TSTP Solution File: GEO210+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO210+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 20:35:42 EDT 2022
% Result : Theorem 0.15s 0.33s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GEO210+1 : TPTP v8.1.0. Released v3.3.0.
% 0.05/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.29 % Computer : n029.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Wed Aug 31 07:07:12 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.30 Usage: tptp [options] [-file:]file
% 0.08/0.30 -h, -? prints this message.
% 0.08/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.30 -m, -model generate model.
% 0.08/0.30 -p, -proof generate proof.
% 0.08/0.30 -c, -core generate unsat core of named formulas.
% 0.08/0.30 -st, -statistics display statistics.
% 0.08/0.30 -t:timeout set timeout (in second).
% 0.08/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.30 -<param>:<value> configuration parameter and value.
% 0.08/0.30 -o:<output-file> file to place output in.
% 0.15/0.33 % SZS status Theorem
% 0.15/0.33 % SZS output start Proof
% 0.15/0.33 tff(apart_point_and_line_type, type, (
% 0.15/0.33 apart_point_and_line: ( $i * $i ) > $o)).
% 0.15/0.33 tff(orthogonal_through_point_type, type, (
% 0.15/0.33 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.15/0.33 tff(tptp_fun_A_2_type, type, (
% 0.15/0.33 tptp_fun_A_2: $i)).
% 0.15/0.33 tff(tptp_fun_M_0_type, type, (
% 0.15/0.33 tptp_fun_M_0: $i)).
% 0.15/0.33 tff(unorthogonal_lines_type, type, (
% 0.15/0.33 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.15/0.33 tff(tptp_fun_L_1_type, type, (
% 0.15/0.33 tptp_fun_L_1: $i)).
% 0.15/0.33 tff(distinct_lines_type, type, (
% 0.15/0.33 distinct_lines: ( $i * $i ) > $o)).
% 0.15/0.33 tff(1,plain,
% 0.15/0.33 (^[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))))),
% 0.15/0.33 inference(bind,[status(th)],[])).
% 0.15/0.33 tff(2,plain,
% 0.15/0.33 (![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)))),
% 0.15/0.33 inference(quant_intro,[status(thm)],[1])).
% 0.15/0.33 tff(3,plain,
% 0.15/0.33 (![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)))),
% 0.15/0.33 inference(rewrite,[status(thm)],[])).
% 0.15/0.33 tff(4,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')).
% 0.15/0.33 tff(5,plain,
% 0.15/0.33 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.15/0.33 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.15/0.33 tff(6,plain,(
% 0.15/0.33 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.15/0.33 inference(skolemize,[status(sab)],[5])).
% 0.15/0.33 tff(7,plain,
% 0.15/0.33 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.15/0.33 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.15/0.33 tff(8,plain,
% 0.15/0.33 ((~![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)))),
% 0.15/0.33 inference(quant_inst,[status(thm)],[])).
% 0.15/0.33 tff(9,plain,
% 0.15/0.33 (~apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2))),
% 0.15/0.33 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.15/0.33 tff(10,plain,
% 0.15/0.33 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.15/0.33 inference(bind,[status(th)],[])).
% 0.15/0.33 tff(11,plain,
% 0.15/0.33 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.15/0.33 inference(quant_intro,[status(thm)],[10])).
% 0.15/0.33 tff(12,plain,
% 0.15/0.33 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.15/0.33 inference(rewrite,[status(thm)],[])).
% 0.15/0.33 tff(13,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.15/0.33 tff(14,plain,
% 0.15/0.33 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.15/0.33 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.15/0.33 tff(15,plain,(
% 0.15/0.33 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.15/0.33 inference(skolemize,[status(sab)],[14])).
% 0.15/0.33 tff(16,plain,
% 0.15/0.33 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.15/0.33 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.15/0.33 tff(17,plain,
% 0.15/0.33 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0))),
% 0.15/0.33 inference(quant_inst,[status(thm)],[])).
% 0.15/0.33 tff(18,plain,
% 0.15/0.33 (~unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0)),
% 0.15/0.33 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.15/0.33 tff(19,plain,
% 0.15/0.33 ((~![A: $i, L: $i, M: $i] : ((~distinct_lines(L, orthogonal_through_point(M, A))) | (~((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M)))))) <=> (~![A: $i, L: $i, M: $i] : ((~distinct_lines(L, orthogonal_through_point(M, A))) | (~((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M))))))),
% 0.15/0.33 inference(rewrite,[status(thm)],[])).
