%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO201+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:17:27 PM UTC 2026
% Result : Theorem 27.40s 9.96s
% Output : Proof 27.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/6.21 % Computer : n008.cluster.edu
% 0.09/6.21 % Model : x86_64 x86_64
% 0.09/6.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/6.21 % Memory : 8046.5625MB
% 0.09/6.21 % OS : Linux 6.8.0-71-generic
% 0.09/6.21 % CPULimit : 300
% 0.09/6.21 % WCLimit : 300
% 0.09/6.21 % DateTime : Wed Sep 23 11:27:49 UTC 2026
% 0.09/6.21 % CPUTime :
% 0.09/6.21 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.40/9.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.40/9.96 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.40/9.96 fof(sdef71, definition, (spl71 <=> (convergent_lines(sk0,sk0))), introduced(definition, [new_symbols(naming, [spl71])], [avatar_definition])).
% 27.40/9.96 cnf(p1432, plain, (convergent_lines(sk0,sk0) | ~spl71), inference(avatar_component_clause, [status(thm)], [sdef71])).
% 27.40/9.96 fof(f2, axiom, ! [X] : ~ convergent_lines(X,X), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', apart3)).
% 27.40/9.96 fof(f2_nnf, plain, ! [X] : (~(convergent_lines(X,X))), inference(nnf_transformation, [status(thm)], [f2])).
% 27.40/9.96 fof(f2_sk, plain, ! [X] : (~(convergent_lines(X,X))), inference(skolemisation, [status(esa)], [f2_nnf])).
% 27.40/9.96 cnf(c2, plain, ~convergent_lines(X0,X0), inference(cnf_transformation, [status(esa)], [f2_sk])).
% 27.40/9.96 cnf(p1441, plain, ($false | ~spl71), inference(resolution, [status(thm)], [p1432, c2])).
% 27.40/9.96 cnf(sct0, plain, (~spl71), inference(avatar_contradiction_clause, [status(thm)], [p1441])).
% 27.40/9.96 fof(sdef72, definition, (spl72 <=> (distinct_lines(sk0,sk0))), introduced(definition, [new_symbols(naming, [spl72])], [avatar_definition])).
% 27.40/9.96 cnf(p1435, plain, (distinct_lines(sk0,sk0) | ~spl72), inference(avatar_component_clause, [status(thm)], [sdef72])).
% 27.40/9.96 fof(f1, axiom, ! [X] : ~ distinct_lines(X,X), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', apart2)).
% 27.40/9.96 fof(f1_nnf, plain, ! [X] : (~(distinct_lines(X,X))), inference(nnf_transformation, [status(thm)], [f1])).
% 27.40/9.96 fof(f1_sk, plain, ! [X] : (~(distinct_lines(X,X))), inference(skolemisation, [status(esa)], [f1_nnf])).
% 27.40/9.96 cnf(c1, plain, ~distinct_lines(X0,X0), inference(cnf_transformation, [status(esa)], [f1_sk])).
% 27.40/9.96 cnf(p1442, plain, ($false | ~spl72), inference(resolution, [status(thm)], [p1435, c1])).
% 27.40/9.96 cnf(sct1, plain, (~spl72), inference(avatar_contradiction_clause, [status(thm)], [p1442])).
% 27.40/9.96 fof(sdef1, definition, (spl1 <=> (apart_point_and_line(intersection_point(sk0,sk1),sk1))), introduced(definition, [new_symbols(naming, [spl1])], [avatar_definition])).
% 27.40/9.96 cnf(p1215, plain, (apart_point_and_line(intersection_point(sk0,sk1),sk1) | ~spl1), inference(avatar_component_clause, [status(thm)], [sdef1])).
% 27.40/9.96 fof(f7, axiom, ! [X,Y,Z] : ( convergent_lines(X,Y) => ( ( apart_point_and_line(Z,X) | apart_point_and_line(Z,Y) ) => distinct_points(Z,intersection_point(X,Y)) ) ), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', con2)).
% 27.40/9.96 fof(f7_nnf, plain, ! [X,Y,Z] : ((~(convergent_lines(X,Y)) | ((~(apart_point_and_line(Z,X)) & ~(apart_point_and_line(Z,Y))) | distinct_points(Z,intersection_point(X,Y))))), inference(nnf_transformation, [status(thm)], [f7])).
% 27.40/9.96 fof(f7_sk, plain, ! [X,Y,Z] : ((~(convergent_lines(X,Y)) | ((~(apart_point_and_line(Z,X)) & ~(apart_point_and_line(Z,Y))) | distinct_points(Z,intersection_point(X,Y))))), inference(skolemisation, [status(esa)], [f7_nnf])).
% 27.40/9.96 cnf(c9, plain, ~convergent_lines(X0,X1) | ~apart_point_and_line(X2,X1) | distinct_points(X2,intersection_point(X0,X1)), inference(cnf_transformation, [status(esa)], [f7_sk])).
% 27.40/9.96 fof(f12, conjecture, ! [X,Y] : ( convergent_lines(X,Y) => ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', con)).
% 27.40/9.96 fof(f12_neg, negated_conjecture, ~(! [X,Y] : ( convergent_lines(X,Y) => ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) )), inference(negated_conjecture, [status(cth)], [f12])).
% 27.40/9.96 fof(f12_nnf, plain, ? [X,Y] : ((convergent_lines(X,Y) & distinct_points(intersection_point(X,Y),intersection_point(Y,X)))), inference(nnf_transformation, [status(thm)], [f12_neg])).
% 27.40/9.96 fof(f12_sk, plain, (convergent_lines(sk0,sk1) & distinct_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0))), inference(skolemisation, [status(esa), new_symbols(skolem, [sk0,sk1])], [f12_nnf])).
% 27.40/9.96 cnf(c14, plain, convergent_lines(sk0,sk1), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 27.40/9.96 cnf(p81, plain, ~apart_point_and_line(X0,sk1) | distinct_points(X0,intersection_point(sk0,sk1)), inference(resolution, [status(thm)], [c9, c14])).
% 27.40/9.96 cnf(p1443, plain, (distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1)) | ~spl1), inference(resolution, [status(thm)], [p1215, p81])).
% 27.40/9.96 fof(f0, axiom, ! [X] : ~ distinct_points(X,X), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', apart1)).
% 27.40/9.96 fof(f0_nnf, plain, ! [X] : (~(distinct_points(X,X))), inference(nnf_transformation, [status(thm)], [f0])).
% 27.40/9.96 fof(f0_sk, plain, ! [X] : (~(distinct_points(X,X))), inference(skolemisation, [status(esa)], [f0_nnf])).
% 27.40/9.96 cnf(c0, plain, ~distinct_points(X0,X0), inference(cnf_transformation, [status(esa)], [f0_sk])).
% 27.40/9.96 cnf(p1682, plain, ($false | ~spl1), inference(resolution, [status(thm)], [p1443, c0])).
% 27.40/9.96 cnf(sct2, plain, (~spl1), inference(avatar_contradiction_clause, [status(thm)], [p1682])).
% 27.40/9.96 fof(sdef2, definition, (spl2 <=> (apart_point_and_line(intersection_point(sk1,sk0),sk0))), introduced(definition, [new_symbols(naming, [spl2])], [avatar_definition])).
% 27.40/9.96 cnf(p1216, plain, (apart_point_and_line(intersection_point(sk1,sk0),sk0) | ~spl2), inference(avatar_component_clause, [status(thm)], [sdef2])).
% 27.40/9.96 fof(f5, axiom, ! [X,Y,Z] : ( convergent_lines(X,Y) => ( convergent_lines(X,Z) | convergent_lines(Y,Z) ) ), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', apart6)).
% 27.40/9.96 fof(f5_nnf, plain, ! [X,Y,Z] : ((~(convergent_lines(X,Y)) | (convergent_lines(X,Z) | convergent_lines(Y,Z)))), inference(nnf_transformation, [status(thm)], [f5])).
% 27.40/9.96 fof(f5_sk, plain, ! [X,Y,Z] : ((~(convergent_lines(X,Y)) | (convergent_lines(X,Z) | convergent_lines(Y,Z)))), inference(skolemisation, [status(esa)], [f5_nnf])).
% 27.40/9.96 cnf(c5, plain, ~convergent_lines(X0,X1) | convergent_lines(X0,X2) | convergent_lines(X1,X2), inference(cnf_transformation, [status(esa)], [f5_sk])).
% 27.40/9.96 cnf(p29, plain, convergent_lines(sk0,X0) | convergent_lines(sk1,X0), inference(resolution, [status(thm)], [c5, c14])).
% 27.40/9.96 cnf(p33, plain, convergent_lines(sk0,X0) | convergent_lines(sk1,X1) | convergent_lines(X0,X1), inference(resolution, [status(thm)], [p29, c5])).
% 27.40/9.96 cnf(p41, plain, convergent_lines(sk0,X0) | convergent_lines(X0,sk1), inference(resolution, [status(thm)], [p33, c2])).
% 27.40/9.96 cnf(p50, plain, convergent_lines(X0,sk1) | convergent_lines(sk0,X1) | convergent_lines(X0,X1), inference(resolution, [status(thm)], [p41, c5])).
% 27.40/9.96 cnf(p110, plain, convergent_lines(X0,sk1) | convergent_lines(X0,sk0), inference(resolution, [status(thm)], [p50, c2])).
% 27.40/9.96 cnf(p123, plain, convergent_lines(sk1,sk0), inference(resolution, [status(thm)], [p110, c2])).
% 27.40/9.96 cnf(p129, plain, ~apart_point_and_line(X0,sk0) | distinct_points(X0,intersection_point(sk1,sk0)), inference(resolution, [status(thm)], [p123, c9])).
% 27.40/9.96 cnf(p1649, plain, (distinct_points(intersection_point(sk1,sk0),intersection_point(sk1,sk0)) | ~spl2), inference(resolution, [status(thm)], [p1216, p129])).
% 27.40/9.96 cnf(p1683, plain, ($false | ~spl2), inference(resolution, [status(thm)], [p1649, c0])).
% 27.40/9.96 cnf(sct3, plain, (~spl2), inference(avatar_contradiction_clause, [status(thm)], [p1683])).
% 27.40/9.96 fof(sdef0, definition, (spl0 <=> (apart_point_and_line(intersection_point(sk0,sk1),sk0))), introduced(definition, [new_symbols(naming, [spl0])], [avatar_definition])).
% 27.40/9.96 cnf(p1214, plain, (apart_point_and_line(intersection_point(sk0,sk1),sk0) | ~spl0), inference(avatar_component_clause, [status(thm)], [sdef0])).
% 27.40/9.96 cnf(c8, plain, ~convergent_lines(X0,X1) | ~apart_point_and_line(X2,X0) | distinct_points(X2,intersection_point(X0,X1)), inference(cnf_transformation, [status(esa)], [f7_sk])).
% 27.40/9.96 cnf(p59, plain, ~apart_point_and_line(X0,sk0) | distinct_points(X0,intersection_point(sk0,sk1)), inference(resolution, [status(thm)], [c8, c14])).
% 27.40/9.96 cnf(p1420, plain, (distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1)) | ~spl0), inference(resolution, [status(thm)], [p1214, p59])).
% 27.40/9.96 cnf(p1685, plain, ($false | ~spl0), inference(resolution, [status(thm)], [p1420, c0])).
% 27.40/9.96 cnf(sct4, plain, (~spl0), inference(avatar_contradiction_clause, [status(thm)], [p1685])).
% 27.40/9.96 fof(sdef3, definition, (spl3 <=> (apart_point_and_line(intersection_point(sk1,sk0),sk1))), introduced(definition, [new_symbols(naming, [spl3])], [avatar_definition])).
% 27.40/9.96 cnf(p1217, plain, (apart_point_and_line(intersection_point(sk1,sk0),sk1) | ~spl3), inference(avatar_component_clause, [status(thm)], [sdef3])).
% 27.40/9.96 cnf(p128, plain, ~apart_point_and_line(X0,sk1) | distinct_points(X0,intersection_point(sk1,sk0)), inference(resolution, [status(thm)], [p123, c8])).
% 27.40/9.96 cnf(p1667, plain, (distinct_points(intersection_point(sk1,sk0),intersection_point(sk1,sk0)) | ~spl3), inference(resolution, [status(thm)], [p1217, p128])).
% 27.40/9.96 cnf(p1686, plain, ($false | ~spl3), inference(resolution, [status(thm)], [p1667, c0])).
% 27.40/9.96 cnf(sct5, plain, (~spl3), inference(avatar_contradiction_clause, [status(thm)], [p1686])).
% 27.40/9.96 fof(f8, axiom, ! [X,Y,U,V] : ( ( distinct_points(X,Y) & distinct_lines(U,V) ) => ( apart_point_and_line(X,U) | apart_point_and_line(X,V) | apart_point_and_line(Y,U) | apart_point_and_line(Y,V) ) ), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cu1)).
% 27.40/9.96 fof(f8_nnf, plain, ! [X,Y,U,V] : (((~(distinct_points(X,Y)) | ~(distinct_lines(U,V))) | (((apart_point_and_line(X,U) | apart_point_and_line(X,V)) | apart_point_and_line(Y,U)) | apart_point_and_line(Y,V)))), inference(nnf_transformation, [status(thm)], [f8])).
% 27.40/9.96 fof(f8_sk, plain, ! [X,Y,U,V] : (((~(distinct_points(X,Y)) | ~(distinct_lines(U,V))) | (((apart_point_and_line(X,U) | apart_point_and_line(X,V)) | apart_point_and_line(Y,U)) | apart_point_and_line(Y,V)))), inference(skolemisation, [status(esa)], [f8_nnf])).
% 27.40/9.96 cnf(c10, plain, ~distinct_points(X0,X1) | ~distinct_lines(X2,X3) | apart_point_and_line(X0,X2) | apart_point_and_line(X0,X3) | apart_point_and_line(X1,X2) | apart_point_and_line(X1,X3), inference(cnf_transformation, [status(esa)], [f8_sk])).
% 27.40/9.96 cnf(c15, plain, distinct_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0)), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 27.40/9.96 cnf(p121, plain, ~distinct_lines(X0,X1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1), inference(resolution, [status(thm)], [c10, c15])).
% 27.40/9.96 fof(f11, axiom, ! [X,Y] : ( convergent_lines(X,Y) => distinct_lines(X,Y) ), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ceq3)).
% 27.40/9.96 fof(f11_nnf, plain, ! [X,Y] : ((~(convergent_lines(X,Y)) | distinct_lines(X,Y))), inference(nnf_transformation, [status(thm)], [f11])).
