%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO223+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:06:02 AM UTC 2025
% Result : Theorem 0.18s 0.50s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO223+3 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 14:43:41 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.50 % SZS status Theorem
% 0.18/0.50 % SZS output start Proof
% 0.18/0.50 tff(unorthogonal_lines_type, type, (
% 0.18/0.50 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.18/0.50 tff(orthogonal_through_point_type, type, (
% 0.18/0.50 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.18/0.50 tff(tptp_fun_A_1_type, type, (
% 0.18/0.50 tptp_fun_A_1: $i)).
% 0.18/0.50 tff(tptp_fun_L_0_type, type, (
% 0.18/0.50 tptp_fun_L_0: $i)).
% 0.18/0.50 tff(parallel_through_point_type, type, (
% 0.18/0.50 parallel_through_point: ( $i * $i ) > $i)).
% 0.18/0.50 tff(convergent_lines_type, type, (
% 0.18/0.50 convergent_lines: ( $i * $i ) > $o)).
% 0.18/0.50 tff(distinct_lines_type, type, (
% 0.18/0.50 distinct_lines: ( $i * $i ) > $o)).
% 0.18/0.50 tff(equal_lines_type, type, (
% 0.18/0.50 equal_lines: ( $i * $i ) > $o)).
% 0.18/0.50 tff(apart_point_and_line_type, type, (
% 0.18/0.50 apart_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.50 tff(1,assumption,(~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))), introduced(assumption)).
% 0.18/0.50 tff(2,plain,
% 0.18/0.50 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(3,plain,
% 0.18/0.50 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.50 tff(4,plain,
% 0.18/0.50 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(5,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.18/0.50 tff(6,plain,
% 0.18/0.50 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.50 tff(7,plain,(
% 0.18/0.50 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.18/0.50 inference(skolemize,[status(sab)],[6])).
% 0.18/0.50 tff(8,plain,
% 0.18/0.50 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.50 tff(9,plain,
% 0.18/0.50 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(10,plain,
% 0.18/0.50 (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.18/0.50 tff(11,plain,
% 0.18/0.50 (^[L: $i, M: $i, N: $i] : refl((unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(12,plain,
% 0.18/0.50 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.50 tff(13,plain,
% 0.18/0.50 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(14,plain,
% 0.18/0.50 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.50 tff(15,plain,
% 0.18/0.50 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(16,plain,
% 0.18/0.50 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(17,plain,
% 0.18/0.50 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.50 tff(18,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.18/0.50 tff(19,plain,
% 0.18/0.50 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.50 tff(20,plain,
% 0.18/0.50 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.50 tff(21,plain,(
% 0.18/0.50 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.18/0.50 inference(skolemize,[status(sab)],[20])).
% 0.18/0.50 tff(22,plain,
% 0.18/0.50 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.50 tff(23,plain,
% 0.18/0.50 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.18/0.50 tff(24,plain,
% 0.18/0.50 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(25,plain,
% 0.18/0.50 ((unorthogonal_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(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(26,plain,
% 0.18/0.50 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_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)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[25])).
% 0.18/0.50 tff(27,plain,
% 0.18/0.50 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_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)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[26, 24])).
% 0.18/0.50 tff(28,plain,
% 0.18/0.50 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_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)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(29,plain,
% 0.18/0.50 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | (~convergent_lines(L!0, L!0))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.50 tff(30,plain,
% 0.18/0.50 (~convergent_lines(L!0, L!0)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[29, 23, 10])).
% 0.18/0.50 tff(31,plain,
% 0.18/0.50 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(32,plain,
% 0.18/0.50 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[31])).
% 0.18/0.50 tff(33,plain,
% 0.18/0.50 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(34,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.18/0.50 tff(35,plain,
% 0.18/0.50 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.50 tff(36,plain,(
% 0.18/0.50 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.18/0.50 inference(skolemize,[status(sab)],[35])).
% 0.18/0.50 tff(37,plain,
% 0.18/0.50 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.50 tff(38,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(L!0, A!1), L!0))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(39,plain,
% 0.18/0.50 (~convergent_lines(parallel_through_point(L!0, A!1), L!0)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.18/0.50 tff(40,plain,
% 0.18/0.50 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(41,plain,
% 0.18/0.50 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[40])).
