%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO210+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:05:58 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
% 0.00/0.12 % Problem : GEO210+3 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 14:42:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(unorthogonal_lines_type, type, (
% 0.19/0.38 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_M_0_type, type, (
% 0.19/0.38 tptp_fun_M_0: $i)).
% 0.19/0.38 tff(tptp_fun_L_1_type, type, (
% 0.19/0.38 tptp_fun_L_1: $i)).
% 0.19/0.38 tff(orthogonal_lines_type, type, (
% 0.19/0.38 orthogonal_lines: ( $i * $i ) > $o)).
% 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_2_type, type, (
% 0.19/0.38 tptp_fun_A_2: $i)).
% 0.19/0.38 tff(equal_lines_type, type, (
% 0.19/0.38 equal_lines: ( $i * $i ) > $o)).
% 0.19/0.38 tff(orthogonal_through_point_type, type, (
% 0.19/0.38 orthogonal_through_point: ( $i * $i ) > $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(distinct_lines_type, type, (
% 0.19/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : refl((~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_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] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_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] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_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((orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))), rewrite((~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))), ((orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> (~(unorthogonal_lines(X, Y) <=> orthogonal_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] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.38 tff(6,axiom,(![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a5')).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(unorthogonal_lines(X, Y) <=> orthogonal_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] : (~(unorthogonal_lines(X, Y) <=> orthogonal_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] : (~(unorthogonal_lines(X, Y) <=> orthogonal_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] : (~(unorthogonal_lines(X, Y) <=> orthogonal_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] : (~(unorthogonal_lines(X, Y) <=> orthogonal_lines(X, Y)))) | (~(unorthogonal_lines(L!1, M!0) <=> orthogonal_lines(L!1, M!0)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (~(unorthogonal_lines(L!1, M!0) <=> orthogonal_lines(L!1, M!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] : ((~(incident_point_and_line(A, L) & orthogonal_lines(L, M))) | equal_lines(L, orthogonal_through_point(M, A)))) <=> (~![A: $i, L: $i, M: $i] : ((~(incident_point_and_line(A, L) & orthogonal_lines(L, M))) | equal_lines(L, orthogonal_through_point(M, A))))),
% 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] : ((incident_point_and_line(A, L) & orthogonal_lines(L, M)) => equal_lines(L, orthogonal_through_point(M, A)))) <=> (~![A: $i, L: $i, M: $i] : ((~(incident_point_and_line(A, L) & orthogonal_lines(L, M))) | equal_lines(L, orthogonal_through_point(M, A))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(15,axiom,(~![A: $i, L: $i, M: $i] : ((incident_point_and_line(A, L) & orthogonal_lines(L, M)) => equal_lines(L, orthogonal_through_point(M, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (~![A: $i, L: $i, M: $i] : ((~(incident_point_and_line(A, L) & orthogonal_lines(L, M))) | equal_lines(L, orthogonal_through_point(M, A)))),
% 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] : ((~(incident_point_and_line(A, L) & orthogonal_lines(L, M))) | equal_lines(L, orthogonal_through_point(M, A)))),
% 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] : ((~(incident_point_and_line(A, L) & orthogonal_lines(L, M))) | equal_lines(L, orthogonal_through_point(M, A)))),
% 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] : ((~(incident_point_and_line(A, L) & orthogonal_lines(L, M))) | equal_lines(L, orthogonal_through_point(M, A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.19/0.38 tff(20,plain,(
% 0.19/0.38 ~((~(incident_point_and_line(A!2, L!1) & orthogonal_lines(L!1, M!0))) | equal_lines(L!1, orthogonal_through_point(M!0, A!2)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (incident_point_and_line(A!2, L!1) & orthogonal_lines(L!1, M!0)),
% 0.19/0.38 inference(or_elim,[status(thm)],[20])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (orthogonal_lines(L!1, M!0)),
% 0.19/0.38 inference(and_elim,[status(thm)],[21])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 ((unorthogonal_lines(L!1, M!0) <=> orthogonal_lines(L!1, M!0)) | (~unorthogonal_lines(L!1, M!0)) | (~orthogonal_lines(L!1, M!0))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 ((unorthogonal_lines(L!1, M!0) <=> orthogonal_lines(L!1, M!0)) | (~unorthogonal_lines(L!1, M!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (~unorthogonal_lines(L!1, M!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[24, 12])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : refl((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : trans(rewrite((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), rewrite((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), ((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.38 tff(31,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.38 tff(34,plain,(
% 0.19/0.38 ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[33])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(A!2, L!1) <=> incident_point_and_line(A!2, L!1)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (~(apart_point_and_line(A!2, L!1) <=> incident_point_and_line(A!2, L!1))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (incident_point_and_line(A!2, L!1)),
% 0.19/0.38 inference(and_elim,[status(thm)],[21])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 ((apart_point_and_line(A!2, L!1) <=> incident_point_and_line(A!2, L!1)) | (~apart_point_and_line(A!2, L!1)) | (~incident_point_and_line(A!2, L!1))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 ((apart_point_and_line(A!2, L!1) <=> incident_point_and_line(A!2, L!1)) | (~apart_point_and_line(A!2, L!1))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (~apart_point_and_line(A!2, L!1)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.19/0.38 tff(42,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(43,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)],[42])).
