%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO190+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 01:17:22 PM UTC 2026
% Result : Theorem 25.41s 8.71s
% Output : Proof 25.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO190+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/5.39 % Computer : n001.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Wed Sep 23 11:28:25 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.41/8.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.41/8.71 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.41/8.71 fof(sdef1, definition, (spl1 <=> (distinct_points(sk2,sk2))), introduced(definition, [new_symbols(naming, [spl1])], [avatar_definition])).
% 25.41/8.71 cnf(p464, plain, (distinct_points(sk2,sk2) | ~spl1), inference(avatar_component_clause, [status(thm)], [sdef1])).
% 25.41/8.71 fof(f0, axiom, ! [X] : ~ distinct_points(X,X), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apart1)).
% 25.41/8.71 fof(f0_nnf, plain, ! [X] : (~(distinct_points(X,X))), inference(nnf_transformation, [status(thm)], [f0])).
% 25.41/8.71 fof(f0_sk, plain, ! [X] : (~(distinct_points(X,X))), inference(skolemisation, [status(esa)], [f0_nnf])).
% 25.41/8.71 cnf(c0, plain, ~distinct_points(X0,X0), inference(cnf_transformation, [status(esa)], [f0_sk])).
% 25.41/8.71 cnf(p500, plain, ($false | ~spl1), inference(resolution, [status(thm)], [p464, c0])).
% 25.41/8.71 cnf(sct0, plain, (~spl1), inference(avatar_contradiction_clause, [status(thm)], [p500])).
% 25.41/8.71 fof(sdef3, definition, (spl3 <=> (distinct_points(sk2,X0) | distinct_points(X0,sk2))), introduced(definition, [new_symbols(naming, [spl3])], [avatar_definition])).
% 25.41/8.71 cnf(p468, plain, (distinct_points(sk2,X0) | distinct_points(X0,sk2) | ~spl3), inference(avatar_component_clause, [status(thm)], [sdef3])).
% 25.41/8.71 cnf(p503, plain, (distinct_points(sk2,sk2) | ~spl3), inference(factoring, [status(thm)], [p468])).
% 25.41/8.71 cnf(p512, plain, ($false | ~spl3), inference(resolution, [status(thm)], [p503, c0])).
% 25.41/8.71 cnf(sct1, plain, (~spl3), inference(avatar_contradiction_clause, [status(thm)], [p512])).
% 25.41/8.71 fof(sdef37, definition, (spl37 <=> (distinct_points(sk0,sk0))), introduced(definition, [new_symbols(naming, [spl37])], [avatar_definition])).
% 25.41/8.71 cnf(p911, plain, (distinct_points(sk0,sk0) | ~spl37), inference(avatar_component_clause, [status(thm)], [sdef37])).
% 25.41/8.71 cnf(p922, plain, ($false | ~spl37), inference(resolution, [status(thm)], [p911, c0])).
% 25.41/8.71 cnf(sct2, plain, (~spl37), inference(avatar_contradiction_clause, [status(thm)], [p922])).
% 25.41/8.71 fof(sdef38, definition, (spl38 <=> (distinct_points(sk1,sk1))), introduced(definition, [new_symbols(naming, [spl38])], [avatar_definition])).
% 25.41/8.71 cnf(p944, plain, (distinct_points(sk1,sk1) | ~spl38), inference(avatar_component_clause, [status(thm)], [sdef38])).
% 25.41/8.71 cnf(p955, plain, ($false | ~spl38), inference(resolution, [status(thm)], [p944, c0])).
% 25.41/8.71 cnf(sct3, plain, (~spl38), inference(avatar_contradiction_clause, [status(thm)], [p955])).
% 25.41/8.71 fof(sdef42, definition, (spl42 <=> (apart_point_and_line(sk0,line_connecting(sk1,sk0)))), introduced(definition, [new_symbols(naming, [spl42])], [avatar_definition])).
% 25.41/8.71 cnf(p991, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | ~spl42), inference(avatar_component_clause, [status(thm)], [sdef42])).
% 25.41/8.71 fof(f6, axiom, ! [X,Y,Z] : ( distinct_points(X,Y) => ( apart_point_and_line(Z,line_connecting(X,Y)) => ( distinct_points(Z,X) & distinct_points(Z,Y) ) ) ), file('/export/starexec/sandbox/benchmark/theBenchmark.p', con1)).
