%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO200+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.11s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO200+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.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 14:40:35 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(distinct_points_type, type, (
% 0.11/0.38 distinct_points: ( $i * $i ) > $o)).
% 0.11/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.11/0.38 tptp_fun_Y_0: $i)).
% 0.11/0.38 tff(tptp_fun_X_1_type, type, (
% 0.11/0.38 tptp_fun_X_1: $i)).
% 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(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] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(4,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![X: $i] : (~distinct_points(X, X))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.38 tff(6,plain,(
% 0.11/0.38 ![X: $i] : (~distinct_points(X, X))),
% 0.11/0.38 inference(skolemize,[status(sab)],[5])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![X: $i] : (~distinct_points(X, X))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!0, Y!0))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (~distinct_points(Y!0, Y!0)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0))) | distinct_points(Y!0, Y!0)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 ((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (((~distinct_points(Y!0, Y!0)) | (~distinct_points(Y!0, X!1))) | distinct_points(Y!0, Y!0)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 ((~distinct_points(Y!0, Y!0)) | (~distinct_points(Y!0, X!1))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[12, 9])).
% 0.11/0.38 tff(14,assumption,(apart_point_and_line(Y!0, line_connecting(Y!0, X!1))), introduced(assumption)).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(X!1, X!1))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (~distinct_points(X!1, X!1)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[15, 7])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))) <=> (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : (distinct_points(X, Y) => (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))) <=> (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(19,axiom,(~![X: $i, Y: $i] : (distinct_points(X, Y) => (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~distinct_lines(line_connecting(X, Y), line_connecting(Y, X))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.11/0.38 tff(24,plain,(
% 0.11/0.38 ~((~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[23])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (distinct_points(X!1, Y!0)),
% 0.11/0.38 inference(or_elim,[status(thm)],[24])).
% 0.11/0.38 tff(26,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(27,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)],[26])).
% 0.11/0.38 tff(28,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(29,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(30,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)],[29])).
% 0.11/0.38 tff(31,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/GEO008+0.ax','apart4')).
% 0.11/0.38 tff(32,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)],[31, 30])).
% 0.11/0.38 tff(33,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)],[32, 28])).
% 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(skolemize,[status(sab)],[33])).
% 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, 27])).
% 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)))) | ((~distinct_points(X!1, Y!0)) | distinct_points(X!1, X!1) | distinct_points(Y!0, 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(X!1, X!1) | distinct_points(Y!0, X!1))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 ((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(X!1, X!1) | distinct_points(Y!0, X!1))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 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(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(X!1, X!1) | distinct_points(Y!0, X!1)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[37])).
% 0.11/0.38 tff(39,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!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(X!1, X!1) | distinct_points(Y!0, X!1))),
% 0.11/0.38 inference(transitivity,[status(thm)],[38, 36])).
% 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!0, X!1) | distinct_points(X!1, X!1) | (~distinct_points(X!1, Y!0)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 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(X!1, Y!0)) | distinct_points(X!1, X!1) | distinct_points(Y!0, X!1)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (distinct_points(Y!0, X!1)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[41, 35, 25, 16])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (^[X: $i, Y: $i, Z: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(Z, X) & distinct_points(Z, Y)) <=> (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))), rewrite(((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[45])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))) <=> ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> (distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))))), rewrite((distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[48])).
% 0.11/0.38 tff(50,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.11/0.38 tff(53,plain,(
% 0.11/0.38 ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[52])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, Y!0)) | (~distinct_points(Y!0, X!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, Y!0)) | (~distinct_points(Y!0, X!1)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, Y!0)) | (~distinct_points(Y!0, X!1)))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(Y!0, X!1)) | (~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))) | (~((~distinct_points(Y!0, Y!0)) | (~distinct_points(Y!0, X!1))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[58, 55, 42, 14, 13])).
