[541, 540])).
% 185.12/185.33 tff(543,plain,
% 185.12/185.33 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 185.12/185.33 inference(modus_ponens,[status(thm)],[542, 538])).
% 185.12/185.33 tff(544,plain,(
% 185.12/185.33 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 185.12/185.33 inference(skolemize,[status(sab)],[543])).
% 185.12/185.33 tff(545,plain,
% 185.12/185.33 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 185.12/185.33 inference(modus_ponens,[status(thm)],[544, 537])).
% 185.12/185.33 tff(546,plain,
% 185.12/185.33 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | ((~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1))),
% 185.12/185.33 inference(rewrite,[status(thm)],[])).
% 185.12/185.33 tff(547,plain,
% 185.12/185.33 ((distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))))) <=> ((~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1))),
% 185.12/185.33 inference(rewrite,[status(thm)],[])).
% 185.12/185.33 tff(548,plain,
% 185.12/185.33 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | ((~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1)))),
% 185.12/185.33 inference(monotonicity,[status(thm)],[547])).
% 185.12/185.33 tff(549,plain,
% 185.12/185.33 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1))),
% 185.12/185.33 inference(transitivity,[status(thm)],[548, 546])).
% 185.12/185.33 tff(550,plain,
% 185.12/185.33 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))))),
% 185.12/185.33 inference(quant_inst,[status(thm)],[])).
% 185.12/185.33 tff(551,plain,
% 185.12/185.33 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))) | distinct_lines(line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)), Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1)),
% 185.12/185.33 inference(modus_ponens,[status(thm)],[550, 549])).
% 185.12/185.33 tff(552,plain,
% 185.12/185.33 (~distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1)))),
% 185.12/185.33 inference(unit_resolution,[status(thm)],[551, 545, 535, 233])).
% 185.12/185.33 tff(553,plain,
% 185.12/185.33 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(Y!1, Y!1))),
% 185.12/185.33 inference(quant_inst,[status(thm)],[])).
% 185.12/185.33 tff(554,plain,
% 185.12/185.33 (~convergent_lines(Y!1, Y!1)),
% 185.12/185.33 inference(unit_resolution,[status(thm)],[553, 8])).
% 185.12/185.33 tff(555,plain,
% 185.12/185.33 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | (~convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Y!1, Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | (~convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.12/185.33 inference(rewrite,[status(thm)],[])).
% 185.12/185.33 tff(556,plain,
% 185.12/185.33 ((distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))) <=> (convergent_lines(Y!1, Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | (~convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.12/185.33 inference(rewrite,[status(thm)],[])).
% 185.12/185.33 tff(557,plain,
% 185.12/185.33 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | (~convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))))),
% 185.12/185.33 inference(monotonicity,[status(thm)],[556])).
% 185.12/185.33 tff(558,plain,
% 185.12/185.33 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Y!1, Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | (~convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.12/185.33 inference(transitivity,[status(thm)],[557, 555])).
% 185.12/185.33 tff(559,plain,
% 185.12/185.33 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.12/185.33 inference(quant_inst,[status(thm)],[])).
% 185.12/185.33 tff(560,plain,
% 185.12/185.33 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Y!1, Y!1) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), Y!1) | (~convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 185.12/185.33 inference(modus_ponens,[status(thm)],[559, 558])).
% 185.12/185.33 tff(561,plain,
% 185.12/185.33 (~convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 185.12/185.33 inference(unit_resolution,[status(thm)],[560, 161, 554, 233])).
% 185.12/185.33 tff(562,plain,
% 185.12/185.33 (((~![X: $i, Y: $i, Z: $i] : (convergent_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(Y!1, X!2), intersection_point(X!2, Y!1))) | convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_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(Y!1, X!2), intersection_point(X!2, Y!1))) | convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 185.12/185.33 inference(rewrite,[status(thm)],[])).
% 185.12/185.33 tff(563,plain,
% 185.12/185.33 ((convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 185.12/185.33 inference(rewrite,[status(thm)],[])).
% 185.12/185.33 tff(564,plain,
% 185.12/185.33 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_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(Y!1, X!2), intersection_point(X!2, Y!1))) | convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.12/185.34 inference(monotonicity,[status(thm)],[563])).
% 185.12/185.34 tff(565,plain,
% 185.12/185.34 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_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(Y!1, X!2), intersection_point(X!2, Y!1))) | convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 185.12/185.34 inference(transitivity,[status(thm)],[564, 562])).
% 185.12/185.34 tff(566,plain,
% 185.12/185.34 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, Y!1)))),
% 185.12/185.34 inference(quant_inst,[status(thm)],[])).
% 185.12/185.34 tff(567,plain,
% 185.12/185.34 ((~![X: $i, Y: $i, Z: $i] : (convergent_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(Y!1, X!2), intersection_point(X!2, Y!1))) | convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 185.12/185.34 inference(modus_ponens,[status(thm)],[566, 565])).
% 185.12/185.34 tff(568,plain,
% 185.12/185.34 (convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | convergent_lines(Y!1, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 185.12/185.34 inference(unit_resolution,[status(thm)],[567, 180, 127])).
% 185.12/185.34 tff(569,plain,
% 185.12/185.34 (convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 185.12/185.34 inference(unit_resolution,[status(thm)],[568, 561])).
% 185.12/185.34 tff(570,plain,
% 185.12/185.34 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(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, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.12/185.34 inference(rewrite,[status(thm)],[])).
% 185.12/185.34 tff(571,plain,
% 185.12/185.34 ((distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))) <=> (convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.12/185.34 inference(rewrite,[status(thm)],[])).
% 185.12/185.34 tff(572,plain,
% 185.12/185.34 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(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, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))))),
% 185.12/185.34 inference(monotonicity,[status(thm)],[571])).
% 185.12/185.34 tff(573,plain,
% 185.12/185.34 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(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, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.12/185.34 inference(transitivity,[status(thm)],[572, 570])).
% 185.12/185.34 tff(574,plain,
% 185.12/185.34 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 185.12/185.34 inference(quant_inst,[status(thm)],[])).
% 185.12/185.34 tff(575,plain,
% 185.12/185.34 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 185.12/185.34 inference(modus_ponens,[status(thm)],[574, 573])).
% 185.12/185.34 tff(576,plain,
% 185.12/185.34 (convergent_lines(X!2, line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | distinct_lines(line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)), line_connecting(intersection_point(X!2, Z!0), intersection_point(X!2, Y!1))) | (~convergent_lines(X!2, line_connecting(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 185.12/185.34 inference(unit_resolution,[status(thm)],[575, 161])).
% 185.12/185.34 tff(577,plain,
% 185.12/185.34 ($false),
% 185.12/185.34 inference(unit_resolution,[status(thm)],[576, 569, 552, 168])).
% 185.12/185.34 % SZS output end Proof
% 185.12/185.34 % E exiting
%------------------------------------------------------------------------------