%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO191+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.12s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO191+2 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:40:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(apart_point_and_line_type, type, (
% 0.12/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_V_0_type, type, (
% 0.12/0.40 tptp_fun_V_0: $i)).
% 0.12/0.40 tff(intersection_point_type, type, (
% 0.12/0.40 intersection_point: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.40 tptp_fun_Y_2: $i)).
% 0.12/0.40 tff(tptp_fun_X_3_type, type, (
% 0.12/0.40 tptp_fun_X_3: $i)).
% 0.12/0.40 tff(distinct_points_type, type, (
% 0.12/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_U_1_type, type, (
% 0.12/0.40 tptp_fun_U_1: $i)).
% 0.12/0.40 tff(convergent_lines_type, type, (
% 0.12/0.40 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.40 tff(distinct_lines_type, type, (
% 0.12/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.40 tff(1,assumption,(distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2))), introduced(assumption)).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.40 tff(7,plain,(
% 0.12/0.40 ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.40 inference(skolemize,[status(sab)],[6])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.40 tff(11,plain,(~distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 ((~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))))) <=> (~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : (((convergent_lines(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(intersection_point(X, Y), U) | apart_point_and_line(intersection_point(X, Y), V))) => (apart_point_and_line(intersection_point(U, V), X) | apart_point_and_line(intersection_point(U, V), Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(15,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((convergent_lines(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(intersection_point(X, Y), U) | apart_point_and_line(intersection_point(X, Y), V))) => (apart_point_and_line(intersection_point(U, V), X) | apart_point_and_line(intersection_point(U, V), Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.12/0.40 tff(20,plain,(
% 0.12/0.40 ~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[19])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.12/0.40 inference(or_elim,[status(thm)],[21])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (convergent_lines(X!3, Y!2)),
% 0.12/0.40 inference(and_elim,[status(thm)],[22])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (^[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))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.40 tff(29,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/sandbox/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.12/0.40 tff(32,plain,(
% 0.12/0.40 ![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))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[31])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (((~![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!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))) <=> ((~![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!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(35,plain,
% 0.12/0.41 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))) <=> ((~convergent_lines(X!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(36,plain,
% 0.12/0.41 ((~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))) <=> (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(37,plain,
% 0.12/0.41 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))) <=> (distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[36])).
% 0.12/0.41 tff(38,plain,
% 0.12/0.41 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))) <=> ((~convergent_lines(X!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[37, 35])).
% 0.12/0.41 tff(39,plain,
% 0.12/0.41 (((~![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!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))) <=> ((~![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!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[38])).
% 0.12/0.41 tff(40,plain,
% 0.12/0.41 (((~![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!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))) <=> ((~![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!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[39, 34])).
% 0.12/0.41 tff(41,plain,
% 0.12/0.41 ((~![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!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((~![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!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[42, 33, 23])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[43, 11])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 ((apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 ((apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(52,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.41 tff(54,plain,(
% 0.20/0.41 ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(skolemize,[status(sab)],[53])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(X!3, X!3))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (~distinct_lines(X!3, X!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.41 tff(63,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.41 tff(66,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.41 inference(skolemize,[status(sab)],[65])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!3, X!3)) | distinct_lines(X!3, X!3))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!3, X!3)) | distinct_lines(X!3, X!3))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!3, X!3)) | distinct_lines(X!3, X!3))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!3, X!3)) | distinct_lines(X!3, X!3)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (~convergent_lines(X!3, X!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[70, 67, 57])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.41 tff(77,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.41 tff(80,plain,(
% 0.20/0.41 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[79])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!3, Y!2)) | convergent_lines(X!3, X!3) | convergent_lines(Y!2, X!3))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!3, Y!2)) | convergent_lines(X!3, X!3) | convergent_lines(Y!2, X!3))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 ((convergent_lines(Y!2, X!3) | convergent_lines(X!3, X!3) | (~convergent_lines(X!3, Y!2))) <=> ((~convergent_lines(X!3, Y!2)) | convergent_lines(X!3, X!3) | convergent_lines(Y!2, X!3))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!2, X!3) | convergent_lines(X!3, X!3) | (~convergent_lines(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!3, Y!2)) | convergent_lines(X!3, X!3) | convergent_lines(Y!2, X!3)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!2, X!3) | convergent_lines(X!3, X!3) | (~convergent_lines(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!3, Y!2)) | convergent_lines(X!3, X!3) | convergent_lines(Y!2, X!3))),