% 25.41/8.71 fof(f6_nnf, plain, ! [X,Y,Z] : ((~(distinct_points(X,Y)) | (~(apart_point_and_line(Z,line_connecting(X,Y))) | (distinct_points(Z,X) & distinct_points(Z,Y))))), inference(nnf_transformation, [status(thm)], [f6])).
% 25.41/8.71 fof(f6_sk, plain, ! [X,Y,Z] : ((~(distinct_points(X,Y)) | (~(apart_point_and_line(Z,line_connecting(X,Y))) | (distinct_points(Z,X) & distinct_points(Z,Y))))), inference(skolemisation, [status(esa)], [f6_nnf])).
% 25.41/8.71 cnf(c7, plain, ~distinct_points(X0,X1) | ~apart_point_and_line(X2,line_connecting(X0,X1)) | distinct_points(X2,X1), inference(cnf_transformation, [status(esa)], [f6_sk])).
% 25.41/8.71 fof(f3, axiom, ! [X,Y,Z] : ( distinct_points(X,Y) => ( distinct_points(X,Z) | distinct_points(Y,Z) ) ), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apart4)).
% 25.41/8.71 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])).
% 25.41/8.71 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])).
% 25.41/8.71 cnf(c3, plain, ~distinct_points(X0,X1) | distinct_points(X0,X2) | distinct_points(X1,X2), inference(cnf_transformation, [status(esa)], [f3_sk])).
% 25.41/8.71 fof(f12, conjecture, ! [X,Y,Z] : ( ( distinct_points(X,Y) & distinct_points(X,Z) & distinct_points(Y,Z) & ~ apart_point_and_line(Z,line_connecting(X,Y)) ) => ~ apart_point_and_line(Z,line_connecting(Y,X)) ), file('/export/starexec/sandbox/benchmark/theBenchmark.p', con)).
% 25.41/8.71 fof(f12_neg, negated_conjecture, ~(! [X,Y,Z] : ( ( distinct_points(X,Y) & distinct_points(X,Z) & distinct_points(Y,Z) & ~ apart_point_and_line(Z,line_connecting(X,Y)) ) => ~ apart_point_and_line(Z,line_connecting(Y,X)) )), inference(negated_conjecture, [status(cth)], [f12])).
% 25.41/8.71 fof(f12_nnf, plain, ? [X,Y,Z] : (((((distinct_points(X,Y) & distinct_points(X,Z)) & distinct_points(Y,Z)) & ~(apart_point_and_line(Z,line_connecting(X,Y)))) & apart_point_and_line(Z,line_connecting(Y,X)))), inference(nnf_transformation, [status(thm)], [f12_neg])).
% 25.41/8.71 fof(f12_sk, plain, ((((distinct_points(sk0,sk1) & distinct_points(sk0,sk2)) & distinct_points(sk1,sk2)) & ~(apart_point_and_line(sk2,line_connecting(sk0,sk1)))) & apart_point_and_line(sk2,line_connecting(sk1,sk0))), inference(skolemisation, [status(esa), new_symbols(skolem, [sk0,sk1,sk2])], [f12_nnf])).
% 25.41/8.71 cnf(c14, plain, distinct_points(sk0,sk1), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 25.41/8.71 cnf(p19, plain, distinct_points(sk0,X0) | distinct_points(sk1,X0), inference(resolution, [status(thm)], [c3, c14])).
% 25.41/8.71 cnf(p22, plain, distinct_points(sk0,X0) | distinct_points(sk1,X1) | distinct_points(X0,X1), inference(resolution, [status(thm)], [p19, c3])).
% 25.41/8.71 cnf(p25, plain, distinct_points(sk0,X0) | distinct_points(X0,sk1), inference(resolution, [status(thm)], [p22, c0])).
% 25.41/8.71 cnf(p29, plain, distinct_points(X0,sk1) | distinct_points(sk0,X1) | distinct_points(X0,X1), inference(resolution, [status(thm)], [p25, c3])).
% 25.41/8.71 cnf(p40, plain, distinct_points(X0,sk1) | distinct_points(X0,sk0), inference(resolution, [status(thm)], [p29, c0])).
