%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO221+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:01 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GEO221+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 14:46:18 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(apart_point_and_line_type, type, (
% 0.13/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.13/0.38 tff(orthogonal_through_point_type, type, (
% 0.13/0.38 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.13/0.38 tff(tptp_fun_B_1_type, type, (
% 0.13/0.38 tptp_fun_B_1: $i)).
% 0.13/0.38 tff(tptp_fun_L_0_type, type, (
% 0.13/0.38 tptp_fun_L_0: $i)).
% 0.13/0.38 tff(unorthogonal_lines_type, type, (
% 0.13/0.38 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.13/0.38 tff(tptp_fun_A_2_type, type, (
% 0.13/0.38 tptp_fun_A_2: $i)).
% 0.13/0.38 tff(distinct_lines_type, type, (
% 0.13/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 (^[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))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 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')).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.38 tff(6,plain,(
% 0.13/0.38 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[5])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 ((~![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)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (~apart_point_and_line(B!1, orthogonal_through_point(L!0, B!1))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 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')).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.38 tff(15,plain,(
% 0.13/0.38 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.13/0.38 inference(skolemize,[status(sab)],[14])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (~unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!2), L!0))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (~unorthogonal_lines(orthogonal_through_point(L!0, A!2), L!0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[19, 16])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 ((~![A: $i, B: $i, L: $i] : ((~distinct_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B))) | apart_point_and_line(B, orthogonal_through_point(L, A)))) <=> (~![A: $i, B: $i, L: $i] : ((~distinct_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B))) | apart_point_and_line(B, orthogonal_through_point(L, A))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 ((~![A: $i, B: $i, L: $i] : ((~apart_point_and_line(B, orthogonal_through_point(L, A))) => (~distinct_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B))))) <=> (~![A: $i, B: $i, L: $i] : ((~distinct_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B))) | apart_point_and_line(B, orthogonal_through_point(L, A))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(23,axiom,(~![A: $i, B: $i, L: $i] : ((~apart_point_and_line(B, orthogonal_through_point(L, A))) => (~distinct_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (~![A: $i, B: $i, L: $i] : ((~distinct_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B))) | apart_point_and_line(B, orthogonal_through_point(L, A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (~![A: $i, B: $i, L: $i] : ((~distinct_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B))) | apart_point_and_line(B, orthogonal_through_point(L, A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (~![A: $i, B: $i, L: $i] : ((~distinct_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B))) | apart_point_and_line(B, orthogonal_through_point(L, A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (~![A: $i, B: $i, L: $i] : ((~distinct_lines(orthogonal_through_point(L, A), orthogonal_through_point(L, B))) | apart_point_and_line(B, orthogonal_through_point(L, A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.13/0.38 tff(28,plain,(
% 0.13/0.38 ~((~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)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[27])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (~apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2))),
% 0.13/0.38 inference(or_elim,[status(thm)],[28])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))),
% 0.13/0.38 inference(or_elim,[status(thm)],[28])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (^[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))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 (^[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)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.39 tff(36,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')).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.13/0.39 tff(39,plain,(
% 0.13/0.39 ![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)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[38])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (((~![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)))) | ((~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)) | 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)))) <=> ((~![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(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)) | 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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((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)))) <=> ((~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)) | 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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (((~![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(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)))) | ((~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)) | 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))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[42])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (((~![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(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)))) | (~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)) | 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)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[43, 41])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 ((~![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(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))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (~distinct_lines(orthogonal_through_point(L!0, A!2), orthogonal_through_point(L!0, B!1))) | apart_point_and_line(B!1, orthogonal_through_point(L!0, A!2)) | unorthogonal_lines(orthogonal_through_point(L!0, A!2), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, B!1), L!0) | apart_point_and_line(B!1, orthogonal_through_point(L!0, B!1))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[46, 40, 30, 29, 20, 18, 9])).
% 0.13/0.39 % SZS output end Proof
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------