% 27.40/9.96 fof(f11_sk, plain, ! [X,Y] : ((~(convergent_lines(X,Y)) | distinct_lines(X,Y))), inference(skolemisation, [status(esa)], [f11_nnf])).
% 27.40/9.96 cnf(c13, plain, ~convergent_lines(X0,X1) | distinct_lines(X0,X1), inference(cnf_transformation, [status(esa)], [f11_sk])).
% 27.40/9.96 cnf(p16, plain, distinct_lines(sk0,sk1), inference(resolution, [status(thm)], [c13, c14])).
% 27.40/9.96 cnf(p1213, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),sk1), inference(resolution, [status(thm)], [p121, p16])).
% 27.40/9.96 cnf(ssp0, plain, (spl0 | spl1 | spl2 | spl3), inference(avatar_split_clause, [status(thm)], [p1213, sdef0, sdef1, sdef2, sdef3])).
% 27.40/9.96 fof(f4, axiom, ! [X,Y,Z] : ( distinct_lines(X,Y) => ( distinct_lines(X,Z) | distinct_lines(Y,Z) ) ), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', apart5)).
% 27.40/9.96 fof(f4_nnf, plain, ! [X,Y,Z] : ((~(distinct_lines(X,Y)) | (distinct_lines(X,Z) | distinct_lines(Y,Z)))), inference(nnf_transformation, [status(thm)], [f4])).
% 27.40/9.96 fof(f4_sk, plain, ! [X,Y,Z] : ((~(distinct_lines(X,Y)) | (distinct_lines(X,Z) | distinct_lines(Y,Z)))), inference(skolemisation, [status(esa)], [f4_nnf])).
% 27.40/9.96 cnf(c4, plain, ~distinct_lines(X0,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(cnf_transformation, [status(esa)], [f4_sk])).
% 27.40/9.96 cnf(p19, plain, distinct_lines(sk0,X0) | distinct_lines(sk1,X0), inference(resolution, [status(thm)], [c4, p16])).
% 27.40/9.96 cnf(p1218, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk0,X0), inference(resolution, [status(thm)], [p121, p19])).
% 27.40/9.96 fof(sdef4, definition, (spl4 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk0,X0))), introduced(definition, [new_symbols(naming, [spl4])], [avatar_definition])).
% 27.40/9.96 cnf(ssp1, plain, (spl1 | spl3 | spl4), inference(avatar_split_clause, [status(thm)], [p1218, sdef1, sdef3, sdef4])).
% 27.40/9.96 cnf(p20, plain, distinct_lines(sk0,X0) | distinct_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p19, c4])).
% 27.40/9.96 cnf(p1220, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p121, p20])).
% 27.40/9.96 fof(sdef5, definition, (spl5 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl5])], [avatar_definition])).
% 27.40/9.96 cnf(ssp2, plain, (spl0 | spl2 | spl5), inference(avatar_split_clause, [status(thm)], [p1220, sdef0, sdef2, sdef5])).
% 27.40/9.96 cnf(p1222, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk0,X1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p121, p20])).
% 27.40/9.96 fof(sdef6, definition, (spl6 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk0,X1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl6])], [avatar_definition])).
% 27.40/9.96 cnf(ssp3, plain, (spl1 | spl3 | spl6), inference(avatar_split_clause, [status(thm)], [p1222, sdef1, sdef3, sdef6])).
% 27.40/9.96 cnf(p1224, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk0,X0) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p20])).
% 27.40/9.96 fof(sdef7, definition, (spl7 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X0))), introduced(definition, [new_symbols(naming, [spl7])], [avatar_definition])).
% 27.40/9.96 cnf(ssp4, plain, (spl4 | spl7), inference(avatar_split_clause, [status(thm)], [p1224, sdef4, sdef7])).
% 27.40/9.96 cnf(p21, plain, distinct_lines(sk0,X0) | distinct_lines(X0,sk1), inference(resolution, [status(thm)], [p20, c1])).
% 27.40/9.96 cnf(p1226, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,sk1), inference(resolution, [status(thm)], [p121, p21])).
% 27.40/9.96 fof(sdef8, definition, (spl8 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,sk1))), introduced(definition, [new_symbols(naming, [spl8])], [avatar_definition])).
% 27.40/9.96 cnf(ssp5, plain, (spl0 | spl2 | spl8), inference(avatar_split_clause, [status(thm)], [p1226, sdef0, sdef2, sdef8])).
% 27.40/9.96 cnf(p25, plain, distinct_lines(X0,sk1) | distinct_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p21, c4])).
% 27.40/9.96 cnf(p1228, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | distinct_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p121, p25])).
% 27.40/9.96 fof(sdef9, definition, (spl9 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk0,X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl9])], [avatar_definition])).
% 27.40/9.96 cnf(ssp6, plain, (spl1 | spl3 | spl9), inference(avatar_split_clause, [status(thm)], [p1228, sdef1, sdef3, sdef9])).
% 27.40/9.96 cnf(p1230, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p121, p25])).
% 27.40/9.96 fof(sdef10, definition, (spl10 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl10])], [avatar_definition])).
% 27.40/9.96 cnf(ssp7, plain, (spl0 | spl2 | spl10), inference(avatar_split_clause, [status(thm)], [p1230, sdef0, sdef2, sdef10])).
% 27.40/9.96 cnf(p1232, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk1) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p25])).
% 27.40/9.96 cnf(ssp8, plain, (spl4 | spl8), inference(avatar_split_clause, [status(thm)], [p1232, sdef4, sdef8])).
% 27.40/9.96 cnf(p26, plain, distinct_lines(X0,sk1) | distinct_lines(X0,sk0), inference(resolution, [status(thm)], [p25, c1])).
% 27.40/9.96 cnf(p1233, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | distinct_lines(X0,sk0), inference(resolution, [status(thm)], [p121, p26])).
% 27.40/9.96 fof(sdef11, definition, (spl11 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,sk0))), introduced(definition, [new_symbols(naming, [spl11])], [avatar_definition])).
% 27.40/9.96 cnf(ssp9, plain, (spl1 | spl3 | spl11), inference(avatar_split_clause, [status(thm)], [p1233, sdef1, sdef3, sdef11])).
% 27.40/9.96 cnf(p31, plain, distinct_lines(X0,sk0) | distinct_lines(X0,X1) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p26, c4])).
% 27.40/9.96 cnf(p1235, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk0) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p31])).
% 27.40/9.96 cnf(ssp10, plain, (spl7 | spl11), inference(avatar_split_clause, [status(thm)], [p1235, sdef7, sdef11])).
% 27.40/9.96 cnf(p1236, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk0) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p121, p31])).
% 27.40/9.96 fof(sdef12, definition, (spl12 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk0) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl12])], [avatar_definition])).
% 27.40/9.96 cnf(ssp11, plain, (spl1 | spl3 | spl12), inference(avatar_split_clause, [status(thm)], [p1236, sdef1, sdef3, sdef12])).
% 27.40/9.96 cnf(p37, plain, distinct_lines(X0,sk0) | distinct_lines(sk1,X0), inference(resolution, [status(thm)], [p31, c1])).
% 27.40/9.96 cnf(p1238, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | distinct_lines(sk1,X0), inference(resolution, [status(thm)], [p121, p37])).
% 27.40/9.96 cnf(ssp12, plain, (spl0 | spl2 | spl7), inference(avatar_split_clause, [status(thm)], [p1238, sdef0, sdef2, sdef7])).
% 27.40/9.96 cnf(p40, plain, distinct_lines(sk1,X0) | distinct_lines(X0,X1) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p37, c4])).
% 27.40/9.96 cnf(p1239, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p121, p40])).
% 27.40/9.96 fof(sdef13, definition, (spl13 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl13])], [avatar_definition])).
% 27.40/9.96 cnf(ssp13, plain, (spl0 | spl2 | spl13), inference(avatar_split_clause, [status(thm)], [p1239, sdef0, sdef2, sdef13])).
% 27.40/9.96 cnf(p44, plain, convergent_lines(sk0,X0) | convergent_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p33, c13])).
% 27.40/9.96 cnf(p1241, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk0,X0) | convergent_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p44])).
% 27.40/9.96 fof(sdef14, definition, (spl14 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X0))), introduced(definition, [new_symbols(naming, [spl14])], [avatar_definition])).
% 27.40/9.96 fof(sdef15, definition, (spl15 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X0))), introduced(definition, [new_symbols(naming, [spl15])], [avatar_definition])).
% 27.40/9.96 cnf(ssp14, plain, (spl14 | spl15), inference(avatar_split_clause, [status(thm)], [p1241, sdef14, sdef15])).
% 27.40/9.96 cnf(p32, plain, convergent_lines(sk0,X0) | distinct_lines(sk1,X0), inference(resolution, [status(thm)], [p29, c13])).
% 27.40/9.96 cnf(p34, plain, distinct_lines(sk1,X0) | convergent_lines(sk0,X1) | convergent_lines(X0,X1), inference(resolution, [status(thm)], [p32, c5])).
% 27.40/9.96 cnf(p56, plain, distinct_lines(sk1,X0) | convergent_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p34, c13])).
% 27.40/9.96 cnf(p1244, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p121, p56])).
% 27.40/9.96 fof(sdef16, definition, (spl16 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl16])], [avatar_definition])).
% 27.40/9.96 cnf(ssp15, plain, (spl1 | spl3 | spl16), inference(avatar_split_clause, [status(thm)], [p1244, sdef1, sdef3, sdef16])).
% 27.40/9.96 cnf(p1246, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk1,X0) | convergent_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p56])).
% 27.40/9.96 cnf(ssp16, plain, (spl7 | spl14), inference(avatar_split_clause, [status(thm)], [p1246, sdef7, sdef14])).
% 27.40/9.96 cnf(p42, plain, convergent_lines(sk1,X0) | convergent_lines(X1,X0) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p33, c13])).
% 27.40/9.96 cnf(p75, plain, convergent_lines(sk1,X0) | distinct_lines(sk0,X1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p42, c13])).
% 27.40/9.96 cnf(p1247, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p121, p75])).
% 27.40/9.96 fof(sdef17, definition, (spl17 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl17])], [avatar_definition])).
% 27.40/9.96 cnf(ssp17, plain, (spl0 | spl2 | spl17), inference(avatar_split_clause, [status(thm)], [p1247, sdef0, sdef2, sdef17])).
% 27.40/9.96 cnf(p1249, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk1,X1) | distinct_lines(sk0,X0), inference(resolution, [status(thm)], [p121, p75])).
% 27.40/9.96 cnf(ssp18, plain, (spl4 | spl15), inference(avatar_split_clause, [status(thm)], [p1249, sdef4, sdef15])).
% 27.40/9.96 cnf(p43, plain, convergent_lines(sk0,X0) | convergent_lines(X0,X1) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p33, c13])).
% 27.40/9.96 cnf(p97, plain, convergent_lines(sk0,X0) | distinct_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p43, c13])).
% 27.40/9.96 cnf(p1250, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p121, p97])).
% 27.40/9.96 fof(sdef18, definition, (spl18 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl18])], [avatar_definition])).
% 27.40/9.96 cnf(ssp19, plain, (spl1 | spl3 | spl18), inference(avatar_split_clause, [status(thm)], [p1250, sdef1, sdef3, sdef18])).
% 27.40/9.96 cnf(p112, plain, convergent_lines(X0,sk1) | convergent_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p50, c13])).
% 27.40/9.96 cnf(p1252, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk1) | convergent_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p112])).
% 27.40/9.96 fof(sdef19, definition, (spl19 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X0,sk1))), introduced(definition, [new_symbols(naming, [spl19])], [avatar_definition])).
% 27.40/9.96 cnf(ssp20, plain, (spl14 | spl19), inference(avatar_split_clause, [status(thm)], [p1252, sdef14, sdef19])).
% 27.40/9.96 cnf(p22, plain, distinct_lines(sk1,X0) | distinct_lines(X1,X0) | distinct_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p20, c4])).
% 27.40/9.96 cnf(p1254, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,X0) | distinct_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p121, p22])).
% 27.40/9.96 fof(sdef20, definition, (spl20 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,X0) | distinct_lines(sk0,X2) | distinct_lines(X1,X2))), introduced(definition, [new_symbols(naming, [spl20])], [avatar_definition])).
% 27.40/9.96 cnf(ssp21, plain, (spl1 | spl3 | spl20), inference(avatar_split_clause, [status(thm)], [p1254, sdef1, sdef3, sdef20])).
% 27.40/9.96 cnf(p1256, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk1,X1) | distinct_lines(sk0,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p121, p22])).
% 27.40/9.96 cnf(ssp22, plain, (spl7 | spl9), inference(avatar_split_clause, [status(thm)], [p1256, sdef7, sdef9])).
% 27.40/9.96 cnf(p1257, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X1) | distinct_lines(X2,X1) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p22])).
% 27.40/9.96 fof(sdef21, definition, (spl21 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X1) | distinct_lines(X2,X1) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl21])], [avatar_definition])).
% 27.40/9.96 cnf(ssp23, plain, (spl0 | spl2 | spl21), inference(avatar_split_clause, [status(thm)], [p1257, sdef0, sdef2, sdef21])).
% 27.40/9.96 cnf(p1259, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk1,X2) | distinct_lines(X0,X2) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p22])).
% 27.40/9.96 cnf(ssp24, plain, (spl4 | spl5), inference(avatar_split_clause, [status(thm)], [p1259, sdef4, sdef5])).
% 27.40/9.96 cnf(p49, plain, convergent_lines(sk0,X0) | distinct_lines(X0,sk1), inference(resolution, [status(thm)], [p41, c13])).
% 27.40/9.96 cnf(p53, plain, distinct_lines(X0,sk1) | convergent_lines(sk0,X1) | convergent_lines(X0,X1), inference(resolution, [status(thm)], [p49, c5])).
% 27.40/9.96 cnf(p133, plain, distinct_lines(X0,sk1) | convergent_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p53, c13])).
% 27.40/9.96 cnf(p1260, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk1) | convergent_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p133])).
% 27.40/9.96 cnf(ssp25, plain, (spl8 | spl14), inference(avatar_split_clause, [status(thm)], [p1260, sdef8, sdef14])).
% 27.40/9.96 cnf(p111, plain, convergent_lines(X0,sk1) | convergent_lines(X0,X1) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p50, c13])).
% 27.40/9.96 cnf(p159, plain, convergent_lines(X0,sk1) | distinct_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p111, c13])).
% 27.40/9.96 cnf(p1261, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p121, p159])).