% 25.41/8.71 cnf(p43, plain, distinct_points(sk1,sk0), inference(resolution, [status(thm)], [p40, c0])).
% 25.41/8.71 cnf(p97, plain, ~apart_point_and_line(X0,line_connecting(sk1,sk0)) | distinct_points(X0,sk0), inference(resolution, [status(thm)], [c7, p43])).
% 25.41/8.71 cnf(p1104, plain, (distinct_points(sk0,sk0) | ~spl42), inference(resolution, [status(thm)], [p991, p97])).
% 25.41/8.71 cnf(p1107, plain, ($false | ~spl42), inference(resolution, [status(thm)], [p1104, c0])).
% 25.41/8.71 cnf(sct4, plain, (~spl42), inference(avatar_contradiction_clause, [status(thm)], [p1107])).
% 25.41/8.71 fof(sdef44, definition, (spl44 <=> (apart_point_and_line(sk1,line_connecting(sk1,sk0)))), introduced(definition, [new_symbols(naming, [spl44])], [avatar_definition])).
% 25.41/8.71 cnf(p993, plain, (apart_point_and_line(sk1,line_connecting(sk1,sk0)) | ~spl44), inference(avatar_component_clause, [status(thm)], [sdef44])).
% 25.41/8.71 cnf(c6, plain, ~distinct_points(X0,X1) | ~apart_point_and_line(X2,line_connecting(X0,X1)) | distinct_points(X2,X0), inference(cnf_transformation, [status(esa)], [f6_sk])).
% 25.41/8.71 cnf(p70, plain, ~apart_point_and_line(X0,line_connecting(sk1,sk0)) | distinct_points(X0,sk1), inference(resolution, [status(thm)], [c6, p43])).
% 25.41/8.71 cnf(p1108, plain, (distinct_points(sk1,sk1) | ~spl44), inference(resolution, [status(thm)], [p993, p70])).
% 25.41/8.71 cnf(p1111, plain, ($false | ~spl44), inference(resolution, [status(thm)], [p1108, c0])).
% 25.41/8.71 cnf(sct5, plain, (~spl44), inference(avatar_contradiction_clause, [status(thm)], [p1111])).
% 25.41/8.71 fof(sdef46, definition, (spl46 <=> (apart_point_and_line(sk0,line_connecting(sk0,sk1)))), introduced(definition, [new_symbols(naming, [spl46])], [avatar_definition])).
% 25.41/8.71 cnf(p997, plain, (apart_point_and_line(sk0,line_connecting(sk0,sk1)) | ~spl46), inference(avatar_component_clause, [status(thm)], [sdef46])).
% 25.41/8.71 cnf(p45, plain, ~apart_point_and_line(X0,line_connecting(sk0,sk1)) | distinct_points(X0,sk0), inference(resolution, [status(thm)], [c6, c14])).
% 25.41/8.71 cnf(p1119, plain, (distinct_points(sk0,sk0) | ~spl46), inference(resolution, [status(thm)], [p997, p45])).
% 25.41/8.71 cnf(p1122, plain, ($false | ~spl46), inference(resolution, [status(thm)], [p1119, c0])).
% 25.41/8.71 cnf(sct6, plain, (~spl46), inference(avatar_contradiction_clause, [status(thm)], [p1122])).
% 25.41/8.71 fof(sdef47, definition, (spl47 <=> (apart_point_and_line(sk1,line_connecting(sk0,sk1)))), introduced(definition, [new_symbols(naming, [spl47])], [avatar_definition])).
% 25.41/8.71 cnf(p998, plain, (apart_point_and_line(sk1,line_connecting(sk0,sk1)) | ~spl47), inference(avatar_component_clause, [status(thm)], [sdef47])).
% 25.41/8.71 cnf(p72, plain, ~apart_point_and_line(X0,line_connecting(sk0,sk1)) | distinct_points(X0,sk1), inference(resolution, [status(thm)], [c7, c14])).
% 25.41/8.71 cnf(p1123, plain, (distinct_points(sk1,sk1) | ~spl47), inference(resolution, [status(thm)], [p998, p72])).
% 25.41/8.71 cnf(p1126, plain, ($false | ~spl47), inference(resolution, [status(thm)], [p1123, c0])).
% 25.41/8.71 cnf(sct7, plain, (~spl47), inference(avatar_contradiction_clause, [status(thm)], [p1126])).
