%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO186+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:49 AM UTC 2025
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO186+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.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 14:40:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(apart_point_and_line_type, type, (
% 0.20/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_U_1_type, type, (
% 0.20/0.40 tptp_fun_U_1: $i)).
% 0.20/0.40 tff(intersection_point_type, type, (
% 0.20/0.40 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_V_0_type, type, (
% 0.20/0.40 tptp_fun_V_0: $i)).
% 0.20/0.40 tff(distinct_points_type, type, (
% 0.20/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.40 tff(convergent_lines_type, type, (
% 0.20/0.40 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_X_3_type, type, (
% 0.20/0.40 tptp_fun_X_3: $i)).
% 0.20/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.20/0.40 tptp_fun_Y_2: $i)).
% 0.20/0.40 tff(distinct_lines_type, type, (
% 0.20/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.40 tff(6,plain,(
% 0.20/0.40 ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.40 inference(skolemize,[status(sab)],[5])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~distinct_points(X, intersection_point(U, V))) | (~(distinct_points(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V)))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~distinct_points(X, intersection_point(U, V))) | (~(distinct_points(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : ((((distinct_points(X, Y) & convergent_lines(U, V)) & (~apart_point_and_line(X, U))) & (~apart_point_and_line(X, V))) => (~distinct_points(X, intersection_point(U, V))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~distinct_points(X, intersection_point(U, V))) | (~(distinct_points(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(12,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : ((((distinct_points(X, Y) & convergent_lines(U, V)) & (~apart_point_and_line(X, U))) & (~apart_point_and_line(X, V))) => (~distinct_points(X, intersection_point(U, V))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~distinct_points(X, intersection_point(U, V))) | (~(distinct_points(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~distinct_points(X, intersection_point(U, V))) | (~(distinct_points(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~distinct_points(X, intersection_point(U, V))) | (~(distinct_points(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~distinct_points(X, intersection_point(U, V))) | (~(distinct_points(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.20/0.40 tff(17,plain,(
% 0.20/0.40 ~((~distinct_points(X!3, intersection_point(U!1, V!0))) | (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(X!3, V!0)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[16])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(X!3, V!0))),
% 0.20/0.40 inference(or_elim,[status(thm)],[17])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (convergent_lines(U!1, V!0)),
% 0.20/0.40 inference(and_elim,[status(thm)],[18])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (^[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)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (^[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))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.40 tff(25,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.40 tff(28,plain,(
% 0.20/0.40 ![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))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[27])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (((~![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(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), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0))))) <=> ((~![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), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ((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), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0)))) <=> ((~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), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 ((~(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) | apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 ((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), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((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), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[33, 31])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (((~![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))))) | (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), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (((~![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))))) | (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), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[35, 30])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ((~![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))))) | (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))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ((~![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(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), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (~(apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[38, 29, 19, 9])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ((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))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (~apart_point_and_line(intersection_point(U!1, V!0), U!1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 ((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), V!0))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.20/0.40 tff(44,assumption,(~distinct_points(intersection_point(U!1, V!0), X!3)), introduced(assumption)).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.40 tff(50,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.40 tff(53,plain,(
% 0.20/0.40 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.40 inference(skolemize,[status(sab)],[52])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (((~![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))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(U!1, V!0)) | distinct_lines(U!1, V!0))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(U!1, V!0)) | distinct_lines(U!1, V!0)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (distinct_lines(U!1, V!0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[57, 54, 19])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (~apart_point_and_line(X!3, V!0)),
% 0.20/0.40 inference(and_elim,[status(thm)],[18])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (~apart_point_and_line(X!3, U!1)),
% 0.20/0.40 inference(and_elim,[status(thm)],[18])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (^[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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(64,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)],[63])).
% 0.20/0.41 tff(65,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(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (^[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))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.41 tff(68,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/sandbox2/benchmark/Axioms/GEO008+0.ax','cu1')).
% 0.20/0.41 tff(69,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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.41 tff(70,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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.41 tff(71,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))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[70])).