% 0.15/0.33 tff(20,plain,
% 0.15/0.34 ((~![A: $i, L: $i, M: $i] : (((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M))) => (~distinct_lines(L, orthogonal_through_point(M, A))))) <=> (~![A: $i, L: $i, M: $i] : ((~distinct_lines(L, orthogonal_through_point(M, A))) | (~((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M))))))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(21,axiom,(~![A: $i, L: $i, M: $i] : (((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M))) => (~distinct_lines(L, orthogonal_through_point(M, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.15/0.34 tff(22,plain,
% 0.15/0.34 (~![A: $i, L: $i, M: $i] : ((~distinct_lines(L, orthogonal_through_point(M, A))) | (~((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M)))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.15/0.34 tff(23,plain,
% 0.15/0.34 (~![A: $i, L: $i, M: $i] : ((~distinct_lines(L, orthogonal_through_point(M, A))) | (~((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M)))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.15/0.34 tff(24,plain,
% 0.15/0.34 (~![A: $i, L: $i, M: $i] : ((~distinct_lines(L, orthogonal_through_point(M, A))) | (~((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M)))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.15/0.34 tff(25,plain,
% 0.15/0.34 (~![A: $i, L: $i, M: $i] : ((~distinct_lines(L, orthogonal_through_point(M, A))) | (~((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M)))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.15/0.34 tff(26,plain,
% 0.15/0.34 (~![A: $i, L: $i, M: $i] : ((~distinct_lines(L, orthogonal_through_point(M, A))) | (~((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M)))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.15/0.34 tff(27,plain,
% 0.15/0.34 (~![A: $i, L: $i, M: $i] : ((~distinct_lines(L, orthogonal_through_point(M, A))) | (~((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M)))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.15/0.34 tff(28,plain,
% 0.15/0.34 (~![A: $i, L: $i, M: $i] : ((~distinct_lines(L, orthogonal_through_point(M, A))) | (~((~apart_point_and_line(A, L)) & (~unorthogonal_lines(L, M)))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.15/0.34 tff(29,plain,(
% 0.15/0.34 ~((~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | (~((~apart_point_and_line(A!2, L!1)) & (~unorthogonal_lines(L!1, M!0)))))),
% 0.15/0.34 inference(skolemize,[status(sab)],[28])).
% 0.15/0.34 tff(30,plain,
% 0.15/0.34 ((~apart_point_and_line(A!2, L!1)) & (~unorthogonal_lines(L!1, M!0))),
% 0.15/0.34 inference(or_elim,[status(thm)],[29])).
% 0.15/0.34 tff(31,plain,
% 0.15/0.34 (~unorthogonal_lines(L!1, M!0)),
% 0.15/0.34 inference(and_elim,[status(thm)],[30])).
% 0.15/0.34 tff(32,plain,
% 0.15/0.34 (~apart_point_and_line(A!2, L!1)),
% 0.15/0.34 inference(and_elim,[status(thm)],[30])).
% 0.15/0.34 tff(33,plain,
% 0.15/0.34 (distinct_lines(L!1, orthogonal_through_point(M!0, A!2))),
% 0.15/0.34 inference(or_elim,[status(thm)],[29])).
% 0.15/0.34 tff(34,plain,
% 0.15/0.34 (^[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))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(35,plain,
% 0.15/0.34 (![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)))),
% 0.15/0.34 inference(quant_intro,[status(thm)],[34])).
% 0.15/0.34 tff(36,plain,
% 0.15/0.34 (![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)))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(37,plain,
% 0.15/0.34 (^[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)))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(38,plain,
% 0.15/0.34 (![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)))),
% 0.15/0.34 inference(quant_intro,[status(thm)],[37])).
% 0.15/0.34 tff(39,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')).
% 0.15/0.34 tff(40,plain,
% 0.15/0.34 (![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)))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.15/0.34 tff(41,plain,
% 0.15/0.34 (![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)))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.15/0.34 tff(42,plain,(
% 0.15/0.34 ![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)))),
% 0.15/0.34 inference(skolemize,[status(sab)],[41])).
% 0.15/0.34 tff(43,plain,
% 0.15/0.34 (![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)))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.15/0.34 tff(44,plain,
% 0.15/0.34 (((~![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)))) | ((~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | apart_point_and_line(A!2, L!1) | unorthogonal_lines(L!1, M!0) | unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, 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)))) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | apart_point_and_line(A!2, L!1) | unorthogonal_lines(L!1, M!0) | unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2)))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(45,plain,
% 0.15/0.34 ((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)))) <=> ((~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | apart_point_and_line(A!2, L!1) | unorthogonal_lines(L!1, M!0) | unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2)))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(46,plain,
% 0.15/0.34 (((~![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)))) | ((~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | apart_point_and_line(A!2, L!1) | unorthogonal_lines(L!1, M!0) | unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2))))),
% 0.15/0.34 inference(monotonicity,[status(thm)],[45])).
% 0.15/0.34 tff(47,plain,
% 0.15/0.34 (((~![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)))) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | apart_point_and_line(A!2, L!1) | unorthogonal_lines(L!1, M!0) | unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2)))),
% 0.15/0.34 inference(transitivity,[status(thm)],[46, 44])).
% 0.15/0.34 tff(48,plain,
% 0.15/0.34 ((~![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))))),
% 0.15/0.34 inference(quant_inst,[status(thm)],[])).
% 0.15/0.34 tff(49,plain,
% 0.15/0.34 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (~distinct_lines(L!1, orthogonal_through_point(M!0, A!2))) | apart_point_and_line(A!2, L!1) | unorthogonal_lines(L!1, M!0) | unorthogonal_lines(orthogonal_through_point(M!0, A!2), M!0) | apart_point_and_line(A!2, orthogonal_through_point(M!0, A!2))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.15/0.35 tff(50,plain,
% 0.15/0.35 ($false),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[49, 43, 33, 32, 31, 18, 9])).
% 0.15/0.35 % SZS output end Proof
%------------------------------------------------------------------------------