% 25.41/8.71 fof(f10, axiom, ! [X,Y,Z] : ( apart_point_and_line(X,Y) => ( distinct_lines(Y,Z) | apart_point_and_line(X,Z) ) ), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ceq2)).
% 25.41/8.71 fof(f10_nnf, plain, ! [X,Y,Z] : ((~(apart_point_and_line(X,Y)) | (distinct_lines(Y,Z) | apart_point_and_line(X,Z)))), inference(nnf_transformation, [status(thm)], [f10])).
% 25.41/8.71 fof(f10_sk, plain, ! [X,Y,Z] : ((~(apart_point_and_line(X,Y)) | (distinct_lines(Y,Z) | apart_point_and_line(X,Z)))), inference(skolemisation, [status(esa)], [f10_nnf])).
% 25.41/8.71 cnf(c12, plain, ~apart_point_and_line(X0,X1) | distinct_lines(X1,X2) | apart_point_and_line(X0,X2), inference(cnf_transformation, [status(esa)], [f10_sk])).
% 25.41/8.71 fof(f9, axiom, ! [X,Y,Z] : ( apart_point_and_line(X,Y) => ( distinct_points(X,Z) | apart_point_and_line(Z,Y) ) ), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ceq1)).
% 25.41/8.71 fof(f9_nnf, plain, ! [X,Y,Z] : ((~(apart_point_and_line(X,Y)) | (distinct_points(X,Z) | apart_point_and_line(Z,Y)))), inference(nnf_transformation, [status(thm)], [f9])).
% 25.41/8.71 fof(f9_sk, plain, ! [X,Y,Z] : ((~(apart_point_and_line(X,Y)) | (distinct_points(X,Z) | apart_point_and_line(Z,Y)))), inference(skolemisation, [status(esa)], [f9_nnf])).
% 25.41/8.71 cnf(c11, plain, ~apart_point_and_line(X0,X1) | distinct_points(X0,X2) | apart_point_and_line(X2,X1), inference(cnf_transformation, [status(esa)], [f9_sk])).
% 25.41/8.71 cnf(c18, plain, apart_point_and_line(sk2,line_connecting(sk1,sk0)), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 25.41/8.71 cnf(p174, plain, distinct_points(sk2,X0) | apart_point_and_line(X0,line_connecting(sk1,sk0)), inference(resolution, [status(thm)], [c11, c18])).
% 25.41/8.71 cnf(p201, plain, distinct_lines(line_connecting(sk1,sk0),X0) | apart_point_and_line(X1,X0) | distinct_points(sk2,X1), inference(resolution, [status(thm)], [c12, p174])).
% 25.41/8.71 cnf(c17, plain, ~apart_point_and_line(sk2,line_connecting(sk0,sk1)), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 25.41/8.71 cnf(p462, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(sk0,sk1)) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p201, c17])).
% 25.41/8.71 fof(sdef0, definition, (spl0 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk0,sk1)))), introduced(definition, [new_symbols(naming, [spl0])], [avatar_definition])).
% 25.41/8.71 cnf(ssp0, plain, (spl0 | spl1), inference(avatar_split_clause, [status(thm)], [p462, sdef0, sdef1])).
% 25.41/8.71 cnf(c15, plain, distinct_points(sk0,sk2), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 25.41/8.71 cnf(p73, plain, ~apart_point_and_line(X0,line_connecting(sk0,sk2)) | distinct_points(X0,sk2), inference(resolution, [status(thm)], [c7, c15])).
% 25.41/8.71 cnf(p466, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(sk0,sk2)) | distinct_points(sk2,X0) | distinct_points(X0,sk2), inference(resolution, [status(thm)], [p201, p73])).
% 25.41/8.71 fof(sdef2, definition, (spl2 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk0,sk2)))), introduced(definition, [new_symbols(naming, [spl2])], [avatar_definition])).
% 25.41/8.71 cnf(ssp1, plain, (spl2 | spl3), inference(avatar_split_clause, [status(thm)], [p466, sdef2, sdef3])).
% 25.41/8.71 cnf(c16, plain, distinct_points(sk1,sk2), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 25.41/8.71 cnf(p74, plain, ~apart_point_and_line(X0,line_connecting(sk1,sk2)) | distinct_points(X0,sk2), inference(resolution, [status(thm)], [c7, c16])).
