%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO215+1 : 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 05:05:59 AM UTC 2025
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO215+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % 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 14:41:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(convergent_lines_type, type, (
% 0.19/0.41 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_L_2_type, type, (
% 0.19/0.41 tptp_fun_L_2: $i)).
% 0.19/0.41 tff(distinct_lines_type, type, (
% 0.19/0.41 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_M_1_type, type, (
% 0.19/0.41 tptp_fun_M_1: $i)).
% 0.19/0.41 tff(apart_point_and_line_type, type, (
% 0.19/0.41 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.41 tff(intersection_point_type, type, (
% 0.19/0.41 intersection_point: ( $i * $i ) > $i)).
% 0.19/0.41 tff(unorthogonal_lines_type, type, (
% 0.19/0.41 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_N_0_type, type, (
% 0.19/0.41 tptp_fun_N_0: $i)).
% 0.19/0.41 tff(1,assumption,(convergent_lines(L!2, L!2)), introduced(assumption)).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.41 tff(7,plain,(
% 0.19/0.41 ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.41 inference(skolemize,[status(sab)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(L!2, L!2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.41 tff(11,plain,(~convergent_lines(L!2, L!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 ((~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))) <=> (~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))) <=> (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 ((~![L: $i, M: $i, N: $i] : (convergent_lines(L, M) => (unorthogonal_lines(L, N) | unorthogonal_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(15,axiom,(~![L: $i, M: $i, N: $i] : (convergent_lines(L, M) => (unorthogonal_lines(L, N) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.19/0.41 tff(20,plain,(
% 0.19/0.41 ~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (convergent_lines(L!2, M!1)),
% 0.19/0.41 inference(or_elim,[status(thm)],[21])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.41 tff(28,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.41 tff(31,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[30])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!2, M!1)) | (~apart_point_and_line(intersection_point(L!2, M!1), L!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!2, M!1)) | (~apart_point_and_line(intersection_point(L!2, M!1), L!2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!2, M!1)) | (~apart_point_and_line(intersection_point(L!2, M!1), L!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!2, M!1)) | (~apart_point_and_line(intersection_point(L!2, M!1), L!2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (~apart_point_and_line(intersection_point(L!2, M!1), L!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[35, 32, 22])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.41 tff(42,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.41 tff(45,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[44])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!2, M!1)) | (~apart_point_and_line(intersection_point(L!2, M!1), M!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!2, M!1)) | (~apart_point_and_line(intersection_point(L!2, M!1), M!1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!2, M!1)) | (~apart_point_and_line(intersection_point(L!2, M!1), M!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!2, M!1)) | (~apart_point_and_line(intersection_point(L!2, M!1), M!1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (~apart_point_and_line(intersection_point(L!2, M!1), M!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[49, 46, 22])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (~unorthogonal_lines(L!2, N!0)),
% 0.19/0.41 inference(or_elim,[status(thm)],[21])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (~unorthogonal_lines(M!1, N!0)),
% 0.19/0.41 inference(or_elim,[status(thm)],[21])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (^[A: $i, L: $i, M: $i, N: $i] : refl((apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (^[A: $i, L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(A, L) | apart_point_and_line(A, M)) <=> (apart_point_and_line(A, M) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> ((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)))), rewrite(((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> ((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)))), rewrite(((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))))), rewrite((distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.41 tff(58,axiom,(![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ouo1')).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.41 tff(61,plain,(
% 0.19/0.41 ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[60])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2) | (~distinct_lines(M!1, L!2)))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2) | (~distinct_lines(M!1, L!2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 ((apart_point_and_line(intersection_point(L!2, M!1), L!2) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | (~distinct_lines(M!1, L!2))) <=> (unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2) | (~distinct_lines(M!1, L!2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(L!2, M!1), L!2) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | (~distinct_lines(M!1, L!2)))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2) | (~distinct_lines(M!1, L!2))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[64])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(L!2, M!1), L!2) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | (~distinct_lines(M!1, L!2)))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2) | (~distinct_lines(M!1, L!2)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[65, 63])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(L!2, M!1), L!2) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | (~distinct_lines(M!1, L!2)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2) | (~distinct_lines(M!1, L!2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (~distinct_lines(M!1, L!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[68, 62, 52, 51, 50, 36])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.42 tff(75,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.19/0.42 tff(78,plain,(
% 0.19/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[77])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(L!2, M!1)) | distinct_lines(M!1, L!2) | convergent_lines(L!2, L!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(L!2, M!1)) | distinct_lines(M!1, L!2) | convergent_lines(L!2, L!2))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 ((distinct_lines(M!1, L!2) | convergent_lines(L!2, L!2) | (~convergent_lines(L!2, M!1))) <=> ((~convergent_lines(L!2, M!1)) | distinct_lines(M!1, L!2) | convergent_lines(L!2, L!2))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(M!1, L!2) | convergent_lines(L!2, L!2) | (~convergent_lines(L!2, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(L!2, M!1)) | distinct_lines(M!1, L!2) | convergent_lines(L!2, L!2)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(M!1, L!2) | convergent_lines(L!2, L!2) | (~convergent_lines(L!2, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(L!2, M!1)) | distinct_lines(M!1, L!2) | convergent_lines(L!2, L!2))),
% 0.19/0.42 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(M!1, L!2) | convergent_lines(L!2, L!2) | (~convergent_lines(L!2, M!1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(L!2, M!1)) | distinct_lines(M!1, L!2) | convergent_lines(L!2, L!2)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[85, 79, 22, 69, 11])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------