% 0.18/0.50 tff(42,plain,
% 0.18/0.50 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(43,plain,
% 0.18/0.50 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(44,plain,
% 0.18/0.50 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[43])).
% 0.18/0.50 tff(45,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.18/0.50 tff(46,plain,
% 0.18/0.50 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.50 tff(47,plain,
% 0.18/0.50 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.18/0.50 tff(48,plain,(
% 0.18/0.50 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.50 inference(skolemize,[status(sab)],[47])).
% 0.18/0.50 tff(49,plain,
% 0.18/0.50 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.18/0.50 tff(50,plain,
% 0.18/0.50 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(L!0, A!1), L!0)) | convergent_lines(parallel_through_point(L!0, A!1), L!0))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0)) | convergent_lines(parallel_through_point(L!0, A!1), L!0))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(51,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(L!0, A!1), L!0)) | convergent_lines(parallel_through_point(L!0, A!1), L!0))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(52,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(L!0, A!1), L!0)) | convergent_lines(parallel_through_point(L!0, A!1), L!0)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.50 tff(53,plain,
% 0.18/0.50 (~distinct_lines(parallel_through_point(L!0, A!1), L!0)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[52, 49, 39])).
% 0.18/0.50 tff(54,plain,
% 0.18/0.50 (^[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))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(55,plain,
% 0.18/0.50 (![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)))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[54])).
% 0.18/0.50 tff(56,plain,
% 0.18/0.50 (![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)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(57,plain,
% 0.18/0.50 (^[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)))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(58,plain,
% 0.18/0.50 (![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)))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[57])).
% 0.18/0.50 tff(59,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.18/0.50 tff(60,plain,
% 0.18/0.50 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.50 tff(61,plain,
% 0.18/0.50 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.18/0.50 tff(62,plain,(
% 0.18/0.50 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.50 inference(skolemize,[status(sab)],[61])).
% 0.18/0.50 tff(63,plain,
% 0.18/0.50 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.18/0.50 tff(64,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(parallel_through_point(L!0, A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, parallel_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(parallel_through_point(L!0, A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(65,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(parallel_through_point(L!0, A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(66,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(parallel_through_point(L!0, A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.50 tff(67,plain,
% 0.18/0.50 (~convergent_lines(L!0, parallel_through_point(L!0, A!1))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[66, 63, 53, 30])).
% 0.18/0.50 tff(68,plain,
% 0.18/0.50 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(L!0, parallel_through_point(L!0, A!1))) | convergent_lines(L!0, parallel_through_point(L!0, A!1)))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(L!0, parallel_through_point(L!0, A!1))) | convergent_lines(L!0, parallel_through_point(L!0, A!1)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(69,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(L!0, parallel_through_point(L!0, A!1))) | convergent_lines(L!0, parallel_through_point(L!0, A!1)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(70,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(L!0, parallel_through_point(L!0, A!1))) | convergent_lines(L!0, parallel_through_point(L!0, A!1))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.18/0.50 tff(71,plain,
% 0.18/0.50 (~distinct_lines(L!0, parallel_through_point(L!0, A!1))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[70, 49, 67])).
% 0.18/0.50 tff(72,plain,
% 0.18/0.50 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(73,plain,
% 0.18/0.50 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[72])).
% 0.18/0.50 tff(74,plain,
% 0.18/0.50 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(75,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.18/0.50 tff(76,plain,
% 0.18/0.50 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.18/0.50 tff(77,plain,(
% 0.18/0.50 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.18/0.50 inference(skolemize,[status(sab)],[76])).
% 0.18/0.50 tff(78,plain,
% 0.18/0.50 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.18/0.50 tff(79,plain,
% 0.18/0.50 (((~![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))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(80,plain,
% 0.18/0.50 ((~![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))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(81,plain,
% 0.18/0.50 ((~![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)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.50 tff(82,plain,
% 0.18/0.50 (convergent_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[81, 78, 10])).