% 25.41/8.71 cnf(p469, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(sk1,sk2)) | distinct_points(sk2,X0) | distinct_points(X0,sk2), inference(resolution, [status(thm)], [p201, p74])).
% 25.41/8.71 fof(sdef4, definition, (spl4 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk1,sk2)))), introduced(definition, [new_symbols(naming, [spl4])], [avatar_definition])).
% 25.41/8.71 cnf(ssp2, plain, (spl3 | spl4), inference(avatar_split_clause, [status(thm)], [p469, sdef3, sdef4])).
% 25.41/8.71 cnf(p71, plain, distinct_points(sk2,sk1), inference(resolution, [status(thm)], [p70, c18])).
% 25.41/8.71 cnf(p98, plain, ~apart_point_and_line(X0,line_connecting(sk2,sk1)) | distinct_points(X0,sk2), inference(resolution, [status(thm)], [p71, c6])).
% 25.41/8.71 cnf(p471, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,sk1)) | distinct_points(sk2,X0) | distinct_points(X0,sk2), inference(resolution, [status(thm)], [p201, p98])).
% 25.41/8.71 fof(sdef5, definition, (spl5 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,sk1)))), introduced(definition, [new_symbols(naming, [spl5])], [avatar_definition])).
% 25.41/8.71 cnf(ssp3, plain, (spl3 | spl5), inference(avatar_split_clause, [status(thm)], [p471, sdef3, sdef5])).
% 25.41/8.71 cnf(p100, plain, distinct_points(sk2,sk0), inference(resolution, [status(thm)], [p97, c18])).
% 25.41/8.71 cnf(p101, plain, ~apart_point_and_line(X0,line_connecting(sk2,sk0)) | distinct_points(X0,sk2), inference(resolution, [status(thm)], [p100, c6])).
% 25.41/8.71 cnf(p473, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,sk0)) | distinct_points(sk2,X0) | distinct_points(X0,sk2), inference(resolution, [status(thm)], [p201, p101])).
% 25.41/8.71 fof(sdef6, definition, (spl6 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,sk0)))), introduced(definition, [new_symbols(naming, [spl6])], [avatar_definition])).
% 25.41/8.71 cnf(ssp4, plain, (spl3 | spl6), inference(avatar_split_clause, [status(thm)], [p473, sdef3, sdef6])).
% 25.41/8.71 cnf(p20, plain, distinct_points(sk0,X0) | distinct_points(sk2,X0), inference(resolution, [status(thm)], [c3, c15])).
% 25.41/8.71 cnf(p49, plain, ~apart_point_and_line(X0,line_connecting(sk2,X1)) | distinct_points(X0,sk2) | distinct_points(sk0,X1), inference(resolution, [status(thm)], [c6, p20])).
% 25.41/8.71 cnf(p476, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(sk2,X1) | distinct_points(X1,sk2) | distinct_points(sk0,X0), inference(resolution, [status(thm)], [p201, p49])).
% 25.41/8.71 fof(sdef7, definition, (spl7 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(sk0,X0))), introduced(definition, [new_symbols(naming, [spl7])], [avatar_definition])).
% 25.41/8.71 cnf(ssp5, plain, (spl3 | spl7), inference(avatar_split_clause, [status(thm)], [p476, sdef3, sdef7])).
% 25.41/8.71 cnf(p21, plain, distinct_points(sk1,X0) | distinct_points(sk2,X0), inference(resolution, [status(thm)], [c3, c16])).
% 25.41/8.71 cnf(p50, plain, ~apart_point_and_line(X0,line_connecting(sk2,X1)) | distinct_points(X0,sk2) | distinct_points(sk1,X1), inference(resolution, [status(thm)], [c6, p21])).
% 25.41/8.71 cnf(p478, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(sk2,X1) | distinct_points(X1,sk2) | distinct_points(sk1,X0), inference(resolution, [status(thm)], [p201, p50])).
% 25.41/8.71 fof(sdef8, definition, (spl8 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(sk1,X0))), introduced(definition, [new_symbols(naming, [spl8])], [avatar_definition])).
% 25.41/8.71 cnf(ssp6, plain, (spl3 | spl8), inference(avatar_split_clause, [status(thm)], [p478, sdef3, sdef8])).
