%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO192+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:05:51 AM UTC 2025
% Result : Theorem 0.11s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO192+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:44:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.39 % SZS status Theorem
% 0.11/0.39 % SZS output start Proof
% 0.11/0.39 tff(distinct_lines_type, type, (
% 0.11/0.39 distinct_lines: ( $i * $i ) > $o)).
% 0.11/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.11/0.39 tptp_fun_Z_0: $i)).
% 0.11/0.39 tff(tptp_fun_X_2_type, type, (
% 0.11/0.39 tptp_fun_X_2: $i)).
% 0.11/0.39 tff(apart_point_and_line_type, type, (
% 0.11/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.11/0.39 tff(intersection_point_type, type, (
% 0.11/0.39 intersection_point: ( $i * $i ) > $i)).
% 0.11/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.39 tptp_fun_Y_1: $i)).
% 0.11/0.39 tff(convergent_lines_type, type, (
% 0.11/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.11/0.39 tff(distinct_points_type, type, (
% 0.11/0.39 distinct_points: ( $i * $i ) > $o)).
% 0.11/0.39 tff(1,plain,
% 0.11/0.39 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(2,plain,
% 0.11/0.39 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.39 tff(3,plain,
% 0.11/0.39 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(4,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart2')).
% 0.11/0.39 tff(5,plain,
% 0.11/0.39 (![X: $i] : (~distinct_lines(X, X))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.39 tff(6,plain,(
% 0.11/0.39 ![X: $i] : (~distinct_lines(X, X))),
% 0.11/0.39 inference(skolemize,[status(sab)],[5])).
% 0.11/0.39 tff(7,plain,
% 0.11/0.39 (![X: $i] : (~distinct_lines(X, X))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.39 tff(8,plain,
% 0.11/0.39 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(Z!0, Z!0))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(9,plain,
% 0.11/0.39 (~distinct_lines(Z!0, Z!0)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.39 tff(10,assumption,(~distinct_lines(Z!0, X!2)), introduced(assumption)).
% 0.11/0.39 tff(11,plain,
% 0.11/0.39 ((~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> (~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(12,plain,
% 0.11/0.39 ((~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))) <=> (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(13,plain,
% 0.11/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (apart_point_and_line(intersection_point(X, Y), Z) => (distinct_lines(X, Z) & distinct_lines(Y, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(14,axiom,(~![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (apart_point_and_line(intersection_point(X, Y), Z) => (distinct_lines(X, Z) & distinct_lines(Y, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.11/0.39 tff(15,plain,
% 0.11/0.39 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.11/0.39 tff(16,plain,
% 0.11/0.39 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.11/0.39 tff(17,plain,
% 0.11/0.39 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.11/0.39 tff(18,plain,
% 0.11/0.39 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.11/0.39 tff(19,plain,(
% 0.11/0.39 ~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[18])).
% 0.11/0.39 tff(20,plain,
% 0.11/0.39 (~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.11/0.39 tff(21,plain,
% 0.11/0.39 (convergent_lines(X!2, Y!1)),
% 0.11/0.39 inference(or_elim,[status(thm)],[20])).
% 0.11/0.39 tff(22,plain,
% 0.11/0.39 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(23,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.11/0.39 tff(24,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(25,plain,
% 0.11/0.39 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(26,plain,
% 0.11/0.39 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.11/0.39 tff(27,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.11/0.39 tff(30,plain,(
% 0.11/0.39 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[29])).
% 0.11/0.39 tff(31,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.11/0.39 tff(32,plain,
% 0.11/0.39 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(33,plain,
% 0.11/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.39 tff(35,plain,
% 0.11/0.39 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.11/0.39 tff(36,plain,
% 0.11/0.39 (apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.11/0.39 inference(or_elim,[status(thm)],[20])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(38,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.11/0.40 tff(39,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(40,plain,
% 0.11/0.40 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(41,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.11/0.40 tff(42,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.11/0.40 tff(43,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.11/0.40 tff(44,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.11/0.40 tff(45,plain,(
% 0.11/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.11/0.40 inference(skolemize,[status(sab)],[44])).