% 0.20/0.41 inference(transitivity,[status(thm)],[84, 82])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!2, X!3) | convergent_lines(X!3, X!3) | (~convergent_lines(X!3, Y!2)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!3, Y!2)) | convergent_lines(X!3, X!3) | convergent_lines(Y!2, X!3)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (convergent_lines(Y!2, X!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[87, 81, 23, 71])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(Y!2, X!3)) | distinct_lines(Y!2, X!3))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(Y!2, X!3)) | distinct_lines(Y!2, X!3))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(Y!2, X!3)) | distinct_lines(Y!2, X!3))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(Y!2, X!3)) | distinct_lines(Y!2, X!3)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (distinct_lines(Y!2, X!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[91, 67, 88])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (~apart_point_and_line(intersection_point(U!1, V!0), X!3)),
% 0.20/0.41 inference(or_elim,[status(thm)],[21])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 0.20/0.41 inference(or_elim,[status(thm)],[21])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (^[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))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.42 tff(102,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')).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.42 tff(105,plain,(
% 0.20/0.42 ![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))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[104])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)))) <=> ((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 ((apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | (~distinct_lines(Y!2, X!3))) <=> (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (((~![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(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | (~distinct_lines(Y!2, X!3)))) <=> ((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (((~![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(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | (~distinct_lines(Y!2, X!3)))) <=> ((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[110, 108])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 ((~![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(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | (~distinct_lines(Y!2, X!3)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 ((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[113, 107, 94, 93, 92, 48, 46])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!3, Y!2)) | distinct_lines(X!3, Y!2))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!3, Y!2)) | distinct_lines(X!3, Y!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!3, Y!2)) | distinct_lines(X!3, Y!2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!3, Y!2)) | distinct_lines(X!3, Y!2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (distinct_lines(X!3, Y!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[117, 67, 23])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))) <=> ((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 ((apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2))) <=> (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))) <=> ((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 (((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))) <=> ((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[121, 119])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 ((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 ((~![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(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[124, 107, 94, 93, 118])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (convergent_lines(U!1, V!0)),
% 0.20/0.43 inference(and_elim,[status(thm)],[22])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (((~![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(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))) <=> ((~![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(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 ((distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))) <=> ((~convergent_lines(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 ((~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))) <=> (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 ((distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))) <=> (distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[129])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 ((distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))) <=> ((~convergent_lines(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[130, 128])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (((~![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(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))) <=> ((~![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(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[131])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (((~![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(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))) <=> ((~![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(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[132, 127])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 ((~![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(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 ((~![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(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[135, 33, 126, 125])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 ((apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[142])).
% 0.20/0.43 tff(144,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/sandbox/benchmark/Axioms/GEO008+0.ax','ceq1')).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.20/0.43 tff(147,plain,(
% 0.20/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[146])).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(150,plain,
% 0.20/0.43 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))) <=> (apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(151,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.43 tff(152,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[151, 149])).
% 0.20/0.43 tff(153,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(154,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[154, 148, 138])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[155, 114])).
% 0.20/0.43 tff(157,assumption,(~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))), introduced(assumption)).
% 0.20/0.43 tff(158,plain,
% 0.20/0.43 ((apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(159,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(U!1, V!0), U!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[158, 136])).
% 0.20/0.43 tff(160,assumption,(apart_point_and_line(intersection_point(X!3, Y!2), U!1)), introduced(assumption)).
% 0.20/0.43 tff(161,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1))) <=> (apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[162])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[163, 161])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[166, 148, 160, 159, 157])).
% 0.20/0.44 tff(168,plain,(distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(169,plain,
% 0.20/0.44 (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[168, 114])).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)),
% 0.20/0.44 inference(and_elim,[status(thm)],[22])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[170, 169, 156])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------