% 25.41/8.71 cnf(p23, plain, distinct_points(sk0,X0) | distinct_points(sk2,X1) | distinct_points(X0,X1), inference(resolution, [status(thm)], [p20, c3])).
% 25.41/8.71 cnf(p30, plain, distinct_points(sk0,X0) | distinct_points(X0,sk2), inference(resolution, [status(thm)], [p23, c0])).
% 25.41/8.71 cnf(p87, plain, ~apart_point_and_line(X0,line_connecting(X1,sk2)) | distinct_points(X0,sk2) | distinct_points(sk0,X1), inference(resolution, [status(thm)], [c7, p30])).
% 25.41/8.71 cnf(p481, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(sk2,X1) | distinct_points(X1,sk2) | distinct_points(sk0,X0), inference(resolution, [status(thm)], [p201, p87])).
% 25.41/8.71 fof(sdef9, definition, (spl9 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(sk0,X0))), introduced(definition, [new_symbols(naming, [spl9])], [avatar_definition])).
% 25.41/8.71 cnf(ssp7, plain, (spl3 | spl9), inference(avatar_split_clause, [status(thm)], [p481, sdef3, sdef9])).
% 25.41/8.71 cnf(p24, plain, distinct_points(sk1,X0) | distinct_points(sk2,X1) | distinct_points(X0,X1), inference(resolution, [status(thm)], [p21, c3])).
% 25.41/8.71 cnf(p35, plain, distinct_points(sk1,X0) | distinct_points(X0,sk2), inference(resolution, [status(thm)], [p24, c0])).
% 25.41/8.71 cnf(p92, plain, ~apart_point_and_line(X0,line_connecting(X1,sk2)) | distinct_points(X0,sk2) | distinct_points(sk1,X1), inference(resolution, [status(thm)], [c7, p35])).
% 25.41/8.71 cnf(p484, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(sk2,X1) | distinct_points(X1,sk2) | distinct_points(sk1,X0), inference(resolution, [status(thm)], [p201, p92])).
% 25.41/8.71 fof(sdef10, definition, (spl10 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(sk1,X0))), introduced(definition, [new_symbols(naming, [spl10])], [avatar_definition])).
% 25.41/8.71 cnf(ssp8, plain, (spl3 | spl10), inference(avatar_split_clause, [status(thm)], [p484, sdef3, sdef10])).
% 25.41/8.71 cnf(p34, plain, distinct_points(X0,sk2) | distinct_points(sk0,X1) | distinct_points(X0,X1), inference(resolution, [status(thm)], [p30, c3])).
% 25.41/8.71 cnf(p103, plain, distinct_points(X0,sk2) | distinct_points(X0,sk0), inference(resolution, [status(thm)], [p34, c0])).
% 25.41/8.71 cnf(p114, plain, distinct_points(X0,sk0) | ~apart_point_and_line(X1,line_connecting(X0,sk2)) | distinct_points(X1,sk2), inference(resolution, [status(thm)], [p103, c7])).
% 25.41/8.71 cnf(p486, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(sk2,X1) | distinct_points(X0,sk0) | distinct_points(X1,sk2), inference(resolution, [status(thm)], [p201, p114])).
% 25.41/8.71 fof(sdef11, definition, (spl11 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(X0,sk0))), introduced(definition, [new_symbols(naming, [spl11])], [avatar_definition])).
% 25.41/8.71 cnf(ssp9, plain, (spl3 | spl11), inference(avatar_split_clause, [status(thm)], [p486, sdef3, sdef11])).
% 25.41/8.71 cnf(p39, plain, distinct_points(X0,sk2) | distinct_points(sk1,X1) | distinct_points(X0,X1), inference(resolution, [status(thm)], [p35, c3])).
% 25.41/8.71 cnf(p141, plain, distinct_points(X0,sk2) | distinct_points(X0,sk1), inference(resolution, [status(thm)], [p39, c0])).
% 25.41/8.71 cnf(p155, plain, distinct_points(X0,sk1) | ~apart_point_and_line(X1,line_connecting(X0,sk2)) | distinct_points(X1,sk2), inference(resolution, [status(thm)], [p141, c7])).