% 27.40/9.96 fof(sdef22, definition, (spl22 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl22])], [avatar_definition])).
% 27.40/9.97 cnf(ssp26, plain, (spl0 | spl2 | spl22), inference(avatar_split_clause, [status(thm)], [p1261, sdef0, sdef2, sdef22])).
% 27.40/9.97 cnf(p1263, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk1) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p159])).
% 27.40/9.97 cnf(ssp27, plain, (spl4 | spl19), inference(avatar_split_clause, [status(thm)], [p1263, sdef4, sdef19])).
% 27.40/9.97 cnf(p23, plain, distinct_lines(sk0,X0) | distinct_lines(X0,X1) | distinct_lines(sk1,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p20, c4])).
% 27.40/9.97 cnf(p1264, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,X1) | distinct_lines(sk1,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p121, p23])).
% 27.40/9.97 fof(sdef23, definition, (spl23 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,X1) | distinct_lines(sk1,X2) | distinct_lines(X1,X2))), introduced(definition, [new_symbols(naming, [spl23])], [avatar_definition])).
% 27.40/9.97 cnf(ssp28, plain, (spl0 | spl2 | spl23), inference(avatar_split_clause, [status(thm)], [p1264, sdef0, sdef2, sdef23])).
% 27.40/9.97 cnf(p1266, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk0,X1) | distinct_lines(X1,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p23])).
% 27.40/9.97 fof(sdef24, definition, (spl24 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk0,X1) | distinct_lines(X1,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl24])], [avatar_definition])).
% 27.40/9.97 cnf(ssp29, plain, (spl1 | spl3 | spl24), inference(avatar_split_clause, [status(thm)], [p1266, sdef1, sdef3, sdef24])).
% 27.40/9.97 cnf(p1268, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk0,X2) | distinct_lines(X2,X0) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p23])).
% 27.40/9.97 cnf(ssp30, plain, (spl6 | spl7), inference(avatar_split_clause, [status(thm)], [p1268, sdef6, sdef7])).
% 27.40/9.97 cnf(p125, plain, convergent_lines(X0,sk0) | convergent_lines(X0,X1) | convergent_lines(sk1,X1), inference(resolution, [status(thm)], [p110, c5])).
% 27.40/9.97 cnf(p191, plain, convergent_lines(X0,sk0) | convergent_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p125, c13])).
% 27.40/9.97 cnf(p1269, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk0) | convergent_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p191])).
% 27.40/9.97 fof(sdef25, definition, (spl25 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X0,sk0))), introduced(definition, [new_symbols(naming, [spl25])], [avatar_definition])).
% 27.40/9.97 cnf(ssp31, plain, (spl15 | spl25), inference(avatar_split_clause, [status(thm)], [p1269, sdef15, sdef25])).
% 27.40/9.97 cnf(p24, plain, distinct_lines(sk0,X0) | distinct_lines(sk1,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p20, c4])).
% 27.40/9.97 cnf(p1271, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p121, p24])).
% 27.40/9.97 fof(sdef26, definition, (spl26 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2))), introduced(definition, [new_symbols(naming, [spl26])], [avatar_definition])).
% 27.40/9.97 cnf(ssp32, plain, (spl0 | spl2 | spl26), inference(avatar_split_clause, [status(thm)], [p1271, sdef0, sdef2, sdef26])).
% 27.40/9.97 cnf(p1273, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk0,X1) | distinct_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p121, p24])).
% 27.40/9.97 fof(sdef27, definition, (spl27 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk0,X1) | distinct_lines(X1,X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl27])], [avatar_definition])).
% 27.40/9.97 cnf(ssp33, plain, (spl1 | spl3 | spl27), inference(avatar_split_clause, [status(thm)], [p1273, sdef1, sdef3, sdef27])).
% 27.40/9.97 cnf(p1275, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk0,X0) | distinct_lines(sk1,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p24])).
% 27.40/9.97 cnf(ssp34, plain, (spl4 | spl13), inference(avatar_split_clause, [status(thm)], [p1275, sdef4, sdef13])).
% 27.40/9.97 cnf(p225, plain, distinct_lines(sk0,X0) | distinct_lines(X0,X1) | distinct_lines(X1,sk1), inference(resolution, [status(thm)], [p23, c1])).
% 27.40/9.97 cnf(p1276, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,X1) | distinct_lines(X1,sk1), inference(resolution, [status(thm)], [p121, p225])).
% 27.40/9.97 fof(sdef28, definition, (spl28 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,X1) | distinct_lines(X1,sk1))), introduced(definition, [new_symbols(naming, [spl28])], [avatar_definition])).
% 27.40/9.97 cnf(ssp35, plain, (spl0 | spl2 | spl28), inference(avatar_split_clause, [status(thm)], [p1276, sdef0, sdef2, sdef28])).
% 27.40/9.97 cnf(p179, plain, convergent_lines(X0,sk1) | distinct_lines(X0,sk0), inference(resolution, [status(thm)], [p112, c2])).
% 27.40/9.97 cnf(p187, plain, distinct_lines(X0,sk0) | convergent_lines(X0,X1) | convergent_lines(sk1,X1), inference(resolution, [status(thm)], [p179, c5])).
% 27.40/9.97 cnf(p234, plain, distinct_lines(X0,sk0) | convergent_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p187, c13])).
% 27.40/9.97 cnf(p1278, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk0) | convergent_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p234])).
% 27.40/9.97 cnf(ssp36, plain, (spl11 | spl15), inference(avatar_split_clause, [status(thm)], [p1278, sdef11, sdef15])).
% 27.40/9.97 cnf(p27, plain, distinct_lines(X0,sk1) | distinct_lines(X0,X1) | distinct_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p25, c4])).
% 27.40/9.97 cnf(p1279, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | distinct_lines(X0,X1) | distinct_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p121, p27])).
% 27.40/9.97 fof(sdef29, definition, (spl29 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,X1) | distinct_lines(sk0,X2) | distinct_lines(X1,X2))), introduced(definition, [new_symbols(naming, [spl29])], [avatar_definition])).
% 27.40/9.97 cnf(ssp37, plain, (spl1 | spl3 | spl29), inference(avatar_split_clause, [status(thm)], [p1279, sdef1, sdef3, sdef29])).
% 27.40/9.97 cnf(p1281, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk1) | distinct_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p121, p27])).
% 27.40/9.97 cnf(ssp38, plain, (spl8 | spl9), inference(avatar_split_clause, [status(thm)], [p1281, sdef8, sdef9])).
% 27.40/9.97 cnf(p1282, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk1) | distinct_lines(X1,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p27])).
% 27.40/9.97 fof(sdef30, definition, (spl30 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk1) | distinct_lines(X1,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl30])], [avatar_definition])).
% 27.40/9.97 cnf(ssp39, plain, (spl0 | spl2 | spl30), inference(avatar_split_clause, [status(thm)], [p1282, sdef0, sdef2, sdef30])).
% 27.40/9.97 cnf(p1284, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X2,sk1) | distinct_lines(X2,X0) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p27])).
% 27.40/9.97 cnf(ssp40, plain, (spl4 | spl10), inference(avatar_split_clause, [status(thm)], [p1284, sdef4, sdef10])).
% 27.40/9.97 cnf(p242, plain, convergent_lines(X0,sk0) | distinct_lines(X0,X1) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p191, c13])).
% 27.40/9.97 cnf(p1285, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk0) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p242])).
% 27.40/9.97 cnf(ssp41, plain, (spl7 | spl25), inference(avatar_split_clause, [status(thm)], [p1285, sdef7, sdef25])).
% 27.40/9.97 cnf(p1286, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk0) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p121, p242])).
% 27.40/9.97 fof(sdef31, definition, (spl31 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk0) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl31])], [avatar_definition])).
% 27.40/9.97 cnf(ssp42, plain, (spl1 | spl3 | spl31), inference(avatar_split_clause, [status(thm)], [p1286, sdef1, sdef3, sdef31])).
% 27.40/9.97 cnf(p272, plain, distinct_lines(X0,sk1) | distinct_lines(X0,X1) | distinct_lines(X1,sk0), inference(resolution, [status(thm)], [p27, c1])).
% 27.40/9.97 cnf(p1288, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | distinct_lines(X0,X1) | distinct_lines(X1,sk0), inference(resolution, [status(thm)], [p121, p272])).
% 27.40/9.97 fof(sdef32, definition, (spl32 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,X1) | distinct_lines(X1,sk0))), introduced(definition, [new_symbols(naming, [spl32])], [avatar_definition])).
% 27.40/9.97 cnf(ssp43, plain, (spl1 | spl3 | spl32), inference(avatar_split_clause, [status(thm)], [p1288, sdef1, sdef3, sdef32])).
% 27.40/9.97 cnf(p1290, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk1) | distinct_lines(X1,sk0), inference(resolution, [status(thm)], [p121, p272])).
% 27.40/9.97 cnf(ssp44, plain, (spl8 | spl11), inference(avatar_split_clause, [status(thm)], [p1290, sdef8, sdef11])).
% 27.40/9.97 cnf(p28, plain, distinct_lines(X0,sk1) | distinct_lines(sk0,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p25, c4])).
% 27.40/9.97 cnf(p1291, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk1) | distinct_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p121, p28])).
% 27.40/9.97 fof(sdef33, definition, (spl33 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk1) | distinct_lines(X1,X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl33])], [avatar_definition])).
% 27.40/9.97 cnf(ssp45, plain, (spl0 | spl2 | spl33), inference(avatar_split_clause, [status(thm)], [p1291, sdef0, sdef2, sdef33])).
% 27.40/9.97 cnf(p1293, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk1) | distinct_lines(sk0,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p28])).
% 27.40/9.97 cnf(ssp46, plain, (spl6 | spl8), inference(avatar_split_clause, [status(thm)], [p1293, sdef6, sdef8])).
% 27.40/9.97 cnf(p190, plain, convergent_lines(X0,sk0) | convergent_lines(sk1,X0), inference(resolution, [status(thm)], [p125, c2])).
% 27.40/9.97 cnf(p202, plain, convergent_lines(sk1,X0) | convergent_lines(X0,X1) | convergent_lines(sk0,X1), inference(resolution, [status(thm)], [p190, c5])).
% 27.40/9.97 cnf(p255, plain, convergent_lines(sk1,X0) | convergent_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p202, c13])).
% 27.40/9.97 cnf(p280, plain, convergent_lines(sk1,X0) | distinct_lines(X0,X1) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p255, c13])).
% 27.40/9.97 cnf(p1294, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p121, p280])).
% 27.40/9.97 fof(sdef34, definition, (spl34 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl34])], [avatar_definition])).
% 27.40/9.97 cnf(ssp47, plain, (spl0 | spl2 | spl34), inference(avatar_split_clause, [status(thm)], [p1294, sdef0, sdef2, sdef34])).
% 27.40/9.97 cnf(p38, plain, distinct_lines(X0,sk0) | distinct_lines(sk1,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p31, c4])).
% 27.40/9.97 cnf(p1296, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk0) | distinct_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p121, p38])).
% 27.40/9.97 fof(sdef35, definition, (spl35 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk0) | distinct_lines(X1,X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl35])], [avatar_definition])).
% 27.40/9.97 cnf(ssp48, plain, (spl1 | spl3 | spl35), inference(avatar_split_clause, [status(thm)], [p1296, sdef1, sdef3, sdef35])).
% 27.40/9.97 cnf(p1298, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk0) | distinct_lines(sk1,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p38])).
% 27.40/9.97 cnf(ssp49, plain, (spl11 | spl13), inference(avatar_split_clause, [status(thm)], [p1298, sdef11, sdef13])).
% 27.40/9.97 cnf(p1299, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X2,sk0) | distinct_lines(sk1,X0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p38])).
% 27.40/9.97 cnf(ssp50, plain, (spl7 | spl12), inference(avatar_split_clause, [status(thm)], [p1299, sdef7, sdef12])).
% 27.40/9.97 cnf(p39, plain, distinct_lines(X0,sk0) | distinct_lines(X0,X1) | distinct_lines(sk1,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p31, c4])).
% 27.40/9.97 cnf(p1300, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk0) | distinct_lines(sk1,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p121, p39])).
% 27.40/9.97 cnf(ssp51, plain, (spl5 | spl11), inference(avatar_split_clause, [status(thm)], [p1300, sdef5, sdef11])).
% 27.40/9.97 cnf(p1301, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk0) | distinct_lines(X1,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p39])).
% 27.40/9.97 fof(sdef36, definition, (spl36 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk0) | distinct_lines(X1,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl36])], [avatar_definition])).
% 27.40/9.97 cnf(ssp52, plain, (spl1 | spl3 | spl36), inference(avatar_split_clause, [status(thm)], [p1301, sdef1, sdef3, sdef36])).
% 27.40/9.97 cnf(p46, plain, convergent_lines(sk0,X0) | convergent_lines(X0,X1) | convergent_lines(sk1,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p33, c5])).
% 27.40/9.97 cnf(p314, plain, convergent_lines(sk0,X0) | convergent_lines(X0,X1) | convergent_lines(X1,sk1), inference(resolution, [status(thm)], [p46, c2])).
% 27.40/9.97 cnf(p327, plain, convergent_lines(X0,X1) | convergent_lines(X1,sk1) | distinct_lines(sk0,X0), inference(resolution, [status(thm)], [p314, c13])).
% 27.40/9.97 cnf(p337, plain, convergent_lines(X0,sk1) | distinct_lines(sk0,X1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p327, c13])).
% 27.40/9.97 cnf(p1303, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p121, p337])).
% 27.40/9.97 fof(sdef37, definition, (spl37 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl37])], [avatar_definition])).
% 27.40/9.97 cnf(ssp53, plain, (spl0 | spl2 | spl37), inference(avatar_split_clause, [status(thm)], [p1303, sdef0, sdef2, sdef37])).
% 27.40/9.97 cnf(p57, plain, distinct_lines(sk1,X0) | convergent_lines(X0,X1) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p34, c5])).
% 27.40/9.97 cnf(p374, plain, distinct_lines(sk1,X0) | convergent_lines(X0,X1) | convergent_lines(X1,sk0), inference(resolution, [status(thm)], [p57, c2])).
% 27.40/9.97 cnf(p386, plain, distinct_lines(sk1,X0) | convergent_lines(X1,sk0) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p374, c13])).
% 27.40/9.97 cnf(p1305, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk0) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p121, p386])).
% 27.40/9.97 fof(sdef38, definition, (spl38 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk0) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl38])], [avatar_definition])).