% 0.11/0.40 tff(46,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.11/0.40 tff(47,plain,
% 0.11/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(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)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(Z!0, X!2))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(48,plain,
% 0.11/0.40 ((distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))) <=> ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(Z!0, X!2))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(49,plain,
% 0.11/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(Z!0, X!2)))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[48])).
% 0.11/0.40 tff(50,plain,
% 0.11/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(Z!0, X!2))),
% 0.11/0.40 inference(transitivity,[status(thm)],[49, 47])).
% 0.11/0.40 tff(51,plain,
% 0.11/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(52,plain,
% 0.11/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(Z!0, X!2)),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.11/0.40 tff(53,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[52, 46, 36, 35, 10])).
% 0.11/0.40 tff(54,plain,(distinct_lines(Z!0, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.40 tff(55,assumption,(~distinct_lines(Y!1, Z!0)), introduced(assumption)).
% 0.11/0.40 tff(56,assumption,(~convergent_lines(X!2, Z!0)), introduced(assumption)).
% 0.11/0.40 tff(57,plain,
% 0.11/0.40 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(58,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.11/0.40 tff(59,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(60,plain,
% 0.11/0.40 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(61,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.11/0.40 tff(62,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.11/0.40 tff(63,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.11/0.40 tff(64,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.11/0.40 tff(65,plain,(
% 0.11/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.11/0.40 inference(skolemize,[status(sab)],[64])).
% 0.11/0.40 tff(66,plain,
% 0.11/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.11/0.40 tff(67,plain,
% 0.11/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | (~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, Z!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(Y!1, Z!0) | (~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, Z!0))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(68,plain,
% 0.11/0.40 ((distinct_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1))) <=> (distinct_lines(Y!1, Z!0) | (~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, Z!0))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(69,plain,
% 0.11/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | (~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, Z!0)))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[68])).
% 0.11/0.40 tff(70,plain,
% 0.11/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(Y!1, Z!0) | (~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, Z!0))),
% 0.11/0.40 inference(transitivity,[status(thm)],[69, 67])).
% 0.11/0.40 tff(71,plain,
% 0.11/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(72,plain,
% 0.11/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(Y!1, Z!0) | (~convergent_lines(X!2, Y!1)) | convergent_lines(X!2, Z!0)),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.11/0.40 tff(73,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[72, 66, 55, 21, 56])).
% 0.11/0.40 tff(74,plain,(convergent_lines(X!2, Z!0) | distinct_lines(Y!1, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.40 tff(75,plain,
% 0.11/0.40 (convergent_lines(X!2, Z!0)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[74, 55])).
% 0.11/0.40 tff(76,plain,
% 0.11/0.40 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(77,plain,
% 0.11/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.11/0.40 tff(78,plain,
% 0.11/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(79,plain,
% 0.11/0.40 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(80,plain,
% 0.11/0.40 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.11/0.40 tff(81,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.11/0.40 tff(82,plain,
% 0.11/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.11/0.40 tff(83,plain,
% 0.11/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.11/0.40 tff(84,plain,(
% 0.11/0.40 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.11/0.40 inference(skolemize,[status(sab)],[83])).
% 0.11/0.40 tff(85,plain,
% 0.11/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.11/0.40 tff(86,plain,
% 0.11/0.40 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(87,plain,
% 0.11/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(88,plain,
% 0.11/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.11/0.40 tff(89,plain,
% 0.11/0.40 (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[88, 85, 75])).
% 0.11/0.40 tff(90,plain,
% 0.11/0.40 (((~![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, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, 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, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(91,plain,
% 0.11/0.40 ((~![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, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(92,plain,
% 0.11/0.40 ((~![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, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.11/0.40 tff(93,plain,
% 0.11/0.40 (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[92, 46, 55, 89])).
% 0.11/0.40 tff(94,plain,
% 0.11/0.40 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(95,plain,
% 0.11/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(96,plain,
% 0.11/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.11/0.41 tff(97,plain,
% 0.11/0.41 (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[96, 31, 75])).
