%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO190+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:05:50 AM UTC 2025
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GEO190+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.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 14:41:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(distinct_points_type, type, (
% 0.20/0.42 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.42 tff(tptp_fun_X_2_type, type, (
% 0.20/0.42 tptp_fun_X_2: $i)).
% 0.20/0.42 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.42 tptp_fun_Y_1: $i)).
% 0.20/0.42 tff(intersection_point_type, type, (
% 0.20/0.42 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.42 tff(line_connecting_type, type, (
% 0.20/0.42 line_connecting: ( $i * $i ) > $i)).
% 0.20/0.42 tff(apart_point_and_line_type, type, (
% 0.20/0.42 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.42 tff(convergent_lines_type, type, (
% 0.20/0.42 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.42 tff(distinct_lines_type, type, (
% 0.20/0.42 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.42 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.42 tptp_fun_Z_0: $i)).
% 0.20/0.42 tff(incident_point_and_line_type, type, (
% 0.20/0.42 incident_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.42 tff(1,assumption,(distinct_points(Y!1, X!2)), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.42 tff(7,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')).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.42 tff(10,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[9])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(Y!1, X!2)) | (~apart_point_and_line(X!2, line_connecting(Y!1, X!2))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(Y!1, X!2)) | (~apart_point_and_line(X!2, line_connecting(Y!1, X!2))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(Y!1, X!2)) | (~apart_point_and_line(X!2, line_connecting(Y!1, X!2))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(Y!1, X!2)) | (~apart_point_and_line(X!2, line_connecting(Y!1, X!2)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ((~distinct_points(Y!1, X!2)) | (~apart_point_and_line(X!2, line_connecting(Y!1, X!2)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (~apart_point_and_line(X!2, line_connecting(Y!1, X!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.20/0.42 tff(17,assumption,(~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))), introduced(assumption)).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : trans(rewrite((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), rewrite((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), ((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.42 tff(23,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.42 tff(26,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[25])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) <=> incident_point_and_line(Z!0, line_connecting(Y!1, X!2))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (~(apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) <=> incident_point_and_line(Z!0, line_connecting(Y!1, X!2)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Z, line_connecting(Y, X)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Z, line_connecting(Y, X))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & incident_point_and_line(Z, line_connecting(X, Y))) => incident_point_and_line(Z, line_connecting(Y, X)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Z, line_connecting(Y, X))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(32,axiom,(~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & incident_point_and_line(Z, line_connecting(X, Y))) => incident_point_and_line(Z, line_connecting(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Z, line_connecting(Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Z, line_connecting(Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Z, line_connecting(Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & incident_point_and_line(Z, line_connecting(X, Y)))) | incident_point_and_line(Z, line_connecting(Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.20/0.42 tff(37,plain,(
% 0.20/0.42 ~((~(distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & incident_point_and_line(Z!0, line_connecting(X!2, Y!1)))) | incident_point_and_line(Z!0, line_connecting(Y!1, X!2)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[36])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (~incident_point_and_line(Z!0, line_connecting(Y!1, X!2))),
% 0.20/0.42 inference(or_elim,[status(thm)],[37])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) <=> incident_point_and_line(Z!0, line_connecting(Y!1, X!2))) | apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | incident_point_and_line(Z!0, line_connecting(Y!1, X!2))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 ((apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) <=> incident_point_and_line(Z!0, line_connecting(Y!1, X!2))) | apart_point_and_line(Z!0, line_connecting(Y!1, X!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (apart_point_and_line(Z!0, line_connecting(Y!1, X!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[40, 29])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> incident_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (~(apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> incident_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[42, 27])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & incident_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.20/0.42 inference(or_elim,[status(thm)],[37])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (incident_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.20/0.42 inference(and_elim,[status(thm)],[44])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 ((apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> incident_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~incident_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 ((apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) <=> incident_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[47, 43])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.42 tff(54,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.42 tff(57,plain,(
% 0.20/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[56])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (((~![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(Z!0, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, X!2))) | distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, X!2))) | distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 ((distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, X!2)))) <=> (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, X!2))) | distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (((~![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(Y!1, X!2), line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(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(Z!0, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, X!2))) | distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (((~![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(Y!1, X!2), line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(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(Z!0, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, X!2))) | distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[61, 59])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 ((~![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(Y!1, X!2), line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, X!2))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, X!2))) | distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[64, 58, 48, 41, 17])).