% 27.40/9.97 cnf(ssp54, plain, (spl1 | spl3 | spl38), inference(avatar_split_clause, [status(thm)], [p1305, sdef1, sdef3, sdef38])).
% 27.40/9.97 cnf(p72, plain, distinct_lines(sk1,X0) | distinct_lines(X0,X1) | distinct_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p40, c4])).
% 27.40/9.97 cnf(p1307, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X1) | distinct_lines(X1,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p72])).
% 27.40/9.97 fof(sdef39, definition, (spl39 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X1) | distinct_lines(X1,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl39])], [avatar_definition])).
% 27.40/9.97 cnf(ssp55, plain, (spl0 | spl2 | spl39), inference(avatar_split_clause, [status(thm)], [p1307, sdef0, sdef2, sdef39])).
% 27.40/9.97 cnf(p103, plain, convergent_lines(sk0,X0) | convergent_lines(sk1,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p44, c4])).
% 27.40/9.97 cnf(p1309, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk0,X0) | convergent_lines(sk1,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p103])).
% 27.40/9.97 cnf(ssp56, plain, (spl14 | spl34), inference(avatar_split_clause, [status(thm)], [p1309, sdef14, sdef34])).
% 27.40/9.97 cnf(p1310, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk0,X2) | convergent_lines(sk1,X0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p103])).
% 27.40/9.97 cnf(ssp57, plain, (spl15 | spl18), inference(avatar_split_clause, [status(thm)], [p1310, sdef15, sdef18])).
% 27.40/9.97 cnf(p104, plain, convergent_lines(sk1,X0) | distinct_lines(X1,X0) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p44, c5])).
% 27.40/9.97 cnf(p1311, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk1,X1) | convergent_lines(sk0,X2) | convergent_lines(X0,X2), inference(resolution, [status(thm)], [p121, p104])).
% 27.40/9.97 fof(sdef40, definition, (spl40 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | convergent_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl40])], [avatar_definition])).
% 27.40/9.97 cnf(ssp58, plain, (spl15 | spl40), inference(avatar_split_clause, [status(thm)], [p1311, sdef15, sdef40])).
% 27.40/9.97 cnf(p105, plain, convergent_lines(sk0,X0) | distinct_lines(X0,X1) | convergent_lines(sk1,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p44, c5])).
% 27.40/9.97 cnf(p1313, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk0,X0) | convergent_lines(sk1,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p121, p105])).
% 27.40/9.97 fof(sdef41, definition, (spl41 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | convergent_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl41])], [avatar_definition])).
% 27.40/9.97 cnf(ssp59, plain, (spl14 | spl41), inference(avatar_split_clause, [status(thm)], [p1313, sdef14, sdef41])).
% 27.40/9.97 cnf(p113, plain, convergent_lines(X0,sk1) | convergent_lines(X0,X1) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p50, c5])).
% 27.40/9.97 cnf(p466, plain, convergent_lines(X0,sk1) | convergent_lines(X0,X1) | convergent_lines(X1,sk0), inference(resolution, [status(thm)], [p113, c2])).
% 27.40/9.97 cnf(p481, plain, convergent_lines(X0,sk1) | convergent_lines(X1,sk0) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p466, c13])).
% 27.40/9.97 cnf(p1315, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk1) | convergent_lines(X1,sk0), inference(resolution, [status(thm)], [p121, p481])).
% 27.40/9.97 cnf(ssp60, plain, (spl19 | spl25), inference(avatar_split_clause, [status(thm)], [p1315, sdef19, sdef25])).
% 27.40/9.97 cnf(p480, plain, convergent_lines(X0,X1) | convergent_lines(X1,sk0) | distinct_lines(X0,sk1), inference(resolution, [status(thm)], [p466, c13])).
% 27.40/9.97 cnf(p491, plain, convergent_lines(X0,sk0) | distinct_lines(X1,sk1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p480, c13])).
% 27.40/9.97 cnf(p1316, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X1,sk0) | distinct_lines(X0,sk1), inference(resolution, [status(thm)], [p121, p491])).
% 27.40/9.97 cnf(ssp61, plain, (spl8 | spl25), inference(avatar_split_clause, [status(thm)], [p1316, sdef8, sdef25])).
% 27.40/9.97 cnf(p498, plain, convergent_lines(X0,sk1) | distinct_lines(X0,X1) | distinct_lines(X1,sk0), inference(resolution, [status(thm)], [p481, c13])).
% 27.40/9.97 cnf(p1317, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk1) | distinct_lines(X1,sk0), inference(resolution, [status(thm)], [p121, p498])).
% 27.40/9.97 cnf(ssp62, plain, (spl11 | spl19), inference(avatar_split_clause, [status(thm)], [p1317, sdef11, sdef19])).
% 27.40/9.97 cnf(p143, plain, convergent_lines(sk0,X0) | distinct_lines(X1,X0) | distinct_lines(sk1,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p56, c4])).
% 27.40/9.97 cnf(p1318, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk0,X1) | distinct_lines(sk1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p121, p143])).
% 27.40/9.97 cnf(ssp63, plain, (spl5 | spl14), inference(avatar_split_clause, [status(thm)], [p1318, sdef5, sdef14])).
% 27.40/9.97 cnf(p1319, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | distinct_lines(X2,X1) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p143])).
% 27.40/9.97 fof(sdef42, definition, (spl42 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | distinct_lines(X2,X1) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl42])], [avatar_definition])).
% 27.40/9.97 cnf(ssp64, plain, (spl1 | spl3 | spl42), inference(avatar_split_clause, [status(thm)], [p1319, sdef1, sdef3, sdef42])).
% 27.40/9.97 cnf(p1321, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk0,X2) | distinct_lines(X0,X2) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p143])).
% 27.40/9.97 cnf(ssp65, plain, (spl7 | spl16), inference(avatar_split_clause, [status(thm)], [p1321, sdef7, sdef16])).
% 27.40/9.97 cnf(p144, plain, distinct_lines(sk1,X0) | convergent_lines(sk0,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p56, c4])).
% 27.40/9.97 cnf(p1322, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p121, p144])).
% 27.40/9.97 fof(sdef43, definition, (spl43 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2))), introduced(definition, [new_symbols(naming, [spl43])], [avatar_definition])).
% 27.40/9.97 cnf(ssp66, plain, (spl1 | spl3 | spl43), inference(avatar_split_clause, [status(thm)], [p1322, sdef1, sdef3, sdef43])).
% 27.40/9.97 cnf(p1324, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk1,X0) | convergent_lines(sk0,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p144])).
% 27.40/9.97 cnf(ssp67, plain, (spl7 | spl18), inference(avatar_split_clause, [status(thm)], [p1324, sdef7, sdef18])).
% 27.40/9.97 cnf(p1325, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk1,X2) | convergent_lines(sk0,X0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p144])).
% 27.40/9.97 cnf(ssp68, plain, (spl13 | spl14), inference(avatar_split_clause, [status(thm)], [p1325, sdef13, sdef14])).
% 27.40/9.97 cnf(p145, plain, distinct_lines(sk1,X0) | distinct_lines(X0,X1) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p56, c5])).
% 27.40/9.97 cnf(p1326, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,X1) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p121, p145])).
% 27.40/9.97 fof(sdef44, definition, (spl44 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,X1) | convergent_lines(sk0,X2) | convergent_lines(X1,X2))), introduced(definition, [new_symbols(naming, [spl44])], [avatar_definition])).
% 27.40/9.97 cnf(ssp69, plain, (spl1 | spl3 | spl44), inference(avatar_split_clause, [status(thm)], [p1326, sdef1, sdef3, sdef44])).
% 27.40/9.97 cnf(p1328, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk1,X0) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p121, p145])).
% 27.40/9.97 cnf(ssp70, plain, (spl7 | spl40), inference(avatar_split_clause, [status(thm)], [p1328, sdef7, sdef40])).
% 27.40/9.97 cnf(p150, plain, convergent_lines(sk1,X0) | distinct_lines(X1,X0) | distinct_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p75, c4])).
% 27.40/9.97 cnf(p1329, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk1,X1) | distinct_lines(sk0,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p121, p150])).
% 27.40/9.97 cnf(ssp71, plain, (spl9 | spl15), inference(avatar_split_clause, [status(thm)], [p1329, sdef9, sdef15])).
% 27.40/9.97 cnf(p1330, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | distinct_lines(X2,X1) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p150])).
% 27.40/9.97 fof(sdef45, definition, (spl45 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | distinct_lines(X2,X1) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl45])], [avatar_definition])).
% 27.40/9.97 cnf(ssp72, plain, (spl0 | spl2 | spl45), inference(avatar_split_clause, [status(thm)], [p1330, sdef0, sdef2, sdef45])).
% 27.40/9.97 cnf(p1332, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk1,X2) | distinct_lines(X0,X2) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p150])).
% 27.40/9.97 cnf(ssp73, plain, (spl4 | spl17), inference(avatar_split_clause, [status(thm)], [p1332, sdef4, sdef17])).
% 27.40/9.97 cnf(p151, plain, convergent_lines(sk1,X0) | distinct_lines(sk0,X1) | distinct_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p75, c4])).
% 27.40/9.97 cnf(p1333, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p121, p151])).
% 27.40/9.97 fof(sdef46, definition, (spl46 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2))), introduced(definition, [new_symbols(naming, [spl46])], [avatar_definition])).
% 27.40/9.97 cnf(ssp74, plain, (spl0 | spl2 | spl46), inference(avatar_split_clause, [status(thm)], [p1333, sdef0, sdef2, sdef46])).
% 27.40/9.97 cnf(p1335, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk1,X2) | distinct_lines(sk0,X0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p151])).
% 27.40/9.97 cnf(ssp75, plain, (spl4 | spl34), inference(avatar_split_clause, [status(thm)], [p1335, sdef4, sdef34])).
% 27.40/9.97 cnf(p1336, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk1,X0) | distinct_lines(sk0,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p151])).
% 27.40/9.97 cnf(ssp76, plain, (spl6 | spl15), inference(avatar_split_clause, [status(thm)], [p1336, sdef6, sdef15])).
% 27.40/9.97 cnf(p152, plain, distinct_lines(sk0,X0) | distinct_lines(X0,X1) | convergent_lines(sk1,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p75, c5])).
% 27.40/9.97 cnf(p1337, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,X1) | convergent_lines(sk1,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p121, p152])).
% 27.40/9.97 fof(sdef47, definition, (spl47 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X0,X1) | convergent_lines(sk1,X2) | convergent_lines(X1,X2))), introduced(definition, [new_symbols(naming, [spl47])], [avatar_definition])).
% 27.40/9.97 cnf(ssp77, plain, (spl0 | spl2 | spl47), inference(avatar_split_clause, [status(thm)], [p1337, sdef0, sdef2, sdef47])).
% 27.40/9.97 cnf(p1339, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk0,X0) | convergent_lines(sk1,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p121, p152])).
% 27.40/9.97 cnf(ssp78, plain, (spl4 | spl41), inference(avatar_split_clause, [status(thm)], [p1339, sdef4, sdef41])).
% 27.40/9.97 cnf(p155, plain, convergent_lines(sk0,X0) | distinct_lines(X0,X1) | distinct_lines(sk1,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p97, c4])).
% 27.40/9.97 cnf(p1340, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | distinct_lines(X1,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p155])).
% 27.40/9.97 fof(sdef48, definition, (spl48 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | distinct_lines(X1,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl48])], [avatar_definition])).
% 27.40/9.97 cnf(ssp79, plain, (spl1 | spl3 | spl48), inference(avatar_split_clause, [status(thm)], [p1340, sdef1, sdef3, sdef48])).
% 27.40/9.97 cnf(p156, plain, distinct_lines(sk1,X0) | distinct_lines(X1,X0) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p97, c5])).
% 27.40/9.97 cnf(p1342, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,X0) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p121, p156])).
% 27.40/9.97 fof(sdef49, definition, (spl49 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,X0) | convergent_lines(sk0,X2) | convergent_lines(X1,X2))), introduced(definition, [new_symbols(naming, [spl49])], [avatar_definition])).
% 27.40/9.97 cnf(ssp80, plain, (spl1 | spl3 | spl49), inference(avatar_split_clause, [status(thm)], [p1342, sdef1, sdef3, sdef49])).
% 27.40/9.97 cnf(p180, plain, convergent_lines(X0,sk1) | convergent_lines(sk0,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p112, c4])).
% 27.40/9.97 cnf(p1344, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk1) | convergent_lines(sk0,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p180])).
% 27.40/9.97 cnf(ssp81, plain, (spl18 | spl19), inference(avatar_split_clause, [status(thm)], [p1344, sdef18, sdef19])).
% 27.40/9.97 cnf(p1345, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X2,sk1) | convergent_lines(sk0,X0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p180])).
% 27.40/9.97 cnf(ssp82, plain, (spl14 | spl22), inference(avatar_split_clause, [status(thm)], [p1345, sdef14, sdef22])).
% 27.40/9.97 cnf(p182, plain, convergent_lines(X0,sk1) | distinct_lines(X0,X1) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p112, c5])).
% 27.40/9.97 cnf(p1346, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk1) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p121, p182])).
% 27.40/9.97 cnf(ssp83, plain, (spl19 | spl40), inference(avatar_split_clause, [status(thm)], [p1346, sdef19, sdef40])).
% 27.40/9.97 cnf(p216, plain, distinct_lines(X0,sk1) | convergent_lines(sk0,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p133, c4])).
% 27.40/9.97 cnf(p1347, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk1) | convergent_lines(sk0,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p216])).
% 27.40/9.97 cnf(ssp84, plain, (spl8 | spl18), inference(avatar_split_clause, [status(thm)], [p1347, sdef8, sdef18])).
% 27.40/9.97 cnf(p1348, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X2,sk1) | convergent_lines(sk0,X0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p216])).
% 27.40/9.97 cnf(ssp85, plain, (spl10 | spl14), inference(avatar_split_clause, [status(thm)], [p1348, sdef10, sdef14])).
% 27.40/9.97 cnf(p217, plain, distinct_lines(X0,sk1) | distinct_lines(X0,X1) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p133, c5])).
% 27.40/9.97 cnf(p1349, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk1) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p121, p217])).
% 27.40/9.97 cnf(ssp86, plain, (spl8 | spl40), inference(avatar_split_clause, [status(thm)], [p1349, sdef8, sdef40])).
% 27.40/9.97 cnf(p220, plain, convergent_lines(X0,sk1) | distinct_lines(X0,X1) | distinct_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p159, c4])).