% 0.11/0.41 tff(98,plain,
% 0.11/0.41 (^[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))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(99,plain,
% 0.11/0.41 (![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)))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[98])).
% 0.11/0.41 tff(100,plain,
% 0.11/0.41 (![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)))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(101,plain,
% 0.11/0.41 (^[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)))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(102,plain,
% 0.11/0.41 (![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)))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[101])).
% 0.11/0.41 tff(103,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.11/0.41 tff(104,plain,
% 0.11/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.11/0.41 tff(105,plain,
% 0.11/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.11/0.41 tff(106,plain,(
% 0.11/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.11/0.41 inference(skolemize,[status(sab)],[105])).
% 0.11/0.41 tff(107,plain,
% 0.11/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.11/0.41 tff(108,plain,
% 0.11/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | (~distinct_lines(Y!1, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Y!1, Y!1)))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(109,plain,
% 0.11/0.41 ((distinct_lines(Y!1, Z!0) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Y!1, Y!1))) <=> (distinct_lines(Y!1, Z!0) | (~distinct_lines(Y!1, Y!1)))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(110,plain,
% 0.11/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Y!1, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | (~distinct_lines(Y!1, Y!1))))),
% 0.11/0.41 inference(monotonicity,[status(thm)],[109])).
% 0.11/0.41 tff(111,plain,
% 0.11/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Y!1, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Y!1, Y!1)))),
% 0.11/0.41 inference(transitivity,[status(thm)],[110, 108])).
% 0.11/0.41 tff(112,plain,
% 0.11/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Y!1, Y!1)))),
% 0.11/0.41 inference(quant_inst,[status(thm)],[])).
% 0.11/0.41 tff(113,plain,
% 0.11/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Y!1, Y!1))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.11/0.41 tff(114,plain,
% 0.11/0.41 (~distinct_lines(Y!1, Y!1)),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[113, 107, 55])).
% 0.11/0.41 tff(115,plain,
% 0.11/0.41 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(116,plain,
% 0.11/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[115])).
% 0.11/0.41 tff(117,plain,
% 0.11/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(118,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.11/0.41 tff(119,plain,
% 0.11/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.11/0.41 tff(120,plain,(
% 0.11/0.41 ![X: $i] : (~convergent_lines(X, X))),
% 0.11/0.41 inference(skolemize,[status(sab)],[119])).
% 0.11/0.41 tff(121,plain,
% 0.11/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.11/0.41 tff(122,plain,
% 0.11/0.41 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!2, X!2))),
% 0.11/0.41 inference(quant_inst,[status(thm)],[])).
% 0.11/0.41 tff(123,plain,
% 0.11/0.41 (~convergent_lines(X!2, X!2)),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.11/0.41 tff(124,assumption,(~distinct_lines(Y!1, X!2)), introduced(assumption)).
% 0.11/0.41 tff(125,plain,
% 0.11/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(126,plain,
% 0.11/0.41 ((distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(127,plain,
% 0.11/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)))),
% 0.11/0.41 inference(monotonicity,[status(thm)],[126])).
% 0.11/0.41 tff(128,plain,
% 0.11/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.11/0.41 inference(transitivity,[status(thm)],[127, 125])).
% 0.11/0.41 tff(129,plain,
% 0.11/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))),
% 0.11/0.41 inference(quant_inst,[status(thm)],[])).
% 0.11/0.41 tff(130,plain,
% 0.11/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[130, 66, 21, 124, 123])).
% 0.19/0.41 tff(132,plain,(distinct_lines(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(133,assumption,(~distinct_lines(X!2, Y!1)), introduced(assumption)).
