%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO262+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:06:11 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO262+3 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.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 14:42:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(left_convergent_lines_type, type, (
% 0.12/0.39 left_convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_N_3_type, type, (
% 0.12/0.39 tptp_fun_N_3: $i)).
% 0.12/0.39 tff(tptp_fun_L_5_type, type, (
% 0.12/0.39 tptp_fun_L_5: $i)).
% 0.12/0.39 tff(reverse_line_type, type, (
% 0.12/0.39 reverse_line: $i > $i)).
% 0.12/0.39 tff(unequally_directed_lines_type, type, (
% 0.12/0.39 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(unequally_directed_opposite_lines_type, type, (
% 0.12/0.39 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(convergent_lines_type, type, (
% 0.12/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(incident_point_and_line_type, type, (
% 0.12/0.39 incident_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_B_1_type, type, (
% 0.12/0.39 tptp_fun_B_1: $i)).
% 0.12/0.39 tff(tptp_fun_M_4_type, type, (
% 0.12/0.39 tptp_fun_M_4: $i)).
% 0.12/0.39 tff(between_on_line_type, type, (
% 0.12/0.39 between_on_line: ( $i * $i * $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_C_0_type, type, (
% 0.12/0.39 tptp_fun_C_0: $i)).
% 0.12/0.39 tff(tptp_fun_A_2_type, type, (
% 0.12/0.39 tptp_fun_A_2: $i)).
% 0.12/0.39 tff(intersection_point_type, type, (
% 0.12/0.39 intersection_point: ( $i * $i ) > $i)).
% 0.12/0.39 tff(parallel_through_point_type, type, (
% 0.12/0.39 parallel_through_point: ( $i * $i ) > $i)).
% 0.12/0.39 tff(1,assumption,(left_convergent_lines(L!5, N!3) | left_convergent_lines(L!5, reverse_line(N!3))), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[L: $i, M: $i] : refl((~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax11_basics')).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.39 tff(7,plain,(
% 0.12/0.39 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!5, N!3) | left_convergent_lines(L!5, reverse_line(N!3))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.39 tff(11,plain,(~(left_convergent_lines(L!5, N!3) | left_convergent_lines(L!5, reverse_line(N!3)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 ((left_convergent_lines(L!5, N!3) | left_convergent_lines(L!5, reverse_line(N!3))) | (~left_convergent_lines(L!5, N!3))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (~left_convergent_lines(L!5, N!3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 ((left_convergent_lines(L!5, N!3) | left_convergent_lines(L!5, reverse_line(N!3))) | (~left_convergent_lines(L!5, reverse_line(N!3)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (~left_convergent_lines(L!5, reverse_line(N!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (^[X: $i, Y: $i] : refl((unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(19,axiom,(![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a1_defns')).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.39 tff(21,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[20])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!5, N!3) <=> unequally_directed_lines(L!5, reverse_line(N!3)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (unequally_directed_opposite_lines(L!5, N!3) <=> unequally_directed_lines(L!5, reverse_line(N!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (^[L: $i, M: $i] : refl((~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M))) <=> ![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (^[L: $i, M: $i] : trans(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))))))), rewrite((convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M))))), rewrite((~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> ![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> ![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(30,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a7_defns')).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.40 tff(32,plain,(
% 0.12/0.40 ![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[31])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 ((~![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))) | (~(((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_opposite_lines(L!5, N!3))) <=> convergent_lines(L!5, N!3)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (~(((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_opposite_lines(L!5, N!3))) <=> convergent_lines(L!5, N!3))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 ((~![L: $i, M: $i, N: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M) & convergent_lines(L, N) & convergent_lines(M, N) & incident_point_and_line(B, N))) | between_on_line(M, intersection_point(M, parallel_through_point(N, A)), B, intersection_point(M, parallel_through_point(N, C))))) <=> (~![L: $i, M: $i, N: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M) & convergent_lines(L, N) & convergent_lines(M, N) & incident_point_and_line(B, N))) | between_on_line(M, intersection_point(M, parallel_through_point(N, A)), B, intersection_point(M, parallel_through_point(N, C)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((~![L: $i, M: $i, N: $i, A: $i, B: $i, C: $i] : ((((((between_on_line(L, A, B, C) & convergent_lines(L, M)) & incident_point_and_line(B, M)) & convergent_lines(L, N)) & convergent_lines(M, N)) & incident_point_and_line(B, N)) => between_on_line(M, intersection_point(M, parallel_through_point(N, A)), B, intersection_point(M, parallel_through_point(N, C))))) <=> (~![L: $i, M: $i, N: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M) & convergent_lines(L, N) & convergent_lines(M, N) & incident_point_and_line(B, N))) | between_on_line(M, intersection_point(M, parallel_through_point(N, A)), B, intersection_point(M, parallel_through_point(N, C)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(39,axiom,(~![L: $i, M: $i, N: $i, A: $i, B: $i, C: $i] : ((((((between_on_line(L, A, B, C) & convergent_lines(L, M)) & incident_point_and_line(B, M)) & convergent_lines(L, N)) & convergent_lines(M, N)) & incident_point_and_line(B, N)) => between_on_line(M, intersection_point(M, parallel_through_point(N, A)), B, intersection_point(M, parallel_through_point(N, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (~![L: $i, M: $i, N: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M) & convergent_lines(L, N) & convergent_lines(M, N) & incident_point_and_line(B, N))) | between_on_line(M, intersection_point(M, parallel_through_point(N, A)), B, intersection_point(M, parallel_through_point(N, C))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (~![L: $i, M: $i, N: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M) & convergent_lines(L, N) & convergent_lines(M, N) & incident_point_and_line(B, N))) | between_on_line(M, intersection_point(M, parallel_through_point(N, A)), B, intersection_point(M, parallel_through_point(N, C))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (~![L: $i, M: $i, N: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M) & convergent_lines(L, N) & convergent_lines(M, N) & incident_point_and_line(B, N))) | between_on_line(M, intersection_point(M, parallel_through_point(N, A)), B, intersection_point(M, parallel_through_point(N, C))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (~![L: $i, M: $i, N: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M) & convergent_lines(L, N) & convergent_lines(M, N) & incident_point_and_line(B, N))) | between_on_line(M, intersection_point(M, parallel_through_point(N, A)), B, intersection_point(M, parallel_through_point(N, C))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[42, 37])).