% 27.40/9.97 cnf(p1350, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk1) | distinct_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p121, p220])).
% 27.40/9.97 cnf(ssp87, plain, (spl9 | spl19), inference(avatar_split_clause, [status(thm)], [p1350, sdef9, sdef19])).
% 27.40/9.97 cnf(p1351, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk1) | distinct_lines(X1,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p220])).
% 27.40/9.97 fof(sdef50, definition, (spl50 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk1) | distinct_lines(X1,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl50])], [avatar_definition])).
% 27.40/9.97 cnf(ssp88, plain, (spl0 | spl2 | spl50), inference(avatar_split_clause, [status(thm)], [p1351, sdef0, sdef2, sdef50])).
% 27.40/9.97 cnf(p1353, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X2,sk1) | distinct_lines(X2,X0) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p220])).
% 27.40/9.97 cnf(ssp89, plain, (spl4 | spl22), inference(avatar_split_clause, [status(thm)], [p1353, sdef4, sdef22])).
% 27.40/9.97 cnf(p221, plain, convergent_lines(X0,sk1) | distinct_lines(sk0,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p159, c4])).
% 27.40/9.97 cnf(p1354, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk1) | distinct_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p121, p221])).
% 27.40/9.97 fof(sdef51, definition, (spl51 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk1) | distinct_lines(X1,X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl51])], [avatar_definition])).
% 27.40/9.97 cnf(ssp90, plain, (spl0 | spl2 | spl51), inference(avatar_split_clause, [status(thm)], [p1354, sdef0, sdef2, sdef51])).
% 27.40/9.97 cnf(p1356, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk1) | distinct_lines(sk0,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p221])).
% 27.40/9.97 cnf(ssp91, plain, (spl6 | spl19), inference(avatar_split_clause, [status(thm)], [p1356, sdef6, sdef19])).
% 27.40/9.97 cnf(p222, plain, distinct_lines(sk0,X0) | distinct_lines(X1,X0) | convergent_lines(X1,X2) | convergent_lines(sk1,X2), inference(resolution, [status(thm)], [p159, c5])).
% 27.40/9.97 cnf(p1357, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,X0) | convergent_lines(X1,X2) | convergent_lines(sk1,X2), inference(resolution, [status(thm)], [p121, p222])).
% 27.40/9.97 fof(sdef52, definition, (spl52 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,X0) | convergent_lines(X1,X2) | convergent_lines(sk1,X2))), introduced(definition, [new_symbols(naming, [spl52])], [avatar_definition])).
% 27.40/9.97 cnf(ssp92, plain, (spl0 | spl2 | spl52), inference(avatar_split_clause, [status(thm)], [p1357, sdef0, sdef2, sdef52])).
% 27.40/9.97 cnf(p243, plain, convergent_lines(X0,sk0) | convergent_lines(sk1,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p191, c4])).
% 27.40/9.97 cnf(p1359, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk0) | convergent_lines(sk1,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p243])).
% 27.40/9.97 cnf(ssp93, plain, (spl25 | spl34), inference(avatar_split_clause, [status(thm)], [p1359, sdef25, sdef34])).
% 27.40/9.97 cnf(p1360, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X2,sk0) | convergent_lines(sk1,X0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p243])).
% 27.40/9.97 cnf(ssp94, plain, (spl15 | spl31), inference(avatar_split_clause, [status(thm)], [p1360, sdef15, sdef31])).
% 27.40/9.97 cnf(p244, plain, convergent_lines(X0,sk0) | distinct_lines(X0,X1) | convergent_lines(sk1,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p191, c5])).
% 27.40/9.97 cnf(p1361, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk0) | convergent_lines(sk1,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p121, p244])).
% 27.40/9.97 cnf(ssp95, plain, (spl25 | spl41), inference(avatar_split_clause, [status(thm)], [p1361, sdef25, sdef41])).
% 27.40/9.97 cnf(p264, plain, distinct_lines(X0,X1) | distinct_lines(X1,sk1) | distinct_lines(sk0,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p225, c4])).
% 27.40/9.97 cnf(p1362, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,X2) | distinct_lines(X2,sk1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p121, p264])).
% 27.40/9.97 fof(sdef53, definition, (spl53 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,X2) | distinct_lines(X2,sk1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl53])], [avatar_definition])).
% 27.40/9.97 cnf(ssp96, plain, (spl0 | spl2 | spl53), inference(avatar_split_clause, [status(thm)], [p1362, sdef0, sdef2, sdef53])).
% 27.40/9.97 cnf(p1364, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,X2) | distinct_lines(X2,sk1) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p264])).
% 27.40/9.97 cnf(ssp97, plain, (spl4 | spl28), inference(avatar_split_clause, [status(thm)], [p1364, sdef4, sdef28])).
% 27.40/9.97 cnf(p265, plain, distinct_lines(X0,sk0) | convergent_lines(sk1,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p234, c4])).
% 27.40/9.97 cnf(p1365, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk0) | convergent_lines(sk1,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p265])).
% 27.40/9.97 cnf(ssp98, plain, (spl11 | spl34), inference(avatar_split_clause, [status(thm)], [p1365, sdef11, sdef34])).
% 27.40/9.97 cnf(p1366, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X2,sk0) | convergent_lines(sk1,X0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p265])).
% 27.40/9.97 cnf(ssp99, plain, (spl12 | spl15), inference(avatar_split_clause, [status(thm)], [p1366, sdef12, sdef15])).
% 27.40/9.97 cnf(p266, plain, distinct_lines(X0,sk0) | distinct_lines(X0,X1) | convergent_lines(sk1,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p234, c5])).
% 27.40/9.97 cnf(p1367, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk0) | convergent_lines(sk1,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p121, p266])).
% 27.40/9.97 cnf(ssp100, plain, (spl11 | spl41), inference(avatar_split_clause, [status(thm)], [p1367, sdef11, sdef41])).
% 27.40/9.97 cnf(p276, plain, convergent_lines(X0,sk0) | distinct_lines(sk1,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p242, c4])).
% 27.40/9.97 cnf(p1368, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk0) | distinct_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p121, p276])).
% 27.40/9.97 fof(sdef54, definition, (spl54 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk0) | distinct_lines(X1,X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl54])], [avatar_definition])).
% 27.40/9.97 cnf(ssp101, plain, (spl1 | spl3 | spl54), inference(avatar_split_clause, [status(thm)], [p1368, sdef1, sdef3, sdef54])).
% 27.40/9.97 cnf(p1370, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk0) | distinct_lines(sk1,X2) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p276])).
% 27.40/9.97 cnf(ssp102, plain, (spl13 | spl25), inference(avatar_split_clause, [status(thm)], [p1370, sdef13, sdef25])).
% 27.40/9.97 cnf(p1371, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X2,sk0) | distinct_lines(sk1,X0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p276])).
% 27.40/9.97 cnf(ssp103, plain, (spl7 | spl31), inference(avatar_split_clause, [status(thm)], [p1371, sdef7, sdef31])).
% 27.40/9.97 cnf(p277, plain, convergent_lines(X0,sk0) | distinct_lines(X0,X1) | distinct_lines(sk1,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p242, c4])).
% 27.40/9.97 cnf(p1372, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk0) | distinct_lines(sk1,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p121, p277])).
% 27.40/9.97 cnf(ssp104, plain, (spl5 | spl25), inference(avatar_split_clause, [status(thm)], [p1372, sdef5, sdef25])).
% 27.40/9.97 cnf(p1373, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk0) | distinct_lines(X1,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p277])).
% 27.40/9.97 fof(sdef55, definition, (spl55 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk0) | distinct_lines(X1,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl55])], [avatar_definition])).
% 27.40/9.97 cnf(ssp105, plain, (spl1 | spl3 | spl55), inference(avatar_split_clause, [status(thm)], [p1373, sdef1, sdef3, sdef55])).
% 27.40/9.97 cnf(p290, plain, distinct_lines(X0,X1) | distinct_lines(X1,sk0) | distinct_lines(X0,X2) | distinct_lines(sk1,X2), inference(resolution, [status(thm)], [p272, c4])).
% 27.40/9.97 cnf(p1375, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,X2) | distinct_lines(X2,sk0) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p290])).
% 27.40/9.97 cnf(ssp106, plain, (spl7 | spl32), inference(avatar_split_clause, [status(thm)], [p1375, sdef7, sdef32])).
% 27.40/9.97 cnf(p1376, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,X2) | distinct_lines(X2,sk0) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p121, p290])).
% 27.40/9.97 fof(sdef56, definition, (spl56 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,X2) | distinct_lines(X2,sk0) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl56])], [avatar_definition])).
% 27.40/9.97 cnf(ssp107, plain, (spl1 | spl3 | spl56), inference(avatar_split_clause, [status(thm)], [p1376, sdef1, sdef3, sdef56])).
% 27.40/9.97 cnf(p291, plain, distinct_lines(X0,sk1) | distinct_lines(X1,sk0) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p272, c4])).
% 27.40/9.97 cnf(p1378, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk1) | distinct_lines(X2,sk0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p291])).
% 27.40/9.97 cnf(ssp108, plain, (spl8 | spl12), inference(avatar_split_clause, [status(thm)], [p1378, sdef8, sdef12])).
% 27.40/9.97 cnf(p1379, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X2,sk1) | distinct_lines(X0,sk0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p291])).
% 27.40/9.97 cnf(ssp109, plain, (spl10 | spl11), inference(avatar_split_clause, [status(thm)], [p1379, sdef10, sdef11])).
% 27.40/9.97 cnf(p293, plain, convergent_lines(sk1,X0) | distinct_lines(X0,X1) | distinct_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p280, c4])).
% 27.40/9.97 cnf(p1380, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | distinct_lines(X1,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p293])).
% 27.40/9.97 fof(sdef57, definition, (spl57 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | distinct_lines(X1,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl57])], [avatar_definition])).
% 27.40/9.97 cnf(ssp110, plain, (spl0 | spl2 | spl57), inference(avatar_split_clause, [status(thm)], [p1380, sdef0, sdef2, sdef57])).
% 27.40/9.97 cnf(p316, plain, convergent_lines(sk0,X0) | convergent_lines(X0,X1) | convergent_lines(sk1,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p46, c13])).
% 27.40/9.97 cnf(p1382, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk0,X2) | convergent_lines(X2,X0) | convergent_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p316])).
% 27.40/9.97 fof(sdef58, definition, (spl58 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | convergent_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl58])], [avatar_definition])).
% 27.40/9.97 cnf(ssp111, plain, (spl15 | spl58), inference(avatar_split_clause, [status(thm)], [p1382, sdef15, sdef58])).
% 27.40/9.97 cnf(p47, plain, convergent_lines(sk0,X0) | convergent_lines(sk1,X1) | convergent_lines(X0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p33, c5])).
% 27.40/9.97 cnf(p354, plain, convergent_lines(sk0,X0) | convergent_lines(sk1,X1) | convergent_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p47, c13])).
% 27.40/9.97 cnf(p1384, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk0,X0) | convergent_lines(sk1,X2) | convergent_lines(X2,X1), inference(resolution, [status(thm)], [p121, p354])).
% 27.40/9.97 fof(sdef59, definition, (spl59 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | convergent_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl59])], [avatar_definition])).
% 27.40/9.97 cnf(ssp112, plain, (spl14 | spl59), inference(avatar_split_clause, [status(thm)], [p1384, sdef14, sdef59])).
% 27.40/9.97 cnf(p365, plain, convergent_lines(X0,sk1) | distinct_lines(X1,X0) | distinct_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p337, c4])).
% 27.40/9.97 cnf(p1386, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk1) | distinct_lines(X2,X1) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p365])).
% 27.40/9.97 fof(sdef60, definition, (spl60 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk1) | distinct_lines(X2,X1) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl60])], [avatar_definition])).
% 27.40/9.97 cnf(ssp113, plain, (spl0 | spl2 | spl60), inference(avatar_split_clause, [status(thm)], [p1386, sdef0, sdef2, sdef60])).
% 27.40/9.97 cnf(p1388, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X2,sk1) | distinct_lines(X0,X2) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p365])).
% 27.40/9.97 cnf(ssp114, plain, (spl4 | spl37), inference(avatar_split_clause, [status(thm)], [p1388, sdef4, sdef37])).
% 27.40/9.97 cnf(p376, plain, distinct_lines(sk1,X0) | convergent_lines(X0,X1) | convergent_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p57, c13])).
% 27.40/9.97 cnf(p1389, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk1,X2) | convergent_lines(X2,X0) | convergent_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p376])).
% 27.40/9.97 fof(sdef61, definition, (spl61 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(sk1,X1) | convergent_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl61])], [avatar_definition])).
% 27.40/9.97 cnf(ssp115, plain, (spl14 | spl61), inference(avatar_split_clause, [status(thm)], [p1389, sdef14, sdef61])).
% 27.40/9.97 cnf(p58, plain, distinct_lines(sk1,X0) | convergent_lines(sk0,X1) | convergent_lines(X0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p34, c5])).
% 27.40/9.97 cnf(p392, plain, distinct_lines(sk1,X0) | convergent_lines(sk0,X1) | convergent_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p58, c13])).
% 27.40/9.97 cnf(p1391, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | convergent_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p121, p392])).
% 27.40/9.97 fof(sdef62, definition, (spl62 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk0,X1) | convergent_lines(X1,X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl62])], [avatar_definition])).
% 27.40/9.97 cnf(ssp116, plain, (spl1 | spl3 | spl62), inference(avatar_split_clause, [status(thm)], [p1391, sdef1, sdef3, sdef62])).
% 27.40/9.97 cnf(p1393, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(sk1,X0) | convergent_lines(sk0,X2) | convergent_lines(X2,X1), inference(resolution, [status(thm)], [p121, p392])).
% 27.40/9.97 cnf(ssp117, plain, (spl7 | spl58), inference(avatar_split_clause, [status(thm)], [p1393, sdef7, sdef58])).
% 27.40/9.97 cnf(p401, plain, convergent_lines(X0,sk0) | distinct_lines(X1,X0) | distinct_lines(sk1,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p386, c4])).
% 27.40/9.97 cnf(p1394, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk0) | distinct_lines(X2,X1) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p121, p401])).
% 27.40/9.97 fof(sdef63, definition, (spl63 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk0) | distinct_lines(X2,X1) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl63])], [avatar_definition])).
% 27.40/9.97 cnf(ssp118, plain, (spl1 | spl3 | spl63), inference(avatar_split_clause, [status(thm)], [p1394, sdef1, sdef3, sdef63])).
% 27.40/9.97 cnf(p1396, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X2,sk0) | distinct_lines(X0,X2) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p401])).