% 0.19/0.41 tff(134,assumption,(~distinct_lines(Y!1, Y!1)), introduced(assumption)).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Y!1) | distinct_lines(X!2, Y!1) | (~distinct_lines(Y!1, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Y!1, Y!1) | distinct_lines(X!2, Y!1) | (~distinct_lines(Y!1, X!2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 ((distinct_lines(X!2, Y!1) | distinct_lines(Y!1, Y!1) | (~distinct_lines(Y!1, X!2))) <=> (distinct_lines(Y!1, Y!1) | distinct_lines(X!2, Y!1) | (~distinct_lines(Y!1, X!2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Y!1) | distinct_lines(Y!1, Y!1) | (~distinct_lines(Y!1, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Y!1) | distinct_lines(X!2, Y!1) | (~distinct_lines(Y!1, X!2))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[136])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Y!1) | distinct_lines(Y!1, Y!1) | (~distinct_lines(Y!1, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Y!1, Y!1) | distinct_lines(X!2, Y!1) | (~distinct_lines(Y!1, X!2)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[137, 135])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Y!1) | distinct_lines(Y!1, Y!1) | (~distinct_lines(Y!1, X!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Y!1, Y!1) | distinct_lines(X!2, Y!1) | (~distinct_lines(Y!1, X!2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[140, 107, 134, 133, 132])).
% 0.19/0.41 tff(142,plain,(distinct_lines(X!2, Y!1) | distinct_lines(Y!1, Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 (distinct_lines(X!2, Y!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[142, 114])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[146, 85, 21])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[148])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(151,plain,
% 0.19/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[150])).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(154,plain,
% 0.19/0.41 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[153])).
% 0.19/0.41 tff(155,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.19/0.41 tff(156,plain,
% 0.19/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.41 tff(157,plain,
% 0.19/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.19/0.41 tff(158,plain,(
% 0.19/0.41 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[157])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[159, 149])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 (((~![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) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | 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))))) <=> ((~![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) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | 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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 ((apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, Y!1))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | 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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(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(X!2, Y!1), X!2) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | 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)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[162])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(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(X!2, Y!1), X!2) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | 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))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[163, 161])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, Y!1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 ((~![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) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | 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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[166, 160, 147, 35, 143, 97, 93])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[168])).
% 0.19/0.42 tff(170,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(171,plain,
% 0.19/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | apart_point_and_line(Z, Y)) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))))), rewrite((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(172,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[171])).
% 0.19/0.42 tff(173,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.19/0.42 tff(174,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.19/0.42 tff(175,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.19/0.42 tff(176,plain,(
% 0.19/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[175])).
% 0.19/0.42 tff(177,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.19/0.42 tff(178,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(179,plain,
% 0.19/0.42 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))) <=> ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(180,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[179])).
% 0.19/0.42 tff(181,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[180, 178])).
% 0.19/0.42 tff(182,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(183,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.19/0.42 tff(184,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[183, 177, 36, 89, 167])).
% 0.19/0.42 tff(185,plain,(distinct_lines(Y!1, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(186,plain,
% 0.19/0.42 ((~(~((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0))))) <=> ((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 ((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) <=> (~((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 ((~(distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0))) <=> (~(~((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[187])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 ((~(distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0))) <=> ((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[188, 186])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 (~(distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0))),
% 0.19/0.43 inference(or_elim,[status(thm)],[20])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 ((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 (~distinct_lines(X!2, Z!0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[191, 185])).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Z!0) | (~distinct_lines(Z!0, X!2)) | distinct_lines(Z!0, Z!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, Z!0) | (~distinct_lines(Z!0, X!2)) | distinct_lines(Z!0, Z!0))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 ((distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2))) <=> (distinct_lines(X!2, Z!0) | (~distinct_lines(Z!0, X!2)) | distinct_lines(Z!0, Z!0))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Z!0) | (~distinct_lines(Z!0, X!2)) | distinct_lines(Z!0, Z!0)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[194])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, Z!0) | (~distinct_lines(Z!0, X!2)) | distinct_lines(Z!0, Z!0))),
% 0.19/0.43 inference(transitivity,[status(thm)],[195, 193])).
% 0.19/0.43 tff(197,plain,
% 0.19/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(198,plain,
% 0.19/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, Z!0) | (~distinct_lines(Z!0, X!2)) | distinct_lines(Z!0, Z!0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[198, 107, 192, 54, 9])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------