% 0.18/0.50 tff(83,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_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(L!0, A!1), L!0)) | distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(84,plain,
% 0.18/0.50 ((distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0))) <=> ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(85,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, 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(L!0, A!1), L!0)) | distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[84])).
% 0.18/0.50 tff(86,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, 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(L!0, A!1), L!0)) | distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[85, 83])).
% 0.18/0.50 tff(87,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(88,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | distinct_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.50 tff(89,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[88, 63, 82, 71, 1])).
% 0.18/0.50 tff(90,plain,(convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(91,assumption,(~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))), introduced(assumption)).
% 0.18/0.51 tff(92,plain,
% 0.18/0.51 ((~![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)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(93,plain,
% 0.18/0.51 (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[92, 8])).
% 0.18/0.51 tff(94,plain,
% 0.18/0.51 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_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(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_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(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(95,plain,
% 0.18/0.51 ((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)) | (~convergent_lines(orthogonal_through_point(L!0, 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(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(96,plain,
% 0.18/0.51 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (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)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_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(L!0, A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[95])).
% 0.18/0.51 tff(97,plain,
% 0.18/0.51 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (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)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_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(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[96, 94])).
% 0.18/0.51 tff(98,plain,
% 0.18/0.51 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (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)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(99,plain,
% 0.18/0.51 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_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(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.51 tff(100,plain,
% 0.18/0.51 (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[99, 23, 93])).
% 0.18/0.51 tff(101,plain,
% 0.18/0.51 (^[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))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(102,plain,
% 0.18/0.51 (![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)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[101])).
% 0.18/0.51 tff(103,plain,
% 0.18/0.51 (![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)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(104,plain,
% 0.18/0.51 (^[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)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(105,plain,
% 0.18/0.51 (![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)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[104])).
% 0.18/0.51 tff(106,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.18/0.51 tff(107,plain,
% 0.18/0.51 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.18/0.51 tff(108,plain,
% 0.18/0.51 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.18/0.51 tff(109,plain,(
% 0.18/0.51 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.51 inference(skolemize,[status(sab)],[108])).
% 0.18/0.51 tff(110,plain,
% 0.18/0.51 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.18/0.51 tff(111,plain,
% 0.18/0.51 (((~![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(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_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(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(112,plain,
% 0.18/0.51 ((convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))) <=> (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(113,plain,
% 0.18/0.51 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_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(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[112])).
% 0.18/0.51 tff(114,plain,
% 0.18/0.51 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_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(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[113, 111])).
% 0.18/0.51 tff(115,plain,
% 0.18/0.51 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(116,plain,
% 0.18/0.51 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.18/0.51 tff(117,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[116, 110, 100, 91, 90])).
% 0.18/0.51 tff(118,plain,(convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(119,plain,
% 0.18/0.51 (((~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)),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(120,plain,
% 0.18/0.51 ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[119, 10])).
% 0.18/0.51 tff(121,assumption,(~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))), introduced(assumption)).
% 0.18/0.51 tff(122,plain,
% 0.18/0.51 (((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(123,plain,
% 0.18/0.51 (unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.18/0.51 tff(124,plain,
% 0.18/0.51 (((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(125,plain,
% 0.18/0.51 (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[124, 121])).
% 0.18/0.51 tff(126,plain,
% 0.18/0.51 (((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0))) | convergent_lines(parallel_through_point(L!0, A!1), L!0)),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(127,plain,
% 0.18/0.51 ((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[126, 39])).
% 0.18/0.51 tff(128,plain,
% 0.18/0.51 (^[L: $i, M: $i, N: $i] : refl(((~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(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(129,plain,
% 0.18/0.51 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(L, M)) | (~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(L, M)) | (~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[128])).
% 0.18/0.51 tff(130,plain,
% 0.18/0.51 (^[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)))) <=> ((~unorthogonal_lines(L, M)) | (~convergent_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)))) <=> ((~unorthogonal_lines(L, M)) | (~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(131,plain,
% 0.18/0.51 (![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] : ((~unorthogonal_lines(L, M)) | (~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[130])).