% 27.40/9.97 cnf(ssp119, plain, (spl7 | spl38), inference(avatar_split_clause, [status(thm)], [p1396, sdef7, sdef38])).
% 27.40/9.97 cnf(p76, plain, convergent_lines(X0,X1) | distinct_lines(sk0,X0) | convergent_lines(sk1,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p42, c5])).
% 27.40/9.97 cnf(p408, plain, convergent_lines(X0,X1) | distinct_lines(sk0,X0) | convergent_lines(sk1,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p76, c13])).
% 27.40/9.97 cnf(p1397, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X2,X0) | distinct_lines(sk0,X2) | convergent_lines(sk1,X1), inference(resolution, [status(thm)], [p121, p408])).
% 27.40/9.97 fof(sdef64, definition, (spl64 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,X0) | distinct_lines(sk0,X1))), introduced(definition, [new_symbols(naming, [spl64])], [avatar_definition])).
% 27.40/9.97 cnf(ssp120, plain, (spl15 | spl64), inference(avatar_split_clause, [status(thm)], [p1397, sdef15, sdef64])).
% 27.40/9.97 cnf(p77, plain, convergent_lines(sk1,X0) | distinct_lines(sk0,X1) | convergent_lines(X1,X2) | convergent_lines(X0,X2), inference(resolution, [status(thm)], [p42, c5])).
% 27.40/9.97 cnf(p418, plain, convergent_lines(sk1,X0) | distinct_lines(sk0,X1) | convergent_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p77, c13])).
% 27.40/9.97 cnf(p1399, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | convergent_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p121, p418])).
% 27.40/9.97 fof(sdef65, definition, (spl65 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(sk1,X1) | convergent_lines(X1,X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl65])], [avatar_definition])).
% 27.40/9.97 cnf(ssp121, plain, (spl0 | spl2 | spl65), inference(avatar_split_clause, [status(thm)], [p1399, sdef0, sdef2, sdef65])).
% 27.40/9.97 cnf(p1401, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk1,X2) | distinct_lines(sk0,X0) | convergent_lines(X2,X1), inference(resolution, [status(thm)], [p121, p418])).
% 27.40/9.97 cnf(ssp122, plain, (spl4 | spl59), inference(avatar_split_clause, [status(thm)], [p1401, sdef4, sdef59])).
% 27.40/9.97 cnf(p98, plain, convergent_lines(X0,X1) | distinct_lines(sk1,X1) | convergent_lines(sk0,X2) | convergent_lines(X0,X2), inference(resolution, [status(thm)], [p43, c5])).
% 27.40/9.97 cnf(p428, plain, convergent_lines(X0,X1) | distinct_lines(sk1,X1) | convergent_lines(sk0,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p98, c13])).
% 27.40/9.97 cnf(p1402, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,X2) | distinct_lines(sk1,X2) | convergent_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p428])).
% 27.40/9.97 fof(sdef66, definition, (spl66 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X0,X1) | distinct_lines(sk1,X1))), introduced(definition, [new_symbols(naming, [spl66])], [avatar_definition])).
% 27.40/9.97 cnf(ssp123, plain, (spl14 | spl66), inference(avatar_split_clause, [status(thm)], [p1402, sdef14, sdef66])).
% 27.40/9.97 cnf(p445, plain, convergent_lines(sk1,X0) | distinct_lines(X1,X0) | convergent_lines(X1,X2) | distinct_lines(sk0,X2), inference(resolution, [status(thm)], [p104, c13])).
% 27.40/9.97 cnf(p1404, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk1,X1) | convergent_lines(X0,X2) | distinct_lines(sk0,X2), inference(resolution, [status(thm)], [p121, p445])).
% 27.40/9.97 fof(sdef67, definition, (spl67 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X0,X1) | distinct_lines(sk0,X1))), introduced(definition, [new_symbols(naming, [spl67])], [avatar_definition])).
% 27.40/9.97 cnf(ssp124, plain, (spl15 | spl67), inference(avatar_split_clause, [status(thm)], [p1404, sdef15, sdef67])).
% 27.40/9.97 cnf(p446, plain, convergent_lines(sk1,X0) | distinct_lines(X1,X0) | convergent_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p104, c13])).
% 27.40/9.97 cnf(p1406, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk1,X1) | convergent_lines(sk0,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p121, p446])).
% 27.40/9.97 cnf(ssp125, plain, (spl15 | spl16), inference(avatar_split_clause, [status(thm)], [p1406, sdef15, sdef16])).
% 27.40/9.97 cnf(p1407, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(sk1,X2) | distinct_lines(X0,X2) | convergent_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p446])).
% 27.40/9.97 cnf(ssp126, plain, (spl14 | spl17), inference(avatar_split_clause, [status(thm)], [p1407, sdef14, sdef17])).
% 27.40/9.97 cnf(p468, plain, convergent_lines(X0,sk1) | convergent_lines(X0,X1) | convergent_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p113, c13])).
% 27.40/9.97 cnf(p1408, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X2,sk1) | convergent_lines(X2,X0) | convergent_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p468])).
% 27.40/9.97 fof(sdef68, definition, (spl68 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | convergent_lines(X1,sk1) | convergent_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl68])], [avatar_definition])).
% 27.40/9.97 cnf(ssp127, plain, (spl14 | spl68), inference(avatar_split_clause, [status(thm)], [p1408, sdef14, sdef68])).
% 27.40/9.97 cnf(p499, plain, convergent_lines(X0,sk1) | convergent_lines(X1,sk0) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p481, c4])).
% 27.40/9.97 cnf(p1410, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk1) | convergent_lines(X2,sk0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p499])).
% 27.40/9.97 cnf(ssp128, plain, (spl19 | spl31), inference(avatar_split_clause, [status(thm)], [p1410, sdef19, sdef31])).
% 27.40/9.97 cnf(p1411, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X2,sk1) | convergent_lines(X0,sk0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p499])).
% 27.40/9.97 cnf(ssp129, plain, (spl22 | spl25), inference(avatar_split_clause, [status(thm)], [p1411, sdef22, sdef25])).
% 27.40/9.97 cnf(p511, plain, convergent_lines(X0,sk0) | distinct_lines(X1,sk1) | distinct_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p491, c4])).
% 27.40/9.97 cnf(p1412, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X2,sk0) | distinct_lines(X0,sk1) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p511])).
% 27.40/9.97 cnf(ssp130, plain, (spl8 | spl31), inference(avatar_split_clause, [status(thm)], [p1412, sdef8, sdef31])).
% 27.40/9.97 cnf(p1413, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk0) | distinct_lines(X2,sk1) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p511])).
% 27.40/9.97 cnf(ssp131, plain, (spl10 | spl25), inference(avatar_split_clause, [status(thm)], [p1413, sdef10, sdef25])).
% 27.40/9.97 cnf(p517, plain, convergent_lines(X0,sk1) | distinct_lines(X1,sk0) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p498, c4])).
% 27.40/9.97 cnf(p1414, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk1) | distinct_lines(X2,sk0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p517])).
% 27.40/9.97 cnf(ssp132, plain, (spl12 | spl19), inference(avatar_split_clause, [status(thm)], [p1414, sdef12, sdef19])).
% 27.40/9.97 cnf(p1415, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X2,sk1) | distinct_lines(X0,sk0) | distinct_lines(X2,X1), inference(resolution, [status(thm)], [p121, p517])).
% 27.40/9.97 cnf(ssp133, plain, (spl11 | spl22), inference(avatar_split_clause, [status(thm)], [p1415, sdef11, sdef22])).
% 27.40/9.97 cnf(p114, plain, convergent_lines(X0,sk1) | convergent_lines(sk0,X1) | convergent_lines(X0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p50, c5])).
% 27.40/9.97 cnf(p521, plain, convergent_lines(X0,sk1) | convergent_lines(sk0,X1) | convergent_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p114, c13])).
% 27.40/9.97 cnf(p1416, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | convergent_lines(X0,sk1) | convergent_lines(sk0,X2) | convergent_lines(X2,X1), inference(resolution, [status(thm)], [p121, p521])).
% 27.40/9.97 cnf(ssp134, plain, (spl19 | spl58), inference(avatar_split_clause, [status(thm)], [p1416, sdef19, sdef58])).
% 27.40/9.97 cnf(p134, plain, distinct_lines(X0,sk1) | convergent_lines(X0,X1) | convergent_lines(sk0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p53, c5])).
% 27.40/9.97 cnf(p533, plain, distinct_lines(X0,sk1) | convergent_lines(X0,X1) | convergent_lines(sk0,X2) | distinct_lines(X1,X2), inference(resolution, [status(thm)], [p134, c13])).
% 27.40/9.97 cnf(p1417, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X2,sk1) | convergent_lines(X2,X0) | convergent_lines(sk0,X1), inference(resolution, [status(thm)], [p121, p533])).
% 27.40/9.97 fof(sdef69, definition, (spl69 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | distinct_lines(X1,sk1) | convergent_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl69])], [avatar_definition])).
% 27.40/9.97 cnf(ssp135, plain, (spl14 | spl69), inference(avatar_split_clause, [status(thm)], [p1417, sdef14, sdef69])).
% 27.40/9.97 cnf(p135, plain, distinct_lines(X0,sk1) | convergent_lines(sk0,X1) | convergent_lines(X0,X2) | convergent_lines(X1,X2), inference(resolution, [status(thm)], [p53, c5])).
% 27.40/9.97 cnf(p543, plain, distinct_lines(X0,sk1) | convergent_lines(sk0,X1) | convergent_lines(X1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p135, c13])).
% 27.40/9.97 cnf(p1419, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | distinct_lines(X0,sk1) | convergent_lines(sk0,X2) | convergent_lines(X2,X1), inference(resolution, [status(thm)], [p121, p543])).
% 27.40/9.97 cnf(ssp136, plain, (spl8 | spl58), inference(avatar_split_clause, [status(thm)], [p1419, sdef8, sdef58])).
% 27.40/9.97 cnf(p64, plain, ~apart_point_and_line(X0,X1) | distinct_points(X0,intersection_point(X1,X2)) | convergent_lines(sk0,X1) | convergent_lines(sk1,X2), inference(resolution, [status(thm)], [c8, p33])).
% 27.40/9.97 cnf(p1430, plain, (distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,X0)) | convergent_lines(sk0,sk0) | convergent_lines(sk1,X0) | ~spl0), inference(resolution, [status(thm)], [p1214, p64])).
% 27.40/9.97 fof(sdef70, definition, (spl70 <=> (distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,X0)) | convergent_lines(sk1,X0))), introduced(definition, [new_symbols(naming, [spl70])], [avatar_definition])).
% 27.40/9.97 cnf(ssp137, plain, (~spl0 | spl70 | spl71), inference(avatar_split_clause, [status(thm)], [p1430, sdef70, sdef71])).
% 27.40/9.97 cnf(p79, plain, convergent_lines(sk1,X0) | distinct_lines(sk0,X1) | ~apart_point_and_line(X2,X1) | distinct_points(X2,intersection_point(X1,X0)), inference(resolution, [status(thm)], [p42, c8])).
% 27.40/9.97 cnf(p1434, plain, (convergent_lines(sk1,X0) | distinct_lines(sk0,sk0) | distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,X0)) | ~spl0), inference(resolution, [status(thm)], [p1214, p79])).
% 27.40/9.97 cnf(ssp138, plain, (~spl0 | spl70 | spl72), inference(avatar_split_clause, [status(thm)], [p1434, sdef70, sdef72])).
% 27.40/9.97 cnf(p120, plain, convergent_lines(X0,sk1) | convergent_lines(sk0,X1) | ~apart_point_and_line(X2,X1) | distinct_points(X2,intersection_point(X0,X1)), inference(resolution, [status(thm)], [p50, c9])).
% 27.40/9.97 cnf(p1439, plain, (convergent_lines(X0,sk1) | convergent_lines(sk0,sk0) | distinct_points(intersection_point(sk0,sk1),intersection_point(X0,sk0)) | ~spl0), inference(resolution, [status(thm)], [p1214, p120])).
% 27.40/9.97 fof(sdef73, definition, (spl73 <=> (convergent_lines(X0,sk1) | distinct_points(intersection_point(sk0,sk1),intersection_point(X0,sk0)))), introduced(definition, [new_symbols(naming, [spl73])], [avatar_definition])).
% 27.40/9.97 cnf(ssp139, plain, (~spl0 | spl71 | spl73), inference(avatar_split_clause, [status(thm)], [p1439, sdef71, sdef73])).
% 27.40/9.97 fof(f3, axiom, ! [X,Y,Z] : ( distinct_points(X,Y) => ( distinct_points(X,Z) | distinct_points(Y,Z) ) ), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', apart4)).
% 27.40/9.97 fof(f3_nnf, plain, ! [X,Y,Z] : ((~(distinct_points(X,Y)) | (distinct_points(X,Z) | distinct_points(Y,Z)))), inference(nnf_transformation, [status(thm)], [f3])).
% 27.40/9.97 fof(f3_sk, plain, ! [X,Y,Z] : ((~(distinct_points(X,Y)) | (distinct_points(X,Z) | distinct_points(Y,Z)))), inference(skolemisation, [status(esa)], [f3_nnf])).
% 27.40/9.97 cnf(c3, plain, ~distinct_points(X0,X1) | distinct_points(X0,X2) | distinct_points(X1,X2), inference(cnf_transformation, [status(esa)], [f3_sk])).
% 27.40/9.97 cnf(p17, plain, distinct_points(intersection_point(sk0,sk1),X0) | distinct_points(intersection_point(sk1,sk0),X0), inference(resolution, [status(thm)], [c3, c15])).
% 27.40/9.97 cnf(p122, plain, ~distinct_lines(X0,X1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),X1) | apart_point_and_line(X2,X0) | apart_point_and_line(X2,X1) | distinct_points(intersection_point(sk0,sk1),X2), inference(resolution, [status(thm)], [c10, p17])).
% 27.40/9.97 cnf(p1458, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(X0,sk0) | apart_point_and_line(X0,sk1) | distinct_points(intersection_point(sk0,sk1),X0), inference(resolution, [status(thm)], [p122, p16])).
% 27.40/9.97 fof(sdef74, definition, (spl74 <=> (apart_point_and_line(X0,sk0) | apart_point_and_line(X0,sk1) | distinct_points(intersection_point(sk0,sk1),X0))), introduced(definition, [new_symbols(naming, [spl74])], [avatar_definition])).