% 25.41/8.71 cnf(p488, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(sk2,X1) | distinct_points(X0,sk1) | distinct_points(X1,sk2), inference(resolution, [status(thm)], [p201, p155])).
% 25.41/8.71 fof(sdef12, definition, (spl12 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(X0,sk1))), introduced(definition, [new_symbols(naming, [spl12])], [avatar_definition])).
% 25.41/8.71 cnf(ssp10, plain, (spl3 | spl12), inference(avatar_split_clause, [status(thm)], [p488, sdef3, sdef12])).
% 25.41/8.71 cnf(p175, plain, distinct_points(sk2,X0) | distinct_points(X0,sk1), inference(resolution, [status(thm)], [p174, p70])).
% 25.41/8.71 cnf(p179, plain, distinct_points(X0,sk1) | ~apart_point_and_line(X1,line_connecting(sk2,X0)) | distinct_points(X1,sk2), inference(resolution, [status(thm)], [p175, c6])).
% 25.41/8.71 cnf(p490, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(sk2,X1) | distinct_points(X0,sk1) | distinct_points(X1,sk2), inference(resolution, [status(thm)], [p201, p179])).
% 25.41/8.71 fof(sdef13, definition, (spl13 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(X0,sk1))), introduced(definition, [new_symbols(naming, [spl13])], [avatar_definition])).
% 25.41/8.71 cnf(ssp11, plain, (spl3 | spl13), inference(avatar_split_clause, [status(thm)], [p490, sdef3, sdef13])).
% 25.41/8.71 cnf(p180, plain, distinct_points(sk2,X0) | ~apart_point_and_line(X1,line_connecting(X0,sk1)) | distinct_points(X1,X0), inference(resolution, [status(thm)], [p175, c6])).
% 25.41/8.71 cnf(p459, plain, distinct_points(sk2,X0) | ~apart_point_and_line(sk2,line_connecting(X0,sk1)), inference(factoring, [status(thm)], [p180])).
% 25.41/8.71 cnf(p493, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk1)) | distinct_points(sk2,sk2) | distinct_points(sk2,X0), inference(resolution, [status(thm)], [p201, p459])).
% 25.41/8.71 fof(sdef14, definition, (spl14 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk1)) | distinct_points(sk2,X0))), introduced(definition, [new_symbols(naming, [spl14])], [avatar_definition])).
% 25.41/8.71 cnf(ssp12, plain, (spl1 | spl14), inference(avatar_split_clause, [status(thm)], [p493, sdef1, sdef14])).
% 25.41/8.71 cnf(p176, plain, distinct_points(sk2,X0) | distinct_points(X0,sk0), inference(resolution, [status(thm)], [p174, p97])).
% 25.41/8.71 cnf(p185, plain, distinct_points(X0,sk0) | ~apart_point_and_line(X1,line_connecting(sk2,X0)) | distinct_points(X1,sk2), inference(resolution, [status(thm)], [p176, c6])).
% 25.41/8.71 cnf(p495, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(sk2,X1) | distinct_points(X0,sk0) | distinct_points(X1,sk2), inference(resolution, [status(thm)], [p201, p185])).
% 25.41/8.71 fof(sdef15, definition, (spl15 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(X0,sk0))), introduced(definition, [new_symbols(naming, [spl15])], [avatar_definition])).
% 25.41/8.71 cnf(ssp13, plain, (spl3 | spl15), inference(avatar_split_clause, [status(thm)], [p495, sdef3, sdef15])).
% 25.41/8.71 cnf(p186, plain, distinct_points(sk2,X0) | ~apart_point_and_line(X1,line_connecting(X0,sk0)) | distinct_points(X1,X0), inference(resolution, [status(thm)], [p176, c6])).
% 25.41/8.71 cnf(p460, plain, distinct_points(sk2,X0) | ~apart_point_and_line(sk2,line_connecting(X0,sk0)), inference(factoring, [status(thm)], [p186])).
% 25.41/8.71 cnf(p498, plain, distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk0)) | distinct_points(sk2,sk2) | distinct_points(sk2,X0), inference(resolution, [status(thm)], [p201, p460])).
% 25.41/8.71 fof(sdef16, definition, (spl16 <=> (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk0)) | distinct_points(sk2,X0))), introduced(definition, [new_symbols(naming, [spl16])], [avatar_definition])).
