%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO204+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:05:55 AM UTC 2025
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO204+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.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 14:40:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(apart_point_and_line_type, type, (
% 0.11/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.11/0.38 tff(line_connecting_type, type, (
% 0.11/0.38 line_connecting: ( $i * $i ) > $i)).
% 0.11/0.38 tff(tptp_fun_Z_0_type, type, (
% 0.11/0.38 tptp_fun_Z_0: $i)).
% 0.11/0.38 tff(tptp_fun_X_2_type, type, (
% 0.11/0.38 tptp_fun_X_2: $i)).
% 0.11/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.38 tptp_fun_Y_1: $i)).
% 0.11/0.38 tff(distinct_points_type, type, (
% 0.11/0.38 distinct_points: ( $i * $i ) > $o)).
% 0.11/0.38 tff(equal_points_type, type, (
% 0.11/0.38 equal_points: ( $i * $i ) > $o)).
% 0.11/0.38 tff(equal_lines_type, type, (
% 0.11/0.38 equal_lines: ( $i * $i ) > $o)).
% 0.11/0.38 tff(distinct_lines_type, type, (
% 0.11/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 (^[X: $i, Y: $i] : refl((~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (^[X: $i, Y: $i] : trans(rewrite((equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y)))), rewrite((~(distinct_points(X, Y) <=> equal_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y)))), ((equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> (~(distinct_points(X, Y) <=> equal_points(X, Y)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.38 tff(6,axiom,(![X: $i, Y: $i] : (equal_points(X, Y) <=> (~distinct_points(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax1')).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.38 tff(9,plain,(
% 0.11/0.38 ![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[8])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : (~(distinct_points(X, Y) <=> equal_points(X, Y)))) | (~(distinct_points(Y!1, Z!0) <=> equal_points(Y!1, Z!0)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (~(distinct_points(Y!1, Z!0) <=> equal_points(Y!1, Z!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & equal_points(Y, Z))) | (distinct_points(X, Z) & equal_lines(line_connecting(X, Y), line_connecting(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & equal_points(Y, Z))) | (distinct_points(X, Z) & equal_lines(line_connecting(X, Y), line_connecting(X, Z)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : ((distinct_points(X, Y) & equal_points(Y, Z)) => (distinct_points(X, Z) & equal_lines(line_connecting(X, Y), line_connecting(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & equal_points(Y, Z))) | (distinct_points(X, Z) & equal_lines(line_connecting(X, Y), line_connecting(X, Z)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(15,axiom,(~![X: $i, Y: $i, Z: $i] : ((distinct_points(X, Y) & equal_points(Y, Z)) => (distinct_points(X, Z) & equal_lines(line_connecting(X, Y), line_connecting(X, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & equal_points(Y, Z))) | (distinct_points(X, Z) & equal_lines(line_connecting(X, Y), line_connecting(X, Z))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & equal_points(Y, Z))) | (distinct_points(X, Z) & equal_lines(line_connecting(X, Y), line_connecting(X, Z))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & equal_points(Y, Z))) | (distinct_points(X, Z) & equal_lines(line_connecting(X, Y), line_connecting(X, Z))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & equal_points(Y, Z))) | (distinct_points(X, Z) & equal_lines(line_connecting(X, Y), line_connecting(X, Z))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.11/0.38 tff(20,plain,(
% 0.11/0.38 ~((~(distinct_points(X!2, Y!1) & equal_points(Y!1, Z!0))) | (distinct_points(X!2, Z!0) & equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[19])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (distinct_points(X!2, Y!1) & equal_points(Y!1, Z!0)),
% 0.11/0.38 inference(or_elim,[status(thm)],[20])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (equal_points(Y!1, Z!0)),
% 0.11/0.38 inference(and_elim,[status(thm)],[21])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 ((distinct_points(Y!1, Z!0) <=> equal_points(Y!1, Z!0)) | (~distinct_points(Y!1, Z!0)) | (~equal_points(Y!1, Z!0))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 ((distinct_points(Y!1, Z!0) <=> equal_points(Y!1, Z!0)) | (~distinct_points(Y!1, Z!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (~distinct_points(Y!1, Z!0)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[24, 12])).
% 0.11/0.38 tff(26,assumption,(~distinct_points(X!2, Z!0)), introduced(assumption)).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (distinct_points(X!2, Y!1)),
% 0.11/0.38 inference(and_elim,[status(thm)],[21])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.11/0.38 tff(33,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart4')).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.11/0.38 tff(36,plain,(
% 0.11/0.38 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[35])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(X!2, Z!0) | (~distinct_points(X!2, Y!1)) | distinct_points(Y!1, Z!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | distinct_points(X!2, Z!0) | (~distinct_points(X!2, Y!1)) | distinct_points(Y!1, Z!0))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 ((distinct_points(Y!1, Z!0) | distinct_points(X!2, Z!0) | (~distinct_points(X!2, Y!1))) <=> (distinct_points(X!2, Z!0) | (~distinct_points(X!2, Y!1)) | distinct_points(Y!1, Z!0))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, Z!0) | distinct_points(X!2, Z!0) | (~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, Z!0) | (~distinct_points(X!2, Y!1)) | distinct_points(Y!1, Z!0)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[39])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, Z!0) | distinct_points(X!2, Z!0) | (~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, Z!0) | (~distinct_points(X!2, Y!1)) | distinct_points(Y!1, Z!0))),
% 0.11/0.38 inference(transitivity,[status(thm)],[40, 38])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, Z!0) | distinct_points(X!2, Z!0) | (~distinct_points(X!2, Y!1)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | distinct_points(X!2, Z!0) | (~distinct_points(X!2, Y!1)) | distinct_points(Y!1, Z!0)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[43, 37, 27, 26, 25])).