% 27.40/9.97 cnf(ssp140, plain, (spl2 | spl3 | spl74), inference(avatar_split_clause, [status(thm)], [p1458, sdef2, sdef3, sdef74])).
% 27.40/9.97 cnf(p1460, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk0,X0), inference(resolution, [status(thm)], [p122, p19])).
% 27.40/9.97 fof(sdef75, definition, (spl75 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk0,X0))), introduced(definition, [new_symbols(naming, [spl75])], [avatar_definition])).
% 27.40/9.97 cnf(ssp141, plain, (spl3 | spl75), inference(avatar_split_clause, [status(thm)], [p1460, sdef3, sdef75])).
% 27.40/9.97 cnf(p1462, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p122, p20])).
% 27.40/9.97 fof(sdef76, definition, (spl76 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl76])], [avatar_definition])).
% 27.40/9.97 cnf(ssp142, plain, (spl2 | spl76), inference(avatar_split_clause, [status(thm)], [p1462, sdef2, sdef76])).
% 27.40/9.97 cnf(p1464, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk0,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p122, p20])).
% 27.40/9.97 fof(sdef77, definition, (spl77 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk0,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl77])], [avatar_definition])).
% 27.40/9.97 cnf(ssp143, plain, (spl3 | spl77), inference(avatar_split_clause, [status(thm)], [p1464, sdef3, sdef77])).
% 27.40/9.97 cnf(p1467, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,sk1), inference(resolution, [status(thm)], [p122, p21])).
% 27.40/9.97 fof(sdef78, definition, (spl78 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,sk1))), introduced(definition, [new_symbols(naming, [spl78])], [avatar_definition])).
% 27.40/9.97 cnf(ssp144, plain, (spl2 | spl78), inference(avatar_split_clause, [status(thm)], [p1467, sdef2, sdef78])).
% 27.40/9.97 cnf(p1469, plain, apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,sk1) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk0,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p122, p25])).
% 27.40/9.97 fof(sdef79, definition, (spl79 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,sk1) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk0,X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl79])], [avatar_definition])).
% 27.40/9.97 cnf(ssp145, plain, (spl3 | spl79), inference(avatar_split_clause, [status(thm)], [p1469, sdef3, sdef79])).
% 27.40/9.97 cnf(p1471, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk1) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p122, p25])).
% 27.40/9.97 fof(sdef80, definition, (spl80 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk1) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl80])], [avatar_definition])).
% 27.40/9.97 cnf(ssp146, plain, (spl2 | spl80), inference(avatar_split_clause, [status(thm)], [p1471, sdef2, sdef80])).
% 27.40/9.97 cnf(p1474, plain, apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,sk1) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,sk0), inference(resolution, [status(thm)], [p122, p26])).
% 27.40/9.97 fof(sdef81, definition, (spl81 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,sk1) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,sk0))), introduced(definition, [new_symbols(naming, [spl81])], [avatar_definition])).
% 27.40/9.97 cnf(ssp147, plain, (spl3 | spl81), inference(avatar_split_clause, [status(thm)], [p1474, sdef3, sdef81])).
% 27.40/9.97 cnf(p1477, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk0) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p122, p31])).
% 27.40/9.97 fof(sdef82, definition, (spl82 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk0) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl82])], [avatar_definition])).
% 27.40/9.97 cnf(ssp148, plain, (spl3 | spl82), inference(avatar_split_clause, [status(thm)], [p1477, sdef3, sdef82])).
% 27.40/9.97 cnf(p1479, plain, apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,sk0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X0), inference(resolution, [status(thm)], [p122, p37])).
% 27.40/9.97 fof(sdef83, definition, (spl83 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,sk0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X0))), introduced(definition, [new_symbols(naming, [spl83])], [avatar_definition])).
% 27.40/9.97 cnf(ssp149, plain, (spl2 | spl83), inference(avatar_split_clause, [status(thm)], [p1479, sdef2, sdef83])).
% 27.40/9.97 cnf(p1481, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p122, p40])).
% 27.40/9.97 fof(sdef84, definition, (spl84 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl84])], [avatar_definition])).
% 27.40/9.97 cnf(ssp150, plain, (spl2 | spl84), inference(avatar_split_clause, [status(thm)], [p1481, sdef2, sdef84])).
% 27.40/9.97 cnf(p1484, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p122, p56])).
% 27.40/9.97 fof(sdef85, definition, (spl85 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl85])], [avatar_definition])).
% 27.40/9.97 cnf(ssp151, plain, (spl3 | spl85), inference(avatar_split_clause, [status(thm)], [p1484, sdef3, sdef85])).
% 27.40/9.97 cnf(p1487, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p122, p75])).
% 27.40/9.97 fof(sdef86, definition, (spl86 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl86])], [avatar_definition])).
% 27.40/9.97 cnf(ssp152, plain, (spl2 | spl86), inference(avatar_split_clause, [status(thm)], [p1487, sdef2, sdef86])).
% 27.40/9.97 cnf(p1490, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p122, p97])).
% 27.40/9.97 fof(sdef87, definition, (spl87 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl87])], [avatar_definition])).
% 27.40/9.97 cnf(ssp153, plain, (spl3 | spl87), inference(avatar_split_clause, [status(thm)], [p1490, sdef3, sdef87])).
% 27.40/9.97 cnf(p1493, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,X0) | distinct_lines(sk0,X3) | distinct_lines(X2,X3), inference(resolution, [status(thm)], [p122, p22])).
% 27.40/9.97 fof(sdef88, definition, (spl88 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,X0) | distinct_lines(sk0,X3) | distinct_lines(X2,X3))), introduced(definition, [new_symbols(naming, [spl88])], [avatar_definition])).
% 27.40/9.97 cnf(ssp154, plain, (spl3 | spl88), inference(avatar_split_clause, [status(thm)], [p1493, sdef3, sdef88])).
% 27.40/9.97 cnf(p1496, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X2) | distinct_lines(X3,X2) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p22])).
% 27.40/9.97 fof(sdef89, definition, (spl89 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X2) | distinct_lines(X3,X2) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl89])], [avatar_definition])).
% 27.40/9.97 cnf(ssp155, plain, (spl2 | spl89), inference(avatar_split_clause, [status(thm)], [p1496, sdef2, sdef89])).
% 27.40/9.97 cnf(p1500, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk1) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p122, p159])).
% 27.40/9.97 fof(sdef90, definition, (spl90 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk1) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl90])], [avatar_definition])).
% 27.40/9.97 cnf(ssp156, plain, (spl2 | spl90), inference(avatar_split_clause, [status(thm)], [p1500, sdef2, sdef90])).
% 27.40/9.97 cnf(p1503, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | distinct_lines(sk1,X3) | distinct_lines(X2,X3), inference(resolution, [status(thm)], [p122, p23])).
% 27.40/9.97 fof(sdef91, definition, (spl91 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | distinct_lines(sk1,X3) | distinct_lines(X2,X3))), introduced(definition, [new_symbols(naming, [spl91])], [avatar_definition])).
% 27.40/9.97 cnf(ssp157, plain, (spl2 | spl91), inference(avatar_split_clause, [status(thm)], [p1503, sdef2, sdef91])).
% 27.40/9.97 cnf(p1505, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk0,X2) | distinct_lines(X2,X3) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p23])).
% 27.40/9.97 fof(sdef92, definition, (spl92 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk0,X2) | distinct_lines(X2,X3) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl92])], [avatar_definition])).
% 27.40/9.97 cnf(ssp158, plain, (spl3 | spl92), inference(avatar_split_clause, [status(thm)], [p1505, sdef3, sdef92])).
% 27.40/9.97 cnf(p1509, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X2) | distinct_lines(X0,X3) | distinct_lines(X2,X3), inference(resolution, [status(thm)], [p122, p24])).
% 27.40/9.97 fof(sdef93, definition, (spl93 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X2) | distinct_lines(X0,X3) | distinct_lines(X2,X3))), introduced(definition, [new_symbols(naming, [spl93])], [avatar_definition])).
% 27.40/9.97 cnf(ssp159, plain, (spl2 | spl93), inference(avatar_split_clause, [status(thm)], [p1509, sdef2, sdef93])).
% 27.40/9.97 cnf(p1511, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk0,X2) | distinct_lines(X2,X3) | distinct_lines(X0,X3), inference(resolution, [status(thm)], [p122, p24])).
% 27.40/9.97 fof(sdef94, definition, (spl94 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk0,X2) | distinct_lines(X2,X3) | distinct_lines(X0,X3))), introduced(definition, [new_symbols(naming, [spl94])], [avatar_definition])).
% 27.40/9.97 cnf(ssp160, plain, (spl3 | spl94), inference(avatar_split_clause, [status(thm)], [p1511, sdef3, sdef94])).
% 27.40/9.97 cnf(p1514, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | distinct_lines(X2,sk1), inference(resolution, [status(thm)], [p122, p225])).
% 27.40/9.97 fof(sdef95, definition, (spl95 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | distinct_lines(X2,sk1))), introduced(definition, [new_symbols(naming, [spl95])], [avatar_definition])).
% 27.40/9.97 cnf(ssp161, plain, (spl2 | spl95), inference(avatar_split_clause, [status(thm)], [p1514, sdef2, sdef95])).
% 27.40/9.97 cnf(p1517, plain, apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,sk1) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | distinct_lines(sk0,X3) | distinct_lines(X2,X3), inference(resolution, [status(thm)], [p122, p27])).
% 27.40/9.97 fof(sdef96, definition, (spl96 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,sk1) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | distinct_lines(sk0,X3) | distinct_lines(X2,X3))), introduced(definition, [new_symbols(naming, [spl96])], [avatar_definition])).
% 27.40/9.97 cnf(ssp162, plain, (spl3 | spl96), inference(avatar_split_clause, [status(thm)], [p1517, sdef3, sdef96])).
% 27.40/9.97 cnf(p1520, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk1) | distinct_lines(X2,X3) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p27])).
% 27.40/9.97 fof(sdef97, definition, (spl97 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk1) | distinct_lines(X2,X3) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl97])], [avatar_definition])).
% 27.40/9.97 cnf(ssp163, plain, (spl2 | spl97), inference(avatar_split_clause, [status(thm)], [p1520, sdef2, sdef97])).
% 27.40/9.97 cnf(p1524, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk0) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p122, p242])).
% 27.40/9.97 fof(sdef98, definition, (spl98 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk0) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl98])], [avatar_definition])).
% 27.40/9.97 cnf(ssp164, plain, (spl3 | spl98), inference(avatar_split_clause, [status(thm)], [p1524, sdef3, sdef98])).
% 27.40/9.97 cnf(p1526, plain, apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,sk1) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | distinct_lines(X2,sk0), inference(resolution, [status(thm)], [p122, p272])).
% 27.40/9.97 fof(sdef99, definition, (spl99 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,sk1) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | distinct_lines(X2,sk0))), introduced(definition, [new_symbols(naming, [spl99])], [avatar_definition])).
% 27.40/9.97 cnf(ssp165, plain, (spl3 | spl99), inference(avatar_split_clause, [status(thm)], [p1526, sdef3, sdef99])).
% 27.40/9.97 cnf(p1529, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk1) | distinct_lines(X2,X3) | distinct_lines(X0,X3), inference(resolution, [status(thm)], [p122, p28])).
% 27.40/9.97 fof(sdef100, definition, (spl100 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk1) | distinct_lines(X2,X3) | distinct_lines(X0,X3))), introduced(definition, [new_symbols(naming, [spl100])], [avatar_definition])).
% 27.40/9.97 cnf(ssp166, plain, (spl2 | spl100), inference(avatar_split_clause, [status(thm)], [p1529, sdef2, sdef100])).
% 27.40/9.97 cnf(p1532, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p122, p280])).
% 27.40/9.97 fof(sdef101, definition, (spl101 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl101])], [avatar_definition])).
% 27.40/9.97 cnf(ssp167, plain, (spl2 | spl101), inference(avatar_split_clause, [status(thm)], [p1532, sdef2, sdef101])).
% 27.40/9.97 cnf(p1534, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk0) | distinct_lines(X2,X3) | distinct_lines(X0,X3), inference(resolution, [status(thm)], [p122, p38])).
% 27.40/9.97 fof(sdef102, definition, (spl102 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk0) | distinct_lines(X2,X3) | distinct_lines(X0,X3))), introduced(definition, [new_symbols(naming, [spl102])], [avatar_definition])).
% 27.40/9.97 cnf(ssp168, plain, (spl3 | spl102), inference(avatar_split_clause, [status(thm)], [p1534, sdef3, sdef102])).
% 27.40/9.97 cnf(p1539, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk0) | distinct_lines(X2,X3) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p39])).
% 27.40/9.97 fof(sdef103, definition, (spl103 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,sk0) | distinct_lines(X2,X3) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl103])], [avatar_definition])).
% 27.40/9.97 cnf(ssp169, plain, (spl3 | spl103), inference(avatar_split_clause, [status(thm)], [p1539, sdef3, sdef103])).
% 27.40/9.97 cnf(p1541, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk1) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p122, p337])).
% 27.40/9.97 fof(sdef104, definition, (spl104 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk1) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl104])], [avatar_definition])).
% 27.40/9.97 cnf(ssp170, plain, (spl2 | spl104), inference(avatar_split_clause, [status(thm)], [p1541, sdef2, sdef104])).
% 27.40/9.97 cnf(p1543, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk0) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p122, p386])).
% 27.40/9.97 fof(sdef105, definition, (spl105 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk0) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl105])], [avatar_definition])).
% 27.40/9.97 cnf(ssp171, plain, (spl3 | spl105), inference(avatar_split_clause, [status(thm)], [p1543, sdef3, sdef105])).
% 27.40/9.97 cnf(p1545, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X2) | distinct_lines(X2,X3) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p72])).
% 27.40/9.97 fof(sdef106, definition, (spl106 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(sk1,X2) | distinct_lines(X2,X3) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl106])], [avatar_definition])).
% 27.40/9.97 cnf(ssp172, plain, (spl2 | spl106), inference(avatar_split_clause, [status(thm)], [p1545, sdef2, sdef106])).
% 27.40/9.97 cnf(p1555, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | distinct_lines(X3,X2) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p143])).
% 27.40/9.97 fof(sdef107, definition, (spl107 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | distinct_lines(X3,X2) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl107])], [avatar_definition])).
% 27.40/9.97 cnf(ssp173, plain, (spl3 | spl107), inference(avatar_split_clause, [status(thm)], [p1555, sdef3, sdef107])).