% 0.19/0.38 tff(44,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(45,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(46,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)],[45])).
% 0.19/0.38 tff(47,axiom,(![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax2')).
% 0.19/0.38 tff(48,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)],[47, 46])).
% 0.19/0.38 tff(49,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)],[48, 44])).
% 0.19/0.38 tff(50,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)],[49])).
% 0.19/0.38 tff(51,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)],[50, 43])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))) | (~(distinct_lines(L!1, orthogonal_through_point(M!0, A!2)) <=> equal_lines(L!1, orthogonal_through_point(M!0, A!2))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (~(distinct_lines(L!1, orthogonal_through_point(M!0, A!2)) <=> equal_lines(L!1, orthogonal_through_point(M!0, A!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (~equal_lines(L!1, orthogonal_through_point(M!0, A!2))),
% 0.19/0.38 inference(or_elim,[status(thm)],[20])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 ((distinct_lines(L!1, orthogonal_through_point(M!0, A!2)) <=> equal_lines(L!1, orthogonal_through_point(M!0, A!2))) | distinct_lines(L!1, orthogonal_through_point(M!0, A!2)) | equal_lines(L!1, orthogonal_through_point(M!0, A!2))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 ((distinct_lines(L!1, orthogonal_through_point(M!0, A!2)) <=> equal_lines(L!1, orthogonal_through_point(M!0, A!2))) | distinct_lines(L!1, orthogonal_through_point(M!0, A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (distinct_lines(L!1, orthogonal_through_point(M!0, A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (^[A: $i, L: $i] : refl((~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> (~apart_point_and_line(A, orthogonal_through_point(L, A))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(61,axiom,(![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc2')).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.38 tff(63,plain,(
% 0.19/0.38 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[62])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (~apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(70,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.38 tff(72,plain,(
% 0.19/0.38 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.38 inference(skolemize,[status(sab)],[71])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 (~unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.38 tff(76,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(77,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(80,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.38 tff(81,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')).
% 0.19/0.38 tff(82,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.38 tff(83,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.38 tff(84,plain,(
% 0.19/0.38 ![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)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[83])).
% 0.19/0.38 tff(85,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (((~![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(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2)) | apart_point_and_line(A!2, L!1) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | unorthogonal_lines(L!1, M!0))) <=> ((~![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(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2)) | apart_point_and_line(A!2, L!1) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | unorthogonal_lines(L!1, M!0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 ((apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2)) | unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | unorthogonal_lines(L!1, M!0) | apart_point_and_line(A!2, L!1) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!2)))) <=> (unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2)) | apart_point_and_line(A!2, L!1) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | unorthogonal_lines(L!1, M!0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 (((~![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(A!2, orthogonal_through_point(M!0, A!2)) | unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | unorthogonal_lines(L!1, M!0) | apart_point_and_line(A!2, L!1) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!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(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2)) | apart_point_and_line(A!2, L!1) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | unorthogonal_lines(L!1, M!0)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 (((~![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(A!2, orthogonal_through_point(M!0, A!2)) | unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | unorthogonal_lines(L!1, M!0) | apart_point_and_line(A!2, L!1) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!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(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2)) | apart_point_and_line(A!2, L!1) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | unorthogonal_lines(L!1, M!0))),
% 0.19/0.39 inference(transitivity,[status(thm)],[88, 86])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 ((~![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(A!2, orthogonal_through_point(M!0, A!2)) | unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | unorthogonal_lines(L!1, M!0) | apart_point_and_line(A!2, L!1) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2)) | apart_point_and_line(A!2, L!1) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | unorthogonal_lines(L!1, M!0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[91, 85, 75, 66, 57, 41, 25])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------