% 0.20/0.41 tff(72,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)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.41 tff(73,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)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.20/0.41 tff(74,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)))) | (apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_points(X!3, X!3)) | (~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, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_points(X!3, X!3)) | (~distinct_lines(U!1, V!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ((apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, X!3)) | (~distinct_lines(U!1, V!0))) <=> (apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_points(X!3, X!3)) | (~distinct_lines(U!1, V!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(76,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)))) | (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, X!3)) | (~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, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_points(X!3, X!3)) | (~distinct_lines(U!1, V!0))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.41 tff(77,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)))) | (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, X!3)) | (~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, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_points(X!3, X!3)) | (~distinct_lines(U!1, V!0)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.41 tff(78,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)))) | (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1) | (~distinct_points(X!3, X!3)) | (~distinct_lines(U!1, V!0)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(79,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)))) | apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_points(X!3, X!3)) | (~distinct_lines(U!1, V!0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (~distinct_points(X!3, X!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[79, 73, 60, 59, 58])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (distinct_points(X!3, intersection_point(U!1, V!0))),
% 0.20/0.41 inference(or_elim,[status(thm)],[17])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | distinct_points(Y, Z)) <=> (distinct_points(Y, Z) | distinct_points(X, Z))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))))), rewrite((distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.41 tff(87,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart4')).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.41 tff(90,plain,(
% 0.20/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[89])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!3, intersection_point(U!1, V!0))) | distinct_points(X!3, X!3) | distinct_points(intersection_point(U!1, V!0), X!3))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | distinct_points(X!3, X!3) | distinct_points(intersection_point(U!1, V!0), X!3))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 ((distinct_points(intersection_point(U!1, V!0), X!3) | distinct_points(X!3, X!3) | (~distinct_points(X!3, intersection_point(U!1, V!0)))) <=> ((~distinct_points(X!3, intersection_point(U!1, V!0))) | distinct_points(X!3, X!3) | distinct_points(intersection_point(U!1, V!0), X!3))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(U!1, V!0), X!3) | distinct_points(X!3, X!3) | (~distinct_points(X!3, intersection_point(U!1, V!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!3, intersection_point(U!1, V!0))) | distinct_points(X!3, X!3) | distinct_points(intersection_point(U!1, V!0), X!3)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(U!1, V!0), X!3) | distinct_points(X!3, X!3) | (~distinct_points(X!3, intersection_point(U!1, V!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | distinct_points(X!3, X!3) | distinct_points(intersection_point(U!1, V!0), X!3))),
% 0.20/0.41 inference(transitivity,[status(thm)],[94, 92])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(U!1, V!0), X!3) | distinct_points(X!3, X!3) | (~distinct_points(X!3, intersection_point(U!1, V!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!3, intersection_point(U!1, V!0))) | distinct_points(X!3, X!3) | distinct_points(intersection_point(U!1, V!0), X!3)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[97, 91, 81, 80, 44])).
% 0.20/0.41 tff(99,plain,(distinct_points(intersection_point(U!1, V!0), X!3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(100,assumption,(~distinct_lines(V!0, U!1)), introduced(assumption)).
% 0.20/0.41 tff(101,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(102,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)],[101])).
% 0.20/0.41 tff(103,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(104,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.41 tff(106,plain,(
% 0.20/0.41 ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(skolemize,[status(sab)],[105])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(U!1, U!1))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (~distinct_lines(U!1, U!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.41 tff(115,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart5')).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.41 tff(118,plain,(
% 0.20/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[117])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(U!1, U!1) | distinct_lines(V!0, U!1) | (~distinct_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(U!1, U!1) | distinct_lines(V!0, U!1) | (~distinct_lines(U!1, V!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 ((distinct_lines(V!0, U!1) | distinct_lines(U!1, U!1) | (~distinct_lines(U!1, V!0))) <=> (distinct_lines(U!1, U!1) | distinct_lines(V!0, U!1) | (~distinct_lines(U!1, V!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(V!0, U!1) | distinct_lines(U!1, U!1) | (~distinct_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(U!1, U!1) | distinct_lines(V!0, U!1) | (~distinct_lines(U!1, V!0))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[121])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(V!0, U!1) | distinct_lines(U!1, U!1) | (~distinct_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(U!1, U!1) | distinct_lines(V!0, U!1) | (~distinct_lines(U!1, V!0)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[122, 120])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(V!0, U!1) | distinct_lines(U!1, U!1) | (~distinct_lines(U!1, V!0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(U!1, U!1) | distinct_lines(V!0, U!1) | (~distinct_lines(U!1, V!0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[125, 119, 58, 109, 100])).
% 0.20/0.42 tff(127,plain,(distinct_lines(V!0, U!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(128,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(X!3, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), 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, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 ((apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, 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) | (~distinct_points(intersection_point(U!1, V!0), X!3)) | (~distinct_lines(V!0, U!1))) <=> (apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(130,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(X!3, U!1) | apart_point_and_line(X!3, 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) | (~distinct_points(intersection_point(U!1, V!0), X!3)) | (~distinct_lines(V!0, U!1)))) <=> ((~![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, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[129])).
% 0.20/0.42 tff(131,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(X!3, U!1) | apart_point_and_line(X!3, 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) | (~distinct_points(intersection_point(U!1, V!0), X!3)) | (~distinct_lines(V!0, U!1)))) <=> ((~![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, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0))),
% 0.20/0.42 inference(transitivity,[status(thm)],[130, 128])).
% 0.20/0.42 tff(132,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(X!3, U!1) | apart_point_and_line(X!3, 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) | (~distinct_points(intersection_point(U!1, V!0), X!3)) | (~distinct_lines(V!0, U!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 ((~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[133, 73, 60, 59])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 (apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[134, 127, 99])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[135, 43, 41])).
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------