% 0.12/0.40 tff(44,plain,(
% 0.12/0.40 ~((~(between_on_line(L!5, A!2, B!1, C!0) & convergent_lines(L!5, M!4) & incident_point_and_line(B!1, M!4) & convergent_lines(L!5, N!3) & convergent_lines(M!4, N!3) & incident_point_and_line(B!1, N!3))) | between_on_line(M!4, intersection_point(M!4, parallel_through_point(N!3, A!2)), B!1, intersection_point(M!4, parallel_through_point(N!3, C!0))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[43])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (between_on_line(L!5, A!2, B!1, C!0) & convergent_lines(L!5, M!4) & incident_point_and_line(B!1, M!4) & convergent_lines(L!5, N!3) & convergent_lines(M!4, N!3) & incident_point_and_line(B!1, N!3)),
% 0.12/0.40 inference(or_elim,[status(thm)],[44])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (convergent_lines(L!5, N!3)),
% 0.12/0.40 inference(and_elim,[status(thm)],[45])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 ((((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_opposite_lines(L!5, N!3))) <=> convergent_lines(L!5, N!3)) | (~((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_opposite_lines(L!5, N!3)))) | (~convergent_lines(L!5, N!3))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 ((((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_opposite_lines(L!5, N!3))) <=> convergent_lines(L!5, N!3)) | (~((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_opposite_lines(L!5, N!3))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (~((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_opposite_lines(L!5, N!3)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[48, 36])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_opposite_lines(L!5, N!3))) | unequally_directed_opposite_lines(L!5, N!3)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (unequally_directed_opposite_lines(L!5, N!3)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 ((~(unequally_directed_opposite_lines(L!5, N!3) <=> unequally_directed_lines(L!5, reverse_line(N!3)))) | (~unequally_directed_opposite_lines(L!5, N!3)) | unequally_directed_lines(L!5, reverse_line(N!3))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 ((~(unequally_directed_opposite_lines(L!5, N!3) <=> unequally_directed_lines(L!5, reverse_line(N!3)))) | unequally_directed_lines(L!5, reverse_line(N!3))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (unequally_directed_lines(L!5, reverse_line(N!3))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[53, 24])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_opposite_lines(L!5, N!3))) | unequally_directed_lines(L!5, N!3)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (unequally_directed_lines(L!5, N!3)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[55, 49])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (^[L: $i, M: $i] : refl((left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (^[L: $i, M: $i] : rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.12/0.40 tff(64,axiom,(![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax9_basics')).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.12/0.40 tff(67,plain,(
% 0.12/0.40 ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[66])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_lines(L!5, reverse_line(N!3))) | left_convergent_lines(L!5, reverse_line(N!3)) | left_convergent_lines(L!5, N!3))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_lines(L!5, reverse_line(N!3))) | left_convergent_lines(L!5, reverse_line(N!3)) | left_convergent_lines(L!5, N!3))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 ((left_convergent_lines(L!5, reverse_line(N!3)) | (~unequally_directed_lines(L!5, N!3)) | left_convergent_lines(L!5, N!3) | (~unequally_directed_lines(L!5, reverse_line(N!3)))) <=> ((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_lines(L!5, reverse_line(N!3))) | left_convergent_lines(L!5, reverse_line(N!3)) | left_convergent_lines(L!5, N!3))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!5, reverse_line(N!3)) | (~unequally_directed_lines(L!5, N!3)) | left_convergent_lines(L!5, N!3) | (~unequally_directed_lines(L!5, reverse_line(N!3))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_lines(L!5, reverse_line(N!3))) | left_convergent_lines(L!5, reverse_line(N!3)) | left_convergent_lines(L!5, N!3)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[71])).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!5, reverse_line(N!3)) | (~unequally_directed_lines(L!5, N!3)) | left_convergent_lines(L!5, N!3) | (~unequally_directed_lines(L!5, reverse_line(N!3))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_lines(L!5, reverse_line(N!3))) | left_convergent_lines(L!5, reverse_line(N!3)) | left_convergent_lines(L!5, N!3))),
% 0.12/0.41 inference(transitivity,[status(thm)],[72, 70])).
% 0.12/0.41 tff(74,plain,
% 0.12/0.41 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!5, reverse_line(N!3)) | (~unequally_directed_lines(L!5, N!3)) | left_convergent_lines(L!5, N!3) | (~unequally_directed_lines(L!5, reverse_line(N!3))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(75,plain,
% 0.12/0.41 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!5, N!3)) | (~unequally_directed_lines(L!5, reverse_line(N!3))) | left_convergent_lines(L!5, reverse_line(N!3)) | left_convergent_lines(L!5, N!3)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.12/0.41 tff(76,plain,
% 0.12/0.41 (left_convergent_lines(L!5, reverse_line(N!3)) | left_convergent_lines(L!5, N!3)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[75, 69, 56, 54])).
% 0.12/0.41 tff(77,plain,
% 0.12/0.41 ($false),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[76, 15, 13])).
% 0.12/0.41 % SZS output end Proof
% 0.12/0.41 % E exiting
%------------------------------------------------------------------------------