%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO179+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:46 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO179+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.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 14:40:17 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(apart_point_and_line_type, type, (
% 0.12/0.36 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.36 tff(line_connecting_type, type, (
% 0.12/0.36 line_connecting: ( $i * $i ) > $i)).
% 0.12/0.36 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.36 tptp_fun_Y_1: $i)).
% 0.12/0.36 tff(tptp_fun_Z_0_type, type, (
% 0.12/0.36 tptp_fun_Z_0: $i)).
% 0.12/0.36 tff(distinct_lines_type, type, (
% 0.12/0.36 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.36 tff(tptp_fun_X_2_type, type, (
% 0.12/0.36 tptp_fun_X_2: $i)).
% 0.12/0.36 tff(distinct_points_type, type, (
% 0.12/0.36 distinct_points: ( $i * $i ) > $o)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(4,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.36 tff(6,plain,(
% 0.12/0.36 ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.36 inference(skolemize,[status(sab)],[5])).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Z!0, Z!0))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (~distinct_points(Z!0, Z!0)),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0))) | distinct_points(Z!0, Z!0)),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 ((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 ((~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 ((~![X: $i, Y: $i, Z: $i] : ((distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y))) => (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(14,axiom,(~![X: $i, Y: $i, Z: $i] : ((distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y))) => (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_lines(line_connecting(X, Y), line_connecting(Z, X)) & distinct_lines(line_connecting(X, Y), line_connecting(Z, Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.12/0.36 tff(19,plain,(
% 0.12/0.36 ~((~(distinct_points(X!2, Y!1) & apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) & distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))))),
% 0.12/0.36 inference(skolemize,[status(sab)],[18])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 (distinct_points(X!2, Y!1) & apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.12/0.36 inference(or_elim,[status(thm)],[19])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 (apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.12/0.36 inference(and_elim,[status(thm)],[20])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 (distinct_points(X!2, Y!1)),
% 0.12/0.36 inference(and_elim,[status(thm)],[20])).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (^[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))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(24,plain,
% 0.12/0.36 (![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)))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.36 tff(25,plain,
% 0.12/0.36 (^[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)))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(26,plain,
% 0.12/0.36 (![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)))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.36 tff(27,plain,
% 0.12/0.36 (![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))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(28,plain,
% 0.12/0.36 (^[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))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(29,plain,
% 0.12/0.36 (![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))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.36 tff(30,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')).
% 0.12/0.36 tff(31,plain,
% 0.12/0.36 (![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))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.36 tff(32,plain,
% 0.12/0.36 (![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))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.12/0.36 tff(33,plain,(
% 0.12/0.36 ![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))))),
% 0.12/0.36 inference(skolemize,[status(sab)],[32])).
% 0.12/0.36 tff(34,plain,
% 0.12/0.36 (![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)))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.12/0.36 tff(35,plain,
% 0.12/0.36 (![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)))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.12/0.36 tff(36,plain,
% 0.12/0.36 (((~![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!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!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(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(37,plain,
% 0.12/0.36 ((~![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!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(38,plain,
% 0.12/0.36 ((~![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!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.36 tff(39,plain,
% 0.12/0.36 (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[38, 35, 22, 21])).
% 0.12/0.36 tff(40,plain,
% 0.12/0.37 (((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))) | distinct_points(Z!0, X!2)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 (distinct_points(Z!0, X!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (((~distinct_points(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, X!2))))) <=> ((~distinct_points(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, X!2)))))) <=> ((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0))))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[43])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, X!2)))))) <=> ((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0)))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[44, 42])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 ((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, X!2)))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 ((~![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(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Z!0))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (~apart_point_and_line(Z!0, line_connecting(Z!0, X!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[47, 35, 41, 11])).
% 0.12/0.37 tff(49,assumption,(~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))), introduced(assumption)).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.37 tff(55,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq2')).
% 0.12/0.37 tff(56,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.37 tff(57,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.12/0.37 tff(58,plain,(
% 0.12/0.37 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[57])).
% 0.12/0.37 tff(59,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.12/0.37 tff(60,plain,
% 0.12/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(61,plain,
% 0.12/0.37 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) <=> (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(62,plain,
% 0.12/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[61])).
% 0.12/0.37 tff(63,plain,
% 0.12/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[62, 60])).
% 0.12/0.37 tff(64,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(65,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, X!2))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.12/0.37 tff(66,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[65, 59, 21, 49, 48])).
% 0.12/0.37 tff(67,plain,(distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(68,plain,
% 0.12/0.37 ((~(~((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))))) <=> ((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(69,plain,
% 0.12/0.37 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) & distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))) <=> (~((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(70,plain,
% 0.12/0.37 ((~(distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) & distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))) <=> (~(~((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[69])).
% 0.12/0.37 tff(71,plain,
% 0.12/0.37 ((~(distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) & distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))) <=> ((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[70, 68])).
% 0.12/0.37 tff(72,plain,
% 0.12/0.37 (~(distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2)) & distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))),
% 0.12/0.37 inference(or_elim,[status(thm)],[19])).
% 0.12/0.37 tff(73,plain,
% 0.12/0.37 ((~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, X!2))) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.12/0.37 tff(74,plain,
% 0.12/0.37 (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[73, 67])).
% 0.12/0.37 tff(75,plain,
% 0.12/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(76,plain,
% 0.12/0.37 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) <=> (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(77,plain,
% 0.12/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[76])).
% 0.12/0.37 tff(78,plain,
% 0.12/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[77, 75])).
% 0.12/0.37 tff(79,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(80,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.12/0.37 tff(81,plain,
% 0.12/0.37 (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Z!0, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[80, 59, 21])).
% 0.12/0.37 tff(82,plain,
% 0.12/0.37 (apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[81, 74])).
% 0.12/0.37 tff(83,plain,
% 0.12/0.37 (((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0))) | distinct_points(Z!0, Z!0)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(84,plain,
% 0.12/0.37 ((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[83, 9])).
% 0.12/0.37 tff(85,plain,
% 0.12/0.37 (((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))) | distinct_points(Z!0, Y!1)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(86,plain,
% 0.12/0.37 (distinct_points(Z!0, Y!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[85, 39])).
% 0.12/0.37 tff(87,plain,
% 0.12/0.37 (((~![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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(88,plain,
% 0.12/0.37 (((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1))))) <=> ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(89,plain,
% 0.12/0.37 (((~![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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0))))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[88])).
% 0.12/0.37 tff(90,plain,
% 0.12/0.37 (((~![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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0)))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[89, 87])).
% 0.12/0.37 tff(91,plain,
% 0.12/0.37 ((~![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(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Z!0)) | (~distinct_points(Z!0, Y!1)))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(92,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))) | (~((~distinct_points(Z!0, Y!1)) | (~distinct_points(Z!0, Z!0))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.12/0.37 tff(93,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[92, 35, 86, 84, 82])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------