%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO200+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:05:54 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO200+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:41:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(distinct_lines_type, type, (
% 0.19/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.38 tff(line_connecting_type, type, (
% 0.19/0.38 line_connecting: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_X_1_type, type, (
% 0.19/0.38 tptp_fun_X_1: $i)).
% 0.19/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.38 tptp_fun_Y_0: $i)).
% 0.19/0.38 tff(equal_lines_type, type, (
% 0.19/0.38 equal_lines: ( $i * $i ) > $o)).
% 0.19/0.38 tff(distinct_points_type, type, (
% 0.19/0.38 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.38 tff(apart_point_and_line_type, type, (
% 0.19/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : refl((~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.38 tff(6,axiom,(![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax2')).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.38 tff(9,plain,(
% 0.19/0.38 ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))) | (~(distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1)) <=> equal_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (~(distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1)) <=> equal_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | equal_lines(line_connecting(X, Y), line_connecting(Y, X)))) <=> (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | equal_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (distinct_points(X, Y) => equal_lines(line_connecting(X, Y), line_connecting(Y, X)))) <=> (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | equal_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(15,axiom,(~![X: $i, Y: $i] : (distinct_points(X, Y) => equal_lines(line_connecting(X, Y), line_connecting(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | equal_lines(line_connecting(X, Y), line_connecting(Y, X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | equal_lines(line_connecting(X, Y), line_connecting(Y, X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | equal_lines(line_connecting(X, Y), line_connecting(Y, X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | equal_lines(line_connecting(X, Y), line_connecting(Y, X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.19/0.38 tff(20,plain,(
% 0.19/0.38 ~((~distinct_points(X!1, Y!0)) | equal_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (~equal_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))),
% 0.19/0.38 inference(or_elim,[status(thm)],[20])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 ((distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1)) <=> equal_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1)) | equal_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 ((distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1)) <=> equal_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[23, 12])).
% 0.19/0.38 tff(25,assumption,(distinct_points(X!1, X!1)), introduced(assumption)).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(29,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart1')).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.38 tff(31,plain,(
% 0.19/0.38 ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.38 inference(skolemize,[status(sab)],[30])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(X!1, X!1))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[33, 32, 25])).
% 0.19/0.38 tff(35,plain,(~distinct_points(X!1, X!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(36,assumption,(~distinct_points(X!1, X!1)), introduced(assumption)).
% 0.19/0.38 tff(37,assumption,(~distinct_points(Y!0, X!1)), introduced(assumption)).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (distinct_points(X!1, Y!0)),
% 0.19/0.38 inference(or_elim,[status(thm)],[20])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.38 tff(44,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')).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.38 tff(47,plain,(
% 0.19/0.38 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[46])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 ((distinct_points(Y!0, X!1) | distinct_points(X!1, X!1) | (~distinct_points(X!1, Y!0))) <=> ((~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!0, X!1) | distinct_points(X!1, X!1) | (~distinct_points(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!0, X!1) | distinct_points(X!1, X!1) | (~distinct_points(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1))),
% 0.19/0.38 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!0, X!1) | distinct_points(X!1, X!1) | (~distinct_points(X!1, Y!0)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!1, Y!0)) | distinct_points(Y!0, X!1) | distinct_points(X!1, X!1)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[54, 48, 38, 37, 36])).
% 0.19/0.38 tff(56,plain,(distinct_points(X!1, X!1) | distinct_points(Y!0, X!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (distinct_points(Y!0, X!1)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[56, 35])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.38 tff(63,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')).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.38 tff(66,plain,(
% 0.19/0.38 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[65])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(70,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[71, 57])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(76,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.39 tff(78,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')).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.19/0.39 tff(81,plain,(
% 0.19/0.39 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[80])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[86, 57])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[90, 82, 38])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[94, 67, 38])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 (^[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))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.39 tff(103,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.19/0.39 tff(106,plain,(
% 0.19/0.39 ![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))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[105])).
% 0.19/0.39 tff(107,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.19/0.39 tff(108,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[107, 97])).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 (((~![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!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!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!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(110,plain,
% 0.19/0.39 ((apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | (~distinct_points(Y!0, X!1))) <=> (apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(111,plain,
% 0.19/0.39 (((~![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(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | (~distinct_points(Y!0, X!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!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[110])).
% 0.19/0.39 tff(112,plain,
% 0.19/0.39 (((~![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(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | (~distinct_points(Y!0, X!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!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[111, 109])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 ((~![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(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | (~distinct_points(Y!0, X!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[114, 108, 95, 91, 57, 87, 72, 24])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------