%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO192+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:05:51 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO192+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.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 14:42:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(distinct_lines_type, type, (
% 0.20/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_X_2_type, type, (
% 0.20/0.38 tptp_fun_X_2: $i)).
% 0.20/0.38 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.38 tptp_fun_Z_0: $i)).
% 0.20/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.38 tptp_fun_Y_1: $i)).
% 0.20/0.38 tff(apart_point_and_line_type, type, (
% 0.20/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.38 tff(intersection_point_type, type, (
% 0.20/0.38 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.38 tff(distinct_points_type, type, (
% 0.20/0.38 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.38 tff(convergent_lines_type, type, (
% 0.20/0.38 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.38 tff(6,plain,(
% 0.20/0.38 ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.38 inference(skolemize,[status(sab)],[5])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(Z!0, Z!0))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (~distinct_lines(Z!0, Z!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.38 tff(10,assumption,(~distinct_lines(Z!0, Y!1)), introduced(assumption)).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(14,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.38 tff(16,plain,(
% 0.20/0.38 ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.38 inference(skolemize,[status(sab)],[15])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 ((~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> (~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))) <=> (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (apart_point_and_line(intersection_point(X, Y), Z) => (distinct_lines(X, Z) & distinct_lines(Y, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(23,axiom,(~![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (apart_point_and_line(intersection_point(X, Y), Z) => (distinct_lines(X, Z) & distinct_lines(Y, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.38 tff(28,plain,(
% 0.20/0.38 ~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[27])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (convergent_lines(X!2, Y!1)),
% 0.20/0.38 inference(or_elim,[status(thm)],[29])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) <=> (apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))))), rewrite(((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))))), rewrite((convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.38 tff(36,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.38 tff(39,plain,(
% 0.20/0.38 ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[38])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 ((~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))) <=> (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[46, 41])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[49, 40, 30, 19])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 ((apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 (apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.20/0.39 inference(or_elim,[status(thm)],[29])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (^[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))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (^[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)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.39 tff(59,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/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq2')).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.39 tff(62,plain,(
% 0.20/0.39 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[61])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | distinct_lines(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)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | distinct_lines(Z!0, Y!1))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))) <=> ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | distinct_lines(Z!0, Y!1))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | distinct_lines(Z!0, Y!1)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | distinct_lines(Z!0, Y!1))),
% 0.20/0.39 inference(transitivity,[status(thm)],[66, 64])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | distinct_lines(Z!0, Y!1)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[69, 63, 53, 52, 10])).
% 0.20/0.39 tff(71,plain,(distinct_lines(Z!0, Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(72,assumption,(~distinct_lines(Y!1, Z!0)), introduced(assumption)).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.39 tff(78,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart5')).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.39 tff(81,plain,(
% 0.20/0.39 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[80])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[85, 82, 72, 9, 71])).
% 0.20/0.39 tff(87,plain,(distinct_lines(Y!1, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 ((~(~((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0))))) <=> ((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 ((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) <=> (~((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 ((~(distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0))) <=> (~(~((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 ((~(distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0))) <=> ((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[90, 88])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 (~(distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0))),
% 0.20/0.39 inference(or_elim,[status(thm)],[29])).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 ((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 (~distinct_lines(X!2, Z!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[93, 87])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 (~distinct_lines(Z!0, X!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[97, 82, 94, 9])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 ((apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[99, 50])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(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)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(Z!0, X!2))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 ((distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))) <=> ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(Z!0, X!2))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(103,plain,
% 0.20/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(Z!0, X!2)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(Z!0, X!2))),
% 0.20/0.39 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(106,plain,
% 0.20/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | distinct_lines(Z!0, X!2)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[106, 63, 53, 100, 98])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------