%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO175+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:45 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO175+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:39:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(apart_point_and_line_type, type, (
% 0.12/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_U_1_type, type, (
% 0.12/0.38 tptp_fun_U_1: $i)).
% 0.12/0.38 tff(intersection_point_type, type, (
% 0.12/0.38 intersection_point: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_V_0_type, type, (
% 0.12/0.38 tptp_fun_V_0: $i)).
% 0.12/0.38 tff(distinct_points_type, type, (
% 0.12/0.38 distinct_points: ( $i * $i ) > $o)).
% 0.12/0.38 tff(convergent_lines_type, type, (
% 0.12/0.38 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_X_3_type, type, (
% 0.12/0.38 tptp_fun_X_3: $i)).
% 0.12/0.38 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.38 tptp_fun_Y_2: $i)).
% 0.12/0.38 tff(distinct_lines_type, type, (
% 0.12/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,(
% 0.12/0.38 ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.38 inference(skolemize,[status(sab)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ((~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & distinct_points(X!3, intersection_point(U!1, V!0)))))) <=> (~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & distinct_points(X!3, intersection_point(U!1, V!0))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V)))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 ((~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & distinct_points(X, intersection_point(U, V))) => (apart_point_and_line(X, U) | apart_point_and_line(X, V)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & distinct_points(X, intersection_point(U, V))) => (apart_point_and_line(X, U) | apart_point_and_line(X, V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & convergent_lines(U, V) & distinct_points(X, intersection_point(U, V)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.12/0.38 tff(18,plain,(
% 0.12/0.38 ~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & distinct_points(X!3, intersection_point(U!1, V!0)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & distinct_points(X!3, intersection_point(U!1, V!0)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & distinct_points(X!3, intersection_point(U!1, V!0))),
% 0.12/0.38 inference(or_elim,[status(thm)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (convergent_lines(U!1, V!0)),
% 0.12/0.38 inference(and_elim,[status(thm)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (^[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))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.38 tff(27,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')).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.38 tff(30,plain,(
% 0.12/0.38 ![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))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (((~![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(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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~(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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((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))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((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))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[35, 33])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (((~![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(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)))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[36])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (((~![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(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))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[37, 32])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 ((~![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(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))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 ((~![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(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)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[40, 31, 21, 9])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((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))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (~apart_point_and_line(intersection_point(U!1, V!0), U!1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 ((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))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[44, 41])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.38 tff(51,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.12/0.38 tff(54,plain,(
% 0.12/0.38 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.12/0.38 inference(skolemize,[status(sab)],[53])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(U!1, V!0)) | distinct_lines(U!1, V!0))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(U!1, V!0)) | distinct_lines(U!1, V!0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(U!1, V!0)) | distinct_lines(U!1, V!0))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(U!1, V!0)) | distinct_lines(U!1, V!0)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (distinct_lines(U!1, V!0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[58, 55, 21])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 (distinct_points(X!3, intersection_point(U!1, V!0))),
% 0.12/0.38 inference(and_elim,[status(thm)],[20])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 (~apart_point_and_line(X!3, U!1)),
% 0.12/0.38 inference(or_elim,[status(thm)],[19])).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 (~apart_point_and_line(X!3, V!0)),
% 0.12/0.38 inference(or_elim,[status(thm)],[19])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[63])).
% 0.12/0.38 tff(65,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[65])).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.12/0.39 tff(70,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')).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.12/0.39 tff(73,plain,(
% 0.12/0.39 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[72])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_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(X!3, intersection_point(U!1, V!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_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(X!3, intersection_point(U!1, V!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 ((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(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | (~distinct_lines(U!1, V!0))) <=> (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_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(X!3, intersection_point(U!1, V!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | (~distinct_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_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(X!3, intersection_point(U!1, V!0)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[77])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | (~distinct_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_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(X!3, intersection_point(U!1, V!0))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[78, 76])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | (~distinct_lines(U!1, V!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_lines(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_points(X!3, intersection_point(U!1, V!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[81, 75, 62, 61, 60, 59, 45, 43])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------