% 0.11/0.38 tff(45,plain,(distinct_points(X!2, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (![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))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 (![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))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (![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))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.11/0.38 tff(51,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.11/0.38 tff(54,plain,(
% 0.11/0.38 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[53])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[58, 55, 45])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[60])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[63])).
% 0.11/0.38 tff(65,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')).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.11/0.38 tff(68,plain,(
% 0.11/0.38 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[67])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(Y!1, Z!0) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | (~apart_point_and_line(Y!1, line_connecting(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)))) | distinct_points(Y!1, Z!0) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(Y!1, Z!0) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(Y!1, Z!0) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[72, 69, 25, 59])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 (^[X: $i, Y: $i] : refl((~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[74])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 (^[X: $i, Y: $i] : trans(rewrite((equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))), rewrite((~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))), ((equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[77])).
% 0.11/0.38 tff(79,axiom,(![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax2')).
% 0.11/0.38 tff(80,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.11/0.38 tff(81,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.11/0.38 tff(82,plain,(
% 0.11/0.38 ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[81])).
% 0.11/0.38 tff(83,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.11/0.38 tff(84,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))) | (~(distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) <=> equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(85,plain,
% 0.11/0.39 (~(distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) <=> equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.11/0.39 tff(86,plain,
% 0.11/0.39 ((~(~((~distinct_points(X!2, Z!0)) | (~equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))))) <=> ((~distinct_points(X!2, Z!0)) | (~equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(87,plain,
% 0.11/0.39 ((distinct_points(X!2, Z!0) & equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) <=> (~((~distinct_points(X!2, Z!0)) | (~equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(88,plain,
% 0.11/0.39 ((~(distinct_points(X!2, Z!0) & equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))) <=> (~(~((~distinct_points(X!2, Z!0)) | (~equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[87])).
% 0.11/0.39 tff(89,plain,
% 0.11/0.39 ((~(distinct_points(X!2, Z!0) & equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))) <=> ((~distinct_points(X!2, Z!0)) | (~equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[88, 86])).
% 0.11/0.39 tff(90,plain,
% 0.11/0.39 (~(distinct_points(X!2, Z!0) & equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))),
% 0.11/0.39 inference(or_elim,[status(thm)],[20])).
% 0.11/0.39 tff(91,plain,
% 0.11/0.39 ((~distinct_points(X!2, Z!0)) | (~equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.11/0.39 tff(92,plain,
% 0.11/0.39 (~equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[91, 45])).
% 0.11/0.39 tff(93,plain,
% 0.11/0.39 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) <=> equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(94,plain,
% 0.11/0.39 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) <=> equal_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.11/0.39 tff(95,plain,
% 0.11/0.39 (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[94, 85])).
% 0.11/0.39 tff(96,plain,
% 0.11/0.39 (^[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)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(97,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[96])).
% 0.11/0.39 tff(98,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(99,plain,
% 0.11/0.39 (^[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)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(100,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[99])).
% 0.11/0.39 tff(101,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.11/0.39 tff(102,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.11/0.39 tff(103,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.11/0.39 tff(104,plain,(
% 0.11/0.39 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[103])).
% 0.11/0.39 tff(105,plain,
% 0.11/0.39 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.11/0.39 tff(106,plain,
% 0.11/0.39 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(107,plain,
% 0.11/0.39 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(108,plain,
% 0.11/0.39 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.11/0.39 tff(109,plain,
% 0.11/0.39 (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[108, 105, 45])).
% 0.11/0.39 tff(110,plain,
% 0.11/0.39 (((~![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(111,plain,
% 0.11/0.39 ((~![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))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(112,plain,
% 0.11/0.39 ((~![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.11/0.39 tff(113,plain,
% 0.11/0.39 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[112, 105, 27])).
% 0.11/0.39 tff(114,plain,
% 0.11/0.39 (((~![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(115,plain,
% 0.11/0.39 ((~![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))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(116,plain,
% 0.11/0.39 ((~![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.11/0.39 tff(117,plain,
% 0.11/0.39 (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[116, 55, 27])).
% 0.11/0.39 tff(118,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(119,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[118])).
% 0.11/0.39 tff(120,plain,
% 0.11/0.39 (^[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)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(121,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[120])).
% 0.11/0.39 tff(122,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(123,plain,
% 0.11/0.39 (^[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))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(124,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[123])).
% 0.11/0.39 tff(125,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')).
% 0.11/0.39 tff(126,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.11/0.39 tff(127,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.11/0.39 tff(128,plain,(
% 0.11/0.39 ![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))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[127])).
% 0.11/0.39 tff(129,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.11/0.39 tff(130,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.11/0.39 tff(131,plain,
% 0.11/0.39 (((~![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)))) | ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(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_lines(U, V)) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(132,plain,
% 0.11/0.39 ((apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(X!2, Y!1))) <=> ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(133,plain,
% 0.11/0.39 (((~![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, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(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)))) | ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[132])).
% 0.11/0.40 tff(134,plain,
% 0.11/0.40 (((~![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, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(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)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)))),
% 0.11/0.40 inference(transitivity,[status(thm)],[133, 131])).
% 0.11/0.40 tff(135,plain,
% 0.11/0.40 ((~![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, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | (~distinct_points(X!2, Y!1)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(136,plain,
% 0.11/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.11/0.40 tff(137,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[136, 130, 27, 117, 113, 109, 95, 73])).
% 0.11/0.40 % SZS output end Proof
% 0.11/0.40 % E exiting
%------------------------------------------------------------------------------