%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO222+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO222+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:42:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 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_1_type, type, (
% 0.20/0.41 tptp_fun_A_1: $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(intersection_point_type, type, (
% 0.20/0.41 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.41 tff(convergent_lines_type, type, (
% 0.20/0.41 convergent_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(distinct_lines_type, type, (
% 0.20/0.41 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41 tff(6,plain,(
% 0.20/0.41 ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(skolemize,[status(sab)],[5])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(13,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.41 tff(15,plain,(
% 0.20/0.41 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.41 inference(skolemize,[status(sab)],[14])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(22,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.41 tff(24,plain,(
% 0.20/0.41 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(skolemize,[status(sab)],[23])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[28, 25, 18])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.42 tff(35,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.42 tff(38,plain,(
% 0.20/0.42 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[37])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 ((convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[42, 40])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[45, 39, 29, 9])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.42 tff(52,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.42 tff(55,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[54])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[59, 56, 46])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.42 tff(66,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.42 tff(69,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[68])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[73, 70, 46])).
% 0.20/0.42 tff(75,assumption,(convergent_lines(L!0, L!0)), introduced(assumption)).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(L!0, L!0))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[76, 7, 75])).
% 0.20/0.42 tff(78,plain,(~convergent_lines(L!0, L!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))) | convergent_lines(L!0, L!0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.20/0.42 tff(81,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!1), L!0))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[81, 16])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.42 tff(85,assumption,(~((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))), introduced(assumption)).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[88, 85])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (^[L: $i, M: $i, N: $i] : refl(((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((convergent_lines(M, N) & unorthogonal_lines(M, N)) <=> (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N))))), rewrite((convergent_lines(L, N) & unorthogonal_lines(L, N)) <=> (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))), trans(monotonicity(rewrite((convergent_lines(L, M) & unorthogonal_lines(L, M)) <=> (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> (~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), rewrite((~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), (((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), rewrite(((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))), (((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite(((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)))), (((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N)))) <=> ((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)))))), rewrite(((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))), (((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N)))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (![L: $i, M: $i, N: $i] : ((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N)))) <=> ![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.43 tff(97,axiom,(![L: $i, M: $i, N: $i] : ((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','oac1')).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.20/0.43 tff(100,plain,(
% 0.20/0.43 ![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[99])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[101, 91])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))) <=> ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[105, 103])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0)))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(L!0, L!0)) | (~unorthogonal_lines(L!0, L!0))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[108, 102, 89, 87, 84, 80])).
% 0.20/0.43 tff(110,plain,((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(111,assumption,(~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))), introduced(assumption)).
% 0.20/0.43 tff(112,assumption,(~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)), introduced(assumption)).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 ((~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))) <=> (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(114,axiom,(~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[115, 113])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[116, 113])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (~![A: $i, L: $i] : (~convergent_lines(L, orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.20/0.43 tff(119,plain,(
% 0.20/0.43 convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.43 inference(skolemize,[status(sab)],[118])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[123])).
% 0.20/0.43 tff(125,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.20/0.43 tff(128,plain,(
% 0.20/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[127])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 ((distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[131])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0))),
% 0.20/0.44 inference(transitivity,[status(thm)],[132, 130])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | convergent_lines(L!0, L!0)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[135, 129, 119, 112, 78])).
% 0.20/0.44 tff(137,plain,(distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[140, 56, 119])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (~apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[144, 70, 119])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[146])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[149])).
% 0.20/0.44 tff(151,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/sandbox2/benchmark/Axioms/GEO006+3.ax','ouo1')).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.20/0.44 tff(154,plain,(
% 0.20/0.44 ![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)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[153])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (((~![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(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!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)))) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 ((apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))) <=> (apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 (((~![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(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!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)))) | (apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[157])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 (((~![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(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!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)))) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[158, 156])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 ((~![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(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), L!0) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[161, 155, 145, 141, 18, 137, 111])).
% 0.20/0.44 tff(163,plain,(unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 ((~((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 (~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[164, 163, 110])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.44 tff(169,plain,
% 0.20/0.44 (convergent_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[168, 25, 82])).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(171,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(172,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.45 tff(173,plain,
% 0.20/0.45 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[172, 56, 169])).
% 0.20/0.45 tff(174,plain,
% 0.20/0.45 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(175,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(176,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.45 tff(177,plain,
% 0.20/0.45 (~apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[176, 70, 169])).
% 0.20/0.45 tff(178,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(179,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[178])).
% 0.20/0.45 tff(180,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) <=> (apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> ((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)))), rewrite(((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))))), rewrite((distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[181])).
% 0.20/0.45 tff(183,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.20/0.45 tff(184,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.45 tff(185,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.20/0.45 tff(186,plain,(
% 0.20/0.45 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[185])).
% 0.20/0.45 tff(187,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.20/0.45 tff(188,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, orthogonal_through_point(L!0, A!1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(189,plain,
% 0.20/0.45 ((convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | (~distinct_lines(L!0, orthogonal_through_point(L!0, A!1)))) <=> (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, orthogonal_through_point(L!0, A!1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(190,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | (~distinct_lines(L!0, orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, orthogonal_through_point(L!0, A!1)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[189])).
% 0.20/0.45 tff(191,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | (~distinct_lines(L!0, orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, orthogonal_through_point(L!0, A!1))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[190, 188])).
% 0.20/0.45 tff(192,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | (~distinct_lines(L!0, orthogonal_through_point(L!0, A!1))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(193,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), L!0), orthogonal_through_point(L!0, A!1)) | convergent_lines(L!0, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.45 tff(194,plain,
% 0.20/0.45 (~distinct_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[193, 187, 177, 173, 165])).
