TSTP Solution File: GEO221+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO221+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 : Fri Sep 16 20:35:50 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO221+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.35 % CPULimit : 300
% 0.20/0.35 % WCLimit : 300
% 0.20/0.35 % DateTime : Wed Aug 31 07:05:20 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(apart_point_and_line_type, type, (
% 0.20/0.41 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.41 tff(orthogonal_through_point_type, type, (
% 0.20/0.41 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_A_2_type, type, (
% 0.20/0.41 tptp_fun_A_2: $i)).
% 0.20/0.41 tff(tptp_fun_L_0_type, type, (
% 0.20/0.41 tptp_fun_L_0: $i)).
% 0.20/0.41 tff(tptp_fun_B_1_type, type, (
% 0.20/0.41 tptp_fun_B_1: $i)).
% 0.20/0.41 tff(incident_point_and_line_type, type, (
% 0.20/0.41 incident_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.41 tff(equal_lines_type, type, (
% 0.20/0.41 equal_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(distinct_lines_type, type, (
% 0.20/0.41 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(unorthogonal_lines_type, type, (
% 0.20/0.41 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,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')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41 tff(6,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[5])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(B!1, orthogonal_through_point(L!0, A!2)) <=> (~apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (incident_point_and_line(B!1, orthogonal_through_point(L!0, A!2)) <=> (~apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ((~![A: $i, B: $i, L: $i] : ((~incident_point_and_line(B, orthogonal_through_point(L, A))) | equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B)))) <=> (~![A: $i, B: $i, L: $i] : ((~incident_point_and_line(B, orthogonal_through_point(L, A))) | equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 ((~![A: $i, B: $i, L: $i] : (incident_point_and_line(B, orthogonal_through_point(L, A)) => equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B)))) <=> (~![A: $i, B: $i, L: $i] : ((~incident_point_and_line(B, orthogonal_through_point(L, A))) | equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(12,axiom,(~![A: $i, B: $i, L: $i] : (incident_point_and_line(B, orthogonal_through_point(L, A)) => equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (~![A: $i, B: $i, L: $i] : ((~incident_point_and_line(B, orthogonal_through_point(L, A))) | equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (~![A: $i, B: $i, L: $i] : ((~incident_point_and_line(B, orthogonal_through_point(L, A))) | equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (~![A: $i, B: $i, L: $i] : ((~incident_point_and_line(B, orthogonal_through_point(L, A))) | equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (~![A: $i, B: $i, L: $i] : ((~incident_point_and_line(B, orthogonal_through_point(L, A))) | equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (~![A: $i, B: $i, L: $i] : ((~incident_point_and_line(B, orthogonal_through_point(L, A))) | equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~![A: $i, B: $i, L: $i] : ((~incident_point_and_line(B, orthogonal_through_point(L, A))) | equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (~![A: $i, B: $i, L: $i] : ((~incident_point_and_line(B, orthogonal_through_point(L, A))) | equal_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.20/0.41 tff(20,plain,(
% 0.20/0.41 ~((~incident_point_and_line(B!1, orthogonal_through_point(L!0, A!2))) | equal_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[19])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (incident_point_and_line(B!1, orthogonal_through_point(L!0, A!2))),
% 0.20/0.41 inference(or_elim,[status(thm)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 ((~(incident_point_and_line(B!1, orthogonal_through_point(L!0, A!2)) <=> (~apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2))))) | (~incident_point_and_line(B!1, orthogonal_through_point(L!0, A!2))) | (~apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 ((~(incident_point_and_line(B!1, orthogonal_through_point(L!0, A!2)) <=> (~apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2))))) | (~apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (~apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[23, 9])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl((equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> (equal_lines(X, Y) <=> (~distinct_lines(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(28,axiom,(![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax2')).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.41 tff(30,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[29])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))) | (equal_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1)) <=> (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (equal_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1)) <=> (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (~equal_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))),
% 0.20/0.41 inference(or_elim,[status(thm)],[20])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 ((~(equal_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1)) <=> (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))))) | equal_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1)) | distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 ((~(equal_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1)) <=> (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))))) | distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(41,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')).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.41 tff(43,plain,(
% 0.20/0.41 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(B!1, orthogonal_through_point(L!0, B!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (~apart_point_and_line(B!1, orthogonal_through_point(L!0, B!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(50,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.42 tff(52,plain,(
% 0.20/0.42 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.42 inference(skolemize,[status(sab)],[51])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (~unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!2), L!0))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (~unorthogonal_lines(orthogonal_through_point(L!0, A!2), L!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (![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))) <=> ![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (![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))) <=> ![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.42 tff(63,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')).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.42 tff(66,plain,(
% 0.20/0.42 ![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)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[65])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (((~![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(orthogonal_through_point(L!0, A!2), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0) | apart_point_and_line(B!1, orthogonal_through_point(L!0, B!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))) | apart_point_and_line(B!1, orthogonal_through_point(L!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(L!0, A!2), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0) | apart_point_and_line(B!1, orthogonal_through_point(L!0, B!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))) | apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 ((apart_point_and_line(B!1, orthogonal_through_point(L!0, B!1)) | unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!2), L!0) | apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2)) | (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1)))) <=> (unorthogonal_lines(orthogonal_through_point(L!0, A!2), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0) | apart_point_and_line(B!1, orthogonal_through_point(L!0, B!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))) | apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (((~![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(B!1, orthogonal_through_point(L!0, B!1)) | unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!2), L!0) | apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2)) | (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))))) <=> ((~![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(L!0, A!2), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0) | apart_point_and_line(B!1, orthogonal_through_point(L!0, B!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))) | apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 (((~![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(B!1, orthogonal_through_point(L!0, B!1)) | unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!2), L!0) | apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2)) | (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))))) <=> ((~![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(L!0, A!2), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0) | apart_point_and_line(B!1, orthogonal_through_point(L!0, B!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))) | apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[70, 68])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 ((~![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(B!1, orthogonal_through_point(L!0, B!1)) | unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!2), L!0) | apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2)) | (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!2), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0) | apart_point_and_line(B!1, orthogonal_through_point(L!0, B!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))) | apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[73, 67, 57, 55, 46, 37, 24])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------