% 0.20/0.43 tff(66,plain,(distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.43 tff(72,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.43 tff(75,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.43 inference(skolemize,[status(sab)],[74])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[79, 76, 66])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.43 tff(86,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.43 tff(89,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[88])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[93, 90, 80])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.43 tff(100,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.20/0.43 tff(103,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[102])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[107, 104, 80])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (distinct_points(X!2, Y!1)),
% 0.20/0.43 inference(and_elim,[status(thm)],[44])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.43 tff(115,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')).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.43 tff(118,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[117])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[122, 119, 109])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))))), rewrite((~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.43 tff(131,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.20/0.43 tff(134,plain,(
% 0.20/0.43 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[133])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 ((apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))) <=> (apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[138])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[139, 137])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 (apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[142, 136, 123, 66, 108, 94])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 (~distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[143, 16])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(Y!1, X!2)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, X!2))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(Y!1, X!2)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, X!2))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(Y!1, X!2)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, X!2))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(Y!1, X!2)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, X!2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 ((~distinct_points(Y!1, X!2)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, X!2)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[147, 119])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (~apart_point_and_line(Y!1, line_connecting(Y!1, X!2))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[148, 1])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[152, 11, 109])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 ((apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))) <=> (apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[155])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[156, 154])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | (~distinct_lines(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(X!2, Y!1)) | apart_point_and_line(intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)), line_connecting(Y!1, X!2)) | (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 (apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[159, 136, 153, 66, 108, 94])).
% 0.20/0.45 tff(161,plain,
% 0.20/0.45 (~distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[160, 149])).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | distinct_points(Y, Z)) <=> (distinct_points(Y, Z) | distinct_points(X, Z))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))))), rewrite((distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(166,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.45 tff(167,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')).
% 0.20/0.45 tff(168,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.45 tff(169,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.20/0.45 tff(170,plain,(
% 0.20/0.45 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[169])).
% 0.20/0.45 tff(171,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.20/0.45 tff(172,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(Y!1, X!2)) | distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Y!1, X!2)) | distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(173,plain,
% 0.20/0.45 ((distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(Y!1, X!2))) <=> ((~distinct_points(Y!1, X!2)) | distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(174,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(Y!1, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(Y!1, X!2)) | distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.45 tff(175,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(Y!1, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Y!1, X!2)) | distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[174, 172])).
% 0.20/0.45 tff(176,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | (~distinct_points(Y!1, X!2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(177,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Y!1, X!2)) | distinct_points(Y!1, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1))) | distinct_points(X!2, intersection_point(line_connecting(Y!1, X!2), line_connecting(X!2, Y!1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.45 tff(178,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[177, 171, 1, 161, 144])).
% 0.20/0.45 tff(179,plain,(~distinct_points(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(180,assumption,(~distinct_points(X!2, X!2)), introduced(assumption)).
% 0.20/0.45 tff(181,assumption,(~distinct_points(Y!1, X!2)), introduced(assumption)).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!2, Y!1)) | distinct_points(Y!1, X!2) | distinct_points(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | distinct_points(Y!1, X!2) | distinct_points(X!2, X!2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 ((distinct_points(Y!1, X!2) | distinct_points(X!2, X!2) | (~distinct_points(X!2, Y!1))) <=> ((~distinct_points(X!2, Y!1)) | distinct_points(Y!1, X!2) | distinct_points(X!2, X!2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, X!2) | distinct_points(X!2, X!2) | (~distinct_points(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!2, Y!1)) | distinct_points(Y!1, X!2) | distinct_points(X!2, X!2)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[183])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, X!2) | distinct_points(X!2, X!2) | (~distinct_points(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | distinct_points(Y!1, X!2) | distinct_points(X!2, X!2))),
% 0.20/0.46 inference(transitivity,[status(thm)],[184, 182])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, X!2) | distinct_points(X!2, X!2) | (~distinct_points(X!2, Y!1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | distinct_points(Y!1, X!2) | distinct_points(X!2, X!2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[187, 171, 109, 181, 180])).
% 0.20/0.46 tff(189,plain,(distinct_points(Y!1, X!2) | distinct_points(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 (distinct_points(X!2, X!2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[189, 179])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[191])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(194,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart1')).
% 0.20/0.46 tff(195,plain,
% 0.20/0.46 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.20/0.46 tff(196,plain,(
% 0.20/0.46 ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.46 inference(skolemize,[status(sab)],[195])).
% 0.20/0.46 tff(197,plain,
% 0.20/0.46 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.20/0.46 tff(198,plain,
% 0.20/0.46 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(X!2, X!2))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(199,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[198, 197, 190])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------