%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO178+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO178+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.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 14:39:23 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(apart_point_and_line_type, type, (
% 0.11/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.11/0.37 tff(line_connecting_type, type, (
% 0.11/0.37 line_connecting: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.37 tptp_fun_Y_1: $i)).
% 0.11/0.37 tff(tptp_fun_X_2_type, type, (
% 0.11/0.37 tptp_fun_X_2: $i)).
% 0.11/0.37 tff(distinct_points_type, type, (
% 0.11/0.37 distinct_points: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_Z_0_type, type, (
% 0.11/0.37 tptp_fun_Z_0: $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 ((~![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)))) <=> (~![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))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 ((~![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)))) <=> (~![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))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(3,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/sandbox2/benchmark/theBenchmark.p','con')).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (~![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)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (~![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)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (~![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)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (~![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)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.11/0.37 tff(8,plain,(
% 0.11/0.37 ~((~(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)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[7])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (distinct_points(X!2, Y!1) & apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.11/0.37 inference(or_elim,[status(thm)],[8])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (distinct_points(X!2, Y!1)),
% 0.11/0.37 inference(and_elim,[status(thm)],[9])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.37 tff(16,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.37 tff(19,plain,(
% 0.11/0.37 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[18])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.11/0.37 tff(30,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.11/0.37 tff(33,plain,(
% 0.11/0.37 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[32])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[37, 34, 10])).
% 0.11/0.37 tff(39,assumption,(~distinct_points(Z!0, Y!1)), introduced(assumption)).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.11/0.37 inference(and_elim,[status(thm)],[9])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[41])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | apart_point_and_line(Z, Y)) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))))), rewrite((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[44])).
% 0.11/0.37 tff(46,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.11/0.37 tff(49,plain,(
% 0.11/0.37 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[48])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(Z!0, Y!1) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(Z!0, Y!1) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(Z!0, Y!1) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(Z!0, Y!1) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.11/0.37 tff(54,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[53, 50, 40, 39, 38])).
% 0.11/0.37 tff(55,plain,(distinct_points(Z!0, Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(56,plain,
% 0.11/0.37 ((~(~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))))) <=> ((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 ((distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1)) <=> (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 ((~(distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1))) <=> (~(~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[57])).
% 0.11/0.37 tff(59,plain,
% 0.11/0.37 ((~(distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1))) <=> ((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[58, 56])).
% 0.11/0.37 tff(60,plain,
% 0.11/0.37 (~(distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1))),
% 0.11/0.37 inference(or_elim,[status(thm)],[8])).
% 0.11/0.37 tff(61,plain,
% 0.11/0.37 ((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.11/0.37 tff(62,plain,
% 0.11/0.37 (~distinct_points(Z!0, X!2)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[61, 55])).
% 0.11/0.37 tff(63,plain,
% 0.11/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(Z!0, X!2) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(Z!0, X!2) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(64,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(Z!0, X!2) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(65,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(Z!0, X!2) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.11/0.37 tff(66,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[65, 50, 40, 62, 24])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------