% 27.40/9.97 cnf(p1558, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | distinct_lines(X0,X3) | distinct_lines(X2,X3), inference(resolution, [status(thm)], [p122, p144])).
% 27.40/9.97 fof(sdef108, definition, (spl108 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | distinct_lines(X0,X3) | distinct_lines(X2,X3))), introduced(definition, [new_symbols(naming, [spl108])], [avatar_definition])).
% 27.40/9.97 cnf(ssp174, plain, (spl3 | spl108), inference(avatar_split_clause, [status(thm)], [p1558, sdef3, sdef108])).
% 27.40/9.97 cnf(p1562, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | convergent_lines(sk0,X3) | convergent_lines(X2,X3), inference(resolution, [status(thm)], [p122, p145])).
% 27.40/9.97 fof(sdef109, definition, (spl109 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | convergent_lines(sk0,X3) | convergent_lines(X2,X3))), introduced(definition, [new_symbols(naming, [spl109])], [avatar_definition])).
% 27.40/9.97 cnf(ssp175, plain, (spl3 | spl109), inference(avatar_split_clause, [status(thm)], [p1562, sdef3, sdef109])).
% 27.40/9.97 cnf(p1566, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | distinct_lines(X3,X2) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p150])).
% 27.40/9.97 fof(sdef110, definition, (spl110 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | distinct_lines(X3,X2) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl110])], [avatar_definition])).
% 27.40/9.97 cnf(ssp176, plain, (spl2 | spl110), inference(avatar_split_clause, [status(thm)], [p1566, sdef2, sdef110])).
% 27.40/9.97 cnf(p1569, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | distinct_lines(X0,X3) | distinct_lines(X2,X3), inference(resolution, [status(thm)], [p122, p151])).
% 27.40/9.97 fof(sdef111, definition, (spl111 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | distinct_lines(X0,X3) | distinct_lines(X2,X3))), introduced(definition, [new_symbols(naming, [spl111])], [avatar_definition])).
% 27.40/9.97 cnf(ssp177, plain, (spl2 | spl111), inference(avatar_split_clause, [status(thm)], [p1569, sdef2, sdef111])).
% 27.40/9.97 cnf(p1573, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | convergent_lines(sk1,X3) | convergent_lines(X2,X3), inference(resolution, [status(thm)], [p122, p152])).
% 27.40/9.97 fof(sdef112, definition, (spl112 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X0,X2) | convergent_lines(sk1,X3) | convergent_lines(X2,X3))), introduced(definition, [new_symbols(naming, [spl112])], [avatar_definition])).
% 27.40/9.97 cnf(ssp178, plain, (spl2 | spl112), inference(avatar_split_clause, [status(thm)], [p1573, sdef2, sdef112])).
% 27.40/9.97 cnf(p1576, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | distinct_lines(X2,X3) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p155])).
% 27.40/9.97 fof(sdef113, definition, (spl113 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | distinct_lines(X2,X3) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl113])], [avatar_definition])).
% 27.40/9.97 cnf(ssp179, plain, (spl3 | spl113), inference(avatar_split_clause, [status(thm)], [p1576, sdef3, sdef113])).
% 27.40/9.97 cnf(p1578, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,X0) | convergent_lines(sk0,X3) | convergent_lines(X2,X3), inference(resolution, [status(thm)], [p122, p156])).
% 27.40/9.97 fof(sdef114, definition, (spl114 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,X0) | convergent_lines(sk0,X3) | convergent_lines(X2,X3))), introduced(definition, [new_symbols(naming, [spl114])], [avatar_definition])).
% 27.40/9.97 cnf(ssp180, plain, (spl3 | spl114), inference(avatar_split_clause, [status(thm)], [p1578, sdef3, sdef114])).
% 27.40/9.97 cnf(p1587, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk1) | distinct_lines(X2,X3) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p220])).
% 27.40/9.97 fof(sdef115, definition, (spl115 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk1) | distinct_lines(X2,X3) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl115])], [avatar_definition])).
% 27.40/9.97 cnf(ssp181, plain, (spl2 | spl115), inference(avatar_split_clause, [status(thm)], [p1587, sdef2, sdef115])).
% 27.40/9.97 cnf(p1590, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk1) | distinct_lines(X2,X3) | distinct_lines(X0,X3), inference(resolution, [status(thm)], [p122, p221])).
% 27.40/9.97 fof(sdef116, definition, (spl116 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk1) | distinct_lines(X2,X3) | distinct_lines(X0,X3))), introduced(definition, [new_symbols(naming, [spl116])], [avatar_definition])).
% 27.40/9.97 cnf(ssp182, plain, (spl2 | spl116), inference(avatar_split_clause, [status(thm)], [p1590, sdef2, sdef116])).
% 27.40/9.97 cnf(p1593, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,X0) | convergent_lines(X2,X3) | convergent_lines(sk1,X3), inference(resolution, [status(thm)], [p122, p222])).
% 27.40/9.97 fof(sdef117, definition, (spl117 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,X0) | convergent_lines(X2,X3) | convergent_lines(sk1,X3))), introduced(definition, [new_symbols(naming, [spl117])], [avatar_definition])).
% 27.40/9.97 cnf(ssp183, plain, (spl2 | spl117), inference(avatar_split_clause, [status(thm)], [p1593, sdef2, sdef117])).
% 27.40/9.97 cnf(p1598, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,X3) | distinct_lines(X3,sk1) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p122, p264])).
% 27.40/9.97 fof(sdef118, definition, (spl118 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,X3) | distinct_lines(X3,sk1) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl118])], [avatar_definition])).
% 27.40/9.97 cnf(ssp184, plain, (spl2 | spl118), inference(avatar_split_clause, [status(thm)], [p1598, sdef2, sdef118])).
% 27.40/9.97 cnf(p1604, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk0) | distinct_lines(X2,X3) | distinct_lines(X0,X3), inference(resolution, [status(thm)], [p122, p276])).
% 27.40/9.97 fof(sdef119, definition, (spl119 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk0) | distinct_lines(X2,X3) | distinct_lines(X0,X3))), introduced(definition, [new_symbols(naming, [spl119])], [avatar_definition])).
% 27.40/9.97 cnf(ssp185, plain, (spl3 | spl119), inference(avatar_split_clause, [status(thm)], [p1604, sdef3, sdef119])).
% 27.40/9.97 cnf(p1609, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk0) | distinct_lines(X2,X3) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p277])).
% 27.40/9.97 fof(sdef120, definition, (spl120 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk0) | distinct_lines(X2,X3) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl120])], [avatar_definition])).
% 27.40/9.97 cnf(ssp186, plain, (spl3 | spl120), inference(avatar_split_clause, [status(thm)], [p1609, sdef3, sdef120])).
% 27.40/9.97 cnf(p1612, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,X3) | distinct_lines(X3,sk0) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p122, p290])).
% 27.40/9.97 fof(sdef121, definition, (spl121 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | distinct_lines(X2,X3) | distinct_lines(X3,sk0) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl121])], [avatar_definition])).
% 27.40/9.97 cnf(ssp187, plain, (spl3 | spl121), inference(avatar_split_clause, [status(thm)], [p1612, sdef3, sdef121])).
% 27.40/9.97 cnf(p1616, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | distinct_lines(X2,X3) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p293])).
% 27.40/9.97 fof(sdef122, definition, (spl122 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | distinct_lines(X2,X3) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl122])], [avatar_definition])).
% 27.40/9.97 cnf(ssp188, plain, (spl2 | spl122), inference(avatar_split_clause, [status(thm)], [p1616, sdef2, sdef122])).
% 27.40/9.97 cnf(p1620, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk1) | distinct_lines(X3,X2) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p365])).
% 27.40/9.97 fof(sdef123, definition, (spl123 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk1) | distinct_lines(X3,X2) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl123])], [avatar_definition])).
% 27.40/9.97 cnf(ssp189, plain, (spl2 | spl123), inference(avatar_split_clause, [status(thm)], [p1620, sdef2, sdef123])).
% 27.40/9.97 cnf(p1624, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | convergent_lines(X2,X3) | distinct_lines(X0,X3), inference(resolution, [status(thm)], [p122, p392])).
% 27.40/9.97 fof(sdef124, definition, (spl124 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk0,X2) | convergent_lines(X2,X3) | distinct_lines(X0,X3))), introduced(definition, [new_symbols(naming, [spl124])], [avatar_definition])).
% 27.40/9.97 cnf(ssp190, plain, (spl3 | spl124), inference(avatar_split_clause, [status(thm)], [p1624, sdef3, sdef124])).
% 27.40/9.97 cnf(p1627, plain, apart_point_and_line(intersection_point(sk1,sk0),sk1) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk0) | distinct_lines(X3,X2) | distinct_lines(X3,X0), inference(resolution, [status(thm)], [p122, p401])).
% 27.40/9.97 fof(sdef125, definition, (spl125 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk1) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(X2,sk0) | distinct_lines(X3,X2) | distinct_lines(X3,X0))), introduced(definition, [new_symbols(naming, [spl125])], [avatar_definition])).
% 27.40/9.97 cnf(ssp191, plain, (spl3 | spl125), inference(avatar_split_clause, [status(thm)], [p1627, sdef3, sdef125])).
% 27.40/9.97 cnf(p1631, plain, apart_point_and_line(intersection_point(sk1,sk0),sk0) | apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | convergent_lines(X2,X3) | distinct_lines(X0,X3), inference(resolution, [status(thm)], [p122, p418])).
% 27.40/9.97 fof(sdef126, definition, (spl126 <=> (apart_point_and_line(intersection_point(sk1,sk0),X0) | apart_point_and_line(X1,sk0) | apart_point_and_line(X1,X0) | distinct_points(intersection_point(sk0,sk1),X1) | convergent_lines(sk1,X2) | convergent_lines(X2,X3) | distinct_lines(X0,X3))), introduced(definition, [new_symbols(naming, [spl126])], [avatar_definition])).
% 27.40/9.97 cnf(ssp192, plain, (spl2 | spl126), inference(avatar_split_clause, [status(thm)], [p1631, sdef2, sdef126])).
% 27.40/9.97 cnf(p1658, plain, (distinct_points(intersection_point(sk1,sk0),intersection_point(sk0,X0)) | convergent_lines(sk0,sk0) | convergent_lines(sk1,X0) | ~spl2), inference(resolution, [status(thm)], [p1216, p64])).
% 27.40/9.97 fof(sdef127, definition, (spl127 <=> (distinct_points(intersection_point(sk1,sk0),intersection_point(sk0,X0)) | convergent_lines(sk1,X0))), introduced(definition, [new_symbols(naming, [spl127])], [avatar_definition])).
% 27.40/9.97 cnf(ssp193, plain, (~spl2 | spl71 | spl127), inference(avatar_split_clause, [status(thm)], [p1658, sdef71, sdef127])).
% 27.40/9.97 cnf(p1661, plain, (convergent_lines(sk1,X0) | distinct_lines(sk0,sk0) | distinct_points(intersection_point(sk1,sk0),intersection_point(sk0,X0)) | ~spl2), inference(resolution, [status(thm)], [p1216, p79])).
% 27.40/9.97 cnf(ssp194, plain, (~spl2 | spl72 | spl127), inference(avatar_split_clause, [status(thm)], [p1661, sdef72, sdef127])).
% 27.40/9.97 cnf(p1665, plain, (convergent_lines(X0,sk1) | convergent_lines(sk0,sk0) | distinct_points(intersection_point(sk1,sk0),intersection_point(X0,sk0)) | ~spl2), inference(resolution, [status(thm)], [p1216, p120])).
% 27.40/9.97 fof(sdef128, definition, (spl128 <=> (convergent_lines(X0,sk1) | distinct_points(intersection_point(sk1,sk0),intersection_point(X0,sk0)))), introduced(definition, [new_symbols(naming, [spl128])], [avatar_definition])).
% 27.40/9.97 cnf(ssp195, plain, (~spl2 | spl71 | spl128), inference(avatar_split_clause, [status(thm)], [p1665, sdef71, sdef128])).
% 27.40/9.97 cnf(sat_ref, plain, $false, inference(avatar_sat_refutation, [status(thm)], [ssp0, ssp1, ssp2, ssp3, ssp4, ssp5, ssp6, ssp7, ssp8, ssp9, ssp10, ssp11, ssp12, ssp13, ssp14, ssp15, ssp16, ssp17, ssp18, ssp19, ssp20, ssp21, ssp22, ssp23, ssp24, ssp25, ssp26, ssp27, ssp28, ssp29, ssp30, ssp31, ssp32, ssp33, ssp34, ssp35, ssp36, ssp37, ssp38, ssp39, ssp40, ssp41, ssp42, ssp43, ssp44, ssp45, ssp46, ssp47, ssp48, ssp49, ssp50, ssp51, ssp52, ssp53, ssp54, ssp55, ssp56, ssp57, ssp58, ssp59, ssp60, ssp61, ssp62, ssp63, ssp64, ssp65, ssp66, ssp67, ssp68, ssp69, ssp70, ssp71, ssp72, ssp73, ssp74, ssp75, ssp76, ssp77, ssp78, ssp79, ssp80, ssp81, ssp82, ssp83, ssp84, ssp85, ssp86, ssp87, ssp88, ssp89, ssp90, ssp91, ssp92, ssp93, ssp94, ssp95, ssp96, ssp97, ssp98, ssp99, ssp100, ssp101, ssp102, ssp103, ssp104, ssp105, ssp106, ssp107, ssp108, ssp109, ssp110, ssp111, ssp112, ssp113, ssp114, ssp115, ssp116, ssp117, ssp118, ssp119, ssp120, ssp121, ssp122, ssp123, ssp124, ssp125, ssp126, ssp127, ssp128, ssp129, ssp130, ssp131, ssp132, ssp133, ssp134, ssp135, ssp136, ssp137, ssp138, ssp139, ssp140, ssp141, ssp142, ssp143, ssp144, ssp145, ssp146, ssp147, ssp148, ssp149, ssp150, ssp151, ssp152, ssp153, ssp154, ssp155, ssp156, ssp157, ssp158, ssp159, ssp160, ssp161, ssp162, ssp163, ssp164, ssp165, ssp166, ssp167, ssp168, ssp169, ssp170, ssp171, ssp172, ssp173, ssp174, ssp175, ssp176, ssp177, ssp178, ssp179, ssp180, ssp181, ssp182, ssp183, ssp184, ssp185, ssp186, ssp187, ssp188, ssp189, ssp190, ssp191, ssp192, ssp193, ssp194, ssp195, sct0, sct1, sct2, sct3, sct4, sct5])).
% 27.40/9.97 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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