% 0.11/0.38 tff(60,plain,(~apart_point_and_line(Y!0, line_connecting(Y!0, X!1))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 (((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!1))) | distinct_points(X!1, X!1)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(62,plain,
% 0.11/0.39 ((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!1))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[61, 16])).
% 0.11/0.39 tff(63,plain,
% 0.11/0.39 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))) | (~((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))) | (~((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!1)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(64,plain,
% 0.11/0.39 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))) | (~((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!1)))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(65,plain,
% 0.11/0.39 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))) | (~((~distinct_points(X!1, Y!0)) | (~distinct_points(X!1, X!1))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.11/0.39 tff(66,plain,
% 0.11/0.39 ((~distinct_points(Y!0, X!1)) | (~apart_point_and_line(X!1, line_connecting(Y!0, X!1)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[65, 55, 62])).
% 0.11/0.39 tff(67,plain,
% 0.11/0.39 (~apart_point_and_line(X!1, line_connecting(Y!0, X!1))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[66, 42])).
% 0.11/0.39 tff(68,plain,
% 0.11/0.39 (((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!0))) | distinct_points(X!1, X!1)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(69,plain,
% 0.11/0.39 ((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!0))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[68, 16])).
% 0.11/0.39 tff(70,plain,
% 0.11/0.39 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))) | (~((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))) | (~((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!0)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(71,plain,
% 0.11/0.39 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))) | (~((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!0)))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(72,plain,
% 0.11/0.39 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!1, Y!0)) | (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))) | (~((~distinct_points(X!1, X!1)) | (~distinct_points(X!1, Y!0))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.11/0.39 tff(73,plain,
% 0.11/0.39 (~apart_point_and_line(X!1, line_connecting(X!1, Y!0))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[72, 55, 25, 69])).
% 0.11/0.39 tff(74,plain,
% 0.11/0.39 (distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))),
% 0.11/0.39 inference(or_elim,[status(thm)],[24])).
% 0.11/0.39 tff(75,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_points(X, Y)) | (~distinct_lines(U, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(76,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(quant_intro,[status(thm)],[75])).
% 0.11/0.39 tff(77,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_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(78,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(quant_intro,[status(thm)],[77])).
% 0.11/0.39 tff(79,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(80,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(81,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)],[80])).
% 0.11/0.39 tff(82,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/GEO008+0.ax','cu1')).
% 0.11/0.39 tff(83,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)],[82, 81])).
% 0.11/0.39 tff(84,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)],[83, 79])).
% 0.11/0.39 tff(85,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)],[84])).
% 0.11/0.39 tff(86,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)],[85, 78])).
% 0.11/0.39 tff(87,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)],[86, 76])).
% 0.11/0.39 tff(88,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)))) | ((~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | 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)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | 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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(89,plain,
% 0.11/0.39 ((apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1)))) <=> ((~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | 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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(90,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)))) | (apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(X!1, Y!0)) | (~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_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | 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))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[89])).
% 0.11/0.39 tff(91,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)))) | (apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(X!1, Y!0)) | (~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_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | 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)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[90, 88])).
% 0.19/0.40 tff(92,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_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0)) | apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(X!1, line_connecting(X!1, Y!0)) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(93,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_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(X!1, Y!0)) | (~distinct_lines(line_connecting(X!1, Y!0), line_connecting(Y!0, X!1))) | 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))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (apart_point_and_line(X!1, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[93, 87, 25, 74, 73])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (apart_point_and_line(Y!0, line_connecting(Y!0, X!1)) | apart_point_and_line(Y!0, line_connecting(X!1, Y!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 67])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (apart_point_and_line(Y!0, line_connecting(X!1, Y!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[95, 60])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!1, Y!0)) | (~apart_point_and_line(Y!0, line_connecting(X!1, Y!0))) | (~((~distinct_points(Y!0, X!1)) | (~distinct_points(Y!0, Y!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[99, 55, 25, 96, 11])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------