% 0.18/0.51 tff(132,plain,
% 0.18/0.51 (![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))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(133,plain,
% 0.18/0.51 (^[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))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(134,plain,
% 0.18/0.51 (![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))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[133])).
% 0.18/0.51 tff(135,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/sandbox/benchmark/Axioms/GEO006+3.ax','oac1')).
% 0.18/0.51 tff(136,plain,
% 0.18/0.51 (![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))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.18/0.51 tff(137,plain,
% 0.18/0.51 (![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))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.18/0.51 tff(138,plain,(
% 0.18/0.51 ![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))))),
% 0.18/0.51 inference(skolemize,[status(sab)],[137])).
% 0.18/0.51 tff(139,plain,
% 0.18/0.51 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(L, M)) | (~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.18/0.51 tff(140,plain,
% 0.18/0.51 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(L, M)) | (~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[139, 129])).
% 0.18/0.51 tff(141,plain,
% 0.18/0.51 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(L, M)) | (~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), 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)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(L, M)) | (~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), 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)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(142,plain,
% 0.18/0.51 (((~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(L!0, A!1), 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(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0))))) <=> ((~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), 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)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(143,plain,
% 0.18/0.51 (((~![L: $i, M: $i, N: $i] : ((~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(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(L!0, A!1), 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(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(L, M)) | (~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), 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))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[142])).
% 0.18/0.51 tff(144,plain,
% 0.18/0.51 (((~![L: $i, M: $i, N: $i] : ((~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(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(L!0, A!1), 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(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(L, M)) | (~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), 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)))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[143, 141])).
% 0.18/0.51 tff(145,plain,
% 0.18/0.51 ((~![L: $i, M: $i, N: $i] : ((~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(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~convergent_lines(parallel_through_point(L!0, A!1), 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(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(146,plain,
% 0.18/0.51 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(L, M)) | (~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.18/0.51 tff(147,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[146, 140, 127, 125, 123, 120])).
% 0.18/0.51 tff(148,plain,((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(149,plain,
% 0.18/0.51 ((~((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(150,plain,
% 0.18/0.51 ((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.18/0.51 tff(151,plain,
% 0.18/0.51 (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[150, 118])).
% 0.18/0.51 tff(152,plain,
% 0.18/0.51 (^[X: $i, Y: $i] : refl((~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(153,plain,
% 0.18/0.51 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[152])).
% 0.18/0.51 tff(154,plain,
% 0.18/0.51 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(155,plain,
% 0.18/0.51 (^[X: $i, Y: $i] : trans(rewrite((equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))), rewrite((~(distinct_lines(X, Y) <=> equal_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))), ((equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(156,plain,
% 0.18/0.51 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[155])).
% 0.18/0.51 tff(157,axiom,(![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax2')).
% 0.18/0.51 tff(158,plain,
% 0.18/0.51 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.18/0.51 tff(159,plain,
% 0.18/0.51 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.18/0.51 tff(160,plain,(
% 0.18/0.51 ![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.18/0.51 inference(skolemize,[status(sab)],[159])).
% 0.18/0.51 tff(161,plain,
% 0.18/0.51 (![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.18/0.51 tff(162,plain,
% 0.18/0.51 ((~![X: $i, Y: $i] : (~(distinct_lines(X, Y) <=> equal_lines(X, Y)))) | (~(distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) <=> equal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(163,plain,
% 0.18/0.51 (~(distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) <=> equal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.18/0.51 tff(164,plain,
% 0.18/0.51 ((~![A: $i, L: $i] : equal_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A))) <=> (~![A: $i, L: $i] : equal_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(165,axiom,(~![A: $i, L: $i] : equal_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.18/0.51 tff(166,plain,
% 0.18/0.51 (~![A: $i, L: $i] : equal_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.18/0.51 tff(167,plain,
% 0.18/0.51 (~![A: $i, L: $i] : equal_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[166, 164])).
% 0.18/0.51 tff(168,plain,
% 0.18/0.51 (~![A: $i, L: $i] : equal_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[167, 164])).