% 0.20/0.45 tff(195,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(196,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[195])).
% 0.20/0.45 tff(197,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(198,axiom,(![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ooc2')).
% 0.20/0.45 tff(199,plain,
% 0.20/0.45 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.45 tff(200,plain,(
% 0.20/0.45 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[199])).
% 0.20/0.45 tff(201,plain,
% 0.20/0.45 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.20/0.45 tff(202,plain,
% 0.20/0.45 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(203,plain,
% 0.20/0.45 (~apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.20/0.45 tff(204,plain,
% 0.20/0.45 (((~![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!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!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!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(205,plain,
% 0.20/0.45 ((apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(206,plain,
% 0.20/0.45 (((~![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!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!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!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[205])).
% 0.20/0.45 tff(207,plain,
% 0.20/0.45 (((~![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!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!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!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[206, 204])).
% 0.20/0.46 tff(208,plain,
% 0.20/0.46 ((~![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!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(209,plain,
% 0.20/0.46 ((~![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!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.20/0.46 tff(210,plain,
% 0.20/0.46 (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[209, 155, 82, 203])).
% 0.20/0.46 tff(211,plain,
% 0.20/0.46 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(212,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[211])).
% 0.20/0.46 tff(213,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(214,plain,
% 0.20/0.46 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(215,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[214])).
% 0.20/0.46 tff(216,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.20/0.46 tff(217,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.20/0.46 tff(218,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.20/0.46 tff(219,plain,(
% 0.20/0.46 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[218])).
% 0.20/0.46 tff(220,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.20/0.46 tff(221,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | distinct_lines(L!0, orthogonal_through_point(L!0, A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | distinct_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(222,plain,
% 0.20/0.46 ((distinct_lines(L!0, orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0))) <=> (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | distinct_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(223,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(L!0, orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | distinct_lines(L!0, orthogonal_through_point(L!0, A!1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[222])).
% 0.20/0.46 tff(224,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(L!0, orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | distinct_lines(L!0, orthogonal_through_point(L!0, A!1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[223, 221])).
% 0.20/0.46 tff(225,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(L!0, orthogonal_through_point(L!0, A!1)) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(226,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)) | distinct_lines(L!0, orthogonal_through_point(L!0, A!1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.20/0.46 tff(227,plain,
% 0.20/0.46 (~distinct_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[226, 220, 210, 194])).
% 0.20/0.46 tff(228,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(229,plain,
% 0.20/0.46 ((distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(230,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[229])).
% 0.20/0.46 tff(231,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.20/0.46 inference(transitivity,[status(thm)],[230, 228])).
% 0.20/0.46 tff(232,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(233,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), L!0) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.46 tff(234,plain,
% 0.20/0.46 (convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[233, 129, 29, 227])).
% 0.20/0.46 tff(235,plain,
% 0.20/0.46 (((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(236,plain,
% 0.20/0.46 ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[235, 18])).
% 0.20/0.46 tff(237,plain,
% 0.20/0.46 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(238,plain,
% 0.20/0.46 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(239,plain,
% 0.20/0.46 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) | (~((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.20/0.46 tff(240,plain,
% 0.20/0.46 ((~((~convergent_lines(L!0, orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(L!0, A!1))))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[239, 102, 119, 236])).
% 0.20/0.46 tff(241,plain,
% 0.20/0.46 (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[240, 110])).
% 0.20/0.46 tff(242,plain,
% 0.20/0.46 (((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) | unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(243,plain,
% 0.20/0.46 ((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.20/0.46 tff(244,plain,
% 0.20/0.46 (((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(245,plain,
% 0.20/0.46 ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[244, 9])).
% 0.20/0.46 tff(246,plain,
% 0.20/0.46 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(247,plain,
% 0.20/0.46 (((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))) <=> ((~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(248,plain,
% 0.20/0.46 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[247])).
% 0.20/0.46 tff(249,plain,
% 0.20/0.46 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[248, 246])).
% 0.20/0.47 tff(250,plain,
% 0.20/0.47 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(251,plain,
% 0.20/0.47 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~((~convergent_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | (~unorthogonal_lines(L!0, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.20/0.47 tff(252,plain,
% 0.20/0.47 (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[251, 102, 245, 243, 234])).
% 0.20/0.47 tff(253,assumption,(~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))), introduced(assumption)).
% 0.20/0.47 tff(254,plain,
% 0.20/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(255,plain,
% 0.20/0.47 ((distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))) <=> (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(256,plain,
% 0.20/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[255])).
% 0.20/0.47 tff(257,plain,
% 0.20/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[256, 254])).
% 0.20/0.47 tff(258,plain,
% 0.20/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(259,plain,
% 0.20/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))) | convergent_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.47 tff(260,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[259, 129, 253, 29, 9])).
% 0.20/0.47 tff(261,plain,(distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(262,plain,
% 0.20/0.47 (((~![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!1), L!0) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!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!1), L!0) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(263,plain,
% 0.20/0.47 ((apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(264,plain,
% 0.20/0.47 (((~![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(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!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!1), L!0) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[263])).
% 0.20/0.47 tff(265,plain,
% 0.20/0.47 (((~![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(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!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!1), L!0) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[264, 262])).
% 0.20/0.47 tff(266,plain,
% 0.20/0.47 ((~![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(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(267,plain,
% 0.20/0.47 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), L!0) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | apart_point_and_line(intersection_point(orthogonal_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)), orthogonal_through_point(L!0, A!1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.20/0.47 tff(268,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[267, 155, 82, 261, 252, 74, 60])).
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47 % E exiting
%------------------------------------------------------------------------------