%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO209+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:05:57 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO209+3 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 14:41:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(convergent_lines_type, type, (
% 0.19/0.38 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_N_0_type, type, (
% 0.19/0.38 tptp_fun_N_0: $i)).
% 0.19/0.38 tff(tptp_fun_M_1_type, type, (
% 0.19/0.38 tptp_fun_M_1: $i)).
% 0.19/0.38 tff(distinct_lines_type, type, (
% 0.19/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.38 tff(equal_lines_type, type, (
% 0.19/0.38 equal_lines: ( $i * $i ) > $o)).
% 0.19/0.38 tff(parallel_lines_type, type, (
% 0.19/0.38 parallel_lines: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_L_2_type, type, (
% 0.19/0.38 tptp_fun_L_2: $i)).
% 0.19/0.38 tff(incident_point_and_line_type, type, (
% 0.19/0.38 incident_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_A_3_type, type, (
% 0.19/0.38 tptp_fun_A_3: $i)).
% 0.19/0.38 tff(apart_point_and_line_type, type, (
% 0.19/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : refl((~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : trans(rewrite((equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))), rewrite((~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))), ((equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.38 tff(6,axiom,(![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','ax2')).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.38 tff(9,plain,(
% 0.19/0.38 ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))) | (~(distinct_lines(M!1, N!0) <=> equal_lines(M!1, N!0)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (~(distinct_lines(M!1, N!0) <=> equal_lines(M!1, N!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 ((~![A: $i, L: $i, M: $i, N: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(A, M) & incident_point_and_line(A, N) & parallel_lines(M, L) & parallel_lines(N, L))) | equal_lines(M, N))) <=> (~![A: $i, L: $i, M: $i, N: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(A, M) & incident_point_and_line(A, N) & parallel_lines(M, L) & parallel_lines(N, L))) | equal_lines(M, N)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 ((~![A: $i, L: $i, M: $i, N: $i] : (((((apart_point_and_line(A, L) & incident_point_and_line(A, M)) & incident_point_and_line(A, N)) & parallel_lines(M, L)) & parallel_lines(N, L)) => equal_lines(M, N))) <=> (~![A: $i, L: $i, M: $i, N: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(A, M) & incident_point_and_line(A, N) & parallel_lines(M, L) & parallel_lines(N, L))) | equal_lines(M, N)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(15,axiom,(~![A: $i, L: $i, M: $i, N: $i] : (((((apart_point_and_line(A, L) & incident_point_and_line(A, M)) & incident_point_and_line(A, N)) & parallel_lines(M, L)) & parallel_lines(N, L)) => equal_lines(M, N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (~![A: $i, L: $i, M: $i, N: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(A, M) & incident_point_and_line(A, N) & parallel_lines(M, L) & parallel_lines(N, L))) | equal_lines(M, N))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (~![A: $i, L: $i, M: $i, N: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(A, M) & incident_point_and_line(A, N) & parallel_lines(M, L) & parallel_lines(N, L))) | equal_lines(M, N))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (~![A: $i, L: $i, M: $i, N: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(A, M) & incident_point_and_line(A, N) & parallel_lines(M, L) & parallel_lines(N, L))) | equal_lines(M, N))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (~![A: $i, L: $i, M: $i, N: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(A, M) & incident_point_and_line(A, N) & parallel_lines(M, L) & parallel_lines(N, L))) | equal_lines(M, N))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.19/0.38 tff(20,plain,(
% 0.19/0.38 ~((~(apart_point_and_line(A!3, L!2) & incident_point_and_line(A!3, M!1) & incident_point_and_line(A!3, N!0) & parallel_lines(M!1, L!2) & parallel_lines(N!0, L!2))) | equal_lines(M!1, N!0))),
% 0.19/0.38 inference(skolemize,[status(sab)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (~equal_lines(M!1, N!0)),
% 0.19/0.38 inference(or_elim,[status(thm)],[20])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 ((distinct_lines(M!1, N!0) <=> equal_lines(M!1, N!0)) | distinct_lines(M!1, N!0) | equal_lines(M!1, N!0)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 ((distinct_lines(M!1, N!0) <=> equal_lines(M!1, N!0)) | distinct_lines(M!1, N!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (distinct_lines(M!1, N!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[23, 12])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.38 tff(30,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.38 tff(33,plain,(
% 0.19/0.38 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.38 inference(skolemize,[status(sab)],[32])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(M!1, N!0)) | convergent_lines(M!1, N!0))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(M!1, N!0)) | convergent_lines(M!1, N!0))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(M!1, N!0)) | convergent_lines(M!1, N!0))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(M!1, N!0)) | convergent_lines(M!1, N!0)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (convergent_lines(M!1, N!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[37, 34, 24])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : refl((~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : trans(rewrite((parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))), rewrite((~(convergent_lines(X, Y) <=> parallel_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))), ((parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.38 tff(44,axiom,(![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a3')).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.38 tff(47,plain,(
% 0.19/0.38 ![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[46])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))) | (~(convergent_lines(N!0, L!2) <=> parallel_lines(N!0, L!2)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (~(convergent_lines(N!0, L!2) <=> parallel_lines(N!0, L!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (apart_point_and_line(A!3, L!2) & incident_point_and_line(A!3, M!1) & incident_point_and_line(A!3, N!0) & parallel_lines(M!1, L!2) & parallel_lines(N!0, L!2)),
% 0.19/0.38 inference(or_elim,[status(thm)],[20])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (parallel_lines(N!0, L!2)),
% 0.19/0.38 inference(and_elim,[status(thm)],[51])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 ((convergent_lines(N!0, L!2) <=> parallel_lines(N!0, L!2)) | (~convergent_lines(N!0, L!2)) | (~parallel_lines(N!0, L!2))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 ((convergent_lines(N!0, L!2) <=> parallel_lines(N!0, L!2)) | (~convergent_lines(N!0, L!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (~convergent_lines(N!0, L!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[54, 50])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~(convergent_lines(X, Y) <=> parallel_lines(X, Y)))) | (~(convergent_lines(M!1, L!2) <=> parallel_lines(M!1, L!2)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (~(convergent_lines(M!1, L!2) <=> parallel_lines(M!1, L!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[56, 48])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (parallel_lines(M!1, L!2)),
% 0.19/0.38 inference(and_elim,[status(thm)],[51])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 ((convergent_lines(M!1, L!2) <=> parallel_lines(M!1, L!2)) | (~convergent_lines(M!1, L!2)) | (~parallel_lines(M!1, L!2))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((convergent_lines(M!1, L!2) <=> parallel_lines(M!1, L!2)) | (~convergent_lines(M!1, L!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (~convergent_lines(M!1, L!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.39 tff(67,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.39 tff(70,plain,(
% 0.19/0.39 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[69])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 ((convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0))) <=> (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[73])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[74, 72])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[77, 71, 61, 55, 38])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------