% 0.18/0.51 tff(169,plain,
% 0.18/0.51 (~![A: $i, L: $i] : equal_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.18/0.52 tff(170,plain,(
% 0.18/0.52 ~equal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.18/0.52 inference(skolemize,[status(sab)],[169])).
% 0.18/0.52 tff(171,plain,
% 0.18/0.52 ((distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) <=> equal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | equal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(172,plain,
% 0.18/0.52 ((distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) <=> equal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.18/0.52 tff(173,plain,
% 0.18/0.52 (distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[172, 163])).
% 0.18/0.52 tff(174,plain,
% 0.18/0.52 (^[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))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(175,plain,
% 0.18/0.52 (![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)))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[174])).
% 0.18/0.52 tff(176,plain,
% 0.18/0.52 (![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)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(177,axiom,(![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc2')).
% 0.18/0.52 tff(178,plain,
% 0.18/0.52 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.18/0.52 tff(179,plain,(
% 0.18/0.52 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.18/0.52 inference(skolemize,[status(sab)],[178])).
% 0.18/0.52 tff(180,plain,
% 0.18/0.52 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.18/0.52 tff(181,plain,
% 0.18/0.52 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(182,plain,
% 0.18/0.52 (~apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.18/0.52 tff(183,plain,
% 0.18/0.52 (^[X: $i, Y: $i] : refl((~apart_point_and_line(X, parallel_through_point(Y, X))) <=> (~apart_point_and_line(X, parallel_through_point(Y, X))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(184,plain,
% 0.18/0.52 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[183])).
% 0.18/0.52 tff(185,plain,
% 0.18/0.52 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(186,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.18/0.52 tff(187,plain,
% 0.18/0.52 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.18/0.52 tff(188,plain,(
% 0.18/0.52 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.18/0.52 inference(skolemize,[status(sab)],[187])).
% 0.18/0.52 tff(189,plain,
% 0.18/0.52 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.18/0.52 tff(190,plain,
% 0.18/0.52 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(A!1, parallel_through_point(L!0, A!1)))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(191,plain,
% 0.18/0.52 (~apart_point_and_line(A!1, parallel_through_point(L!0, A!1))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.18/0.52 tff(192,plain,
% 0.18/0.52 (^[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))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(193,plain,
% 0.18/0.52 (![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)))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[192])).
% 0.18/0.52 tff(194,plain,
% 0.18/0.52 (![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)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(195,plain,
% 0.18/0.52 (^[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)))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(196,plain,
% 0.18/0.52 (![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)))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[195])).
% 0.18/0.52 tff(197,axiom,(![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ouo1')).
% 0.18/0.52 tff(198,plain,
% 0.18/0.52 (![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)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.18/0.52 tff(199,plain,
% 0.18/0.52 (![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)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.18/0.52 tff(200,plain,(
% 0.18/0.52 ![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)))),
% 0.18/0.52 inference(skolemize,[status(sab)],[199])).
% 0.18/0.52 tff(201,plain,
% 0.18/0.52 (![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)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[200, 193])).
% 0.18/0.52 tff(202,plain,
% 0.18/0.52 (((~![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, parallel_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(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_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)))) | apart_point_and_line(A!1, parallel_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(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(203,plain,
% 0.18/0.52 ((apart_point_and_line(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(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> (apart_point_and_line(A!1, parallel_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(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(204,plain,
% 0.18/0.52 (((~![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(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(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_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)))) | (apart_point_and_line(A!1, parallel_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(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[203])).
% 0.18/0.52 tff(205,plain,
% 0.18/0.52 (((~![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(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(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_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)))) | apart_point_and_line(A!1, parallel_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(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.18/0.52 inference(transitivity,[status(thm)],[204, 202])).
% 0.18/0.52 tff(206,plain,
% 0.18/0.52 ((~![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(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(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(207,plain,
% 0.18/0.52 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.18/0.52 tff(208,plain,
% 0.18/0.52 ($false),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[207, 201, 191, 93, 182, 173, 151])).
% 0.18/0.52 % SZS output end Proof
% 0.18/0.52 % E exiting
%------------------------------------------------------------------------------