% 25.41/8.71 cnf(ssp14, plain, (spl1 | spl16), inference(avatar_split_clause, [status(thm)], [p498, sdef1, sdef16])).
% 25.41/8.71 cnf(p57, plain, ~apart_point_and_line(X0,line_connecting(sk2,X1)) | distinct_points(X0,sk2) | distinct_points(sk0,X2) | distinct_points(X2,X1), inference(resolution, [status(thm)], [c6, p23])).
% 25.41/8.71 cnf(p514, plain, distinct_points(X0,sk2) | distinct_points(sk0,X1) | distinct_points(X1,X2) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X2)) | distinct_points(sk2,X0), inference(resolution, [status(thm)], [p57, p201])).
% 25.41/8.71 fof(sdef17, definition, (spl17 <=> (distinct_points(sk0,X0) | distinct_points(X0,X1) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X1)))), introduced(definition, [new_symbols(naming, [spl17])], [avatar_definition])).
% 25.41/8.71 cnf(ssp15, plain, (spl3 | spl17), inference(avatar_split_clause, [status(thm)], [p514, sdef3, sdef17])).
% 25.41/8.71 cnf(p62, plain, ~apart_point_and_line(X0,line_connecting(sk2,X1)) | distinct_points(X0,sk2) | distinct_points(sk1,X2) | distinct_points(X2,X1), inference(resolution, [status(thm)], [c6, p24])).
% 25.41/8.71 cnf(p529, plain, distinct_points(X0,sk2) | distinct_points(sk1,X1) | distinct_points(X1,X2) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X2)) | distinct_points(sk2,X0), inference(resolution, [status(thm)], [p62, p201])).
% 25.41/8.71 fof(sdef18, definition, (spl18 <=> (distinct_points(sk1,X0) | distinct_points(X0,X1) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X1)))), introduced(definition, [new_symbols(naming, [spl18])], [avatar_definition])).
% 25.41/8.71 cnf(ssp16, plain, (spl3 | spl18), inference(avatar_split_clause, [status(thm)], [p529, sdef3, sdef18])).
% 25.41/8.71 cnf(p200, plain, distinct_lines(line_connecting(sk1,sk0),X0) | apart_point_and_line(sk2,X0), inference(resolution, [status(thm)], [c12, c18])).
% 25.41/8.71 fof(f4, axiom, ! [X,Y,Z] : ( distinct_lines(X,Y) => ( distinct_lines(X,Z) | distinct_lines(Y,Z) ) ), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apart5)).
% 25.41/8.71 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])).
% 25.41/8.71 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])).
% 25.41/8.71 cnf(c4, plain, ~distinct_lines(X0,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(cnf_transformation, [status(esa)], [f4_sk])).
% 25.41/8.71 cnf(p202, plain, apart_point_and_line(sk2,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p200, c4])).
% 25.41/8.71 cnf(p543, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk0,sk2),X0) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p202, p73])).
% 25.41/8.71 fof(sdef19, definition, (spl19 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk0,sk2),X0))), introduced(definition, [new_symbols(naming, [spl19])], [avatar_definition])).
% 25.41/8.71 cnf(ssp17, plain, (spl1 | spl19), inference(avatar_split_clause, [status(thm)], [p543, sdef1, sdef19])).
% 25.41/8.71 cnf(p545, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk1,sk2),X0) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p202, p74])).
% 25.41/8.71 fof(sdef20, definition, (spl20 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk1,sk2),X0))), introduced(definition, [new_symbols(naming, [spl20])], [avatar_definition])).
% 25.41/8.71 cnf(ssp18, plain, (spl1 | spl20), inference(avatar_split_clause, [status(thm)], [p545, sdef1, sdef20])).
% 25.41/8.71 cnf(p547, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk1),X0) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p202, p98])).
% 25.41/8.71 fof(sdef21, definition, (spl21 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk1),X0))), introduced(definition, [new_symbols(naming, [spl21])], [avatar_definition])).
% 25.41/8.71 cnf(ssp19, plain, (spl1 | spl21), inference(avatar_split_clause, [status(thm)], [p547, sdef1, sdef21])).
% 25.41/8.71 cnf(p549, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk0),X0) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p202, p101])).
% 25.41/8.71 fof(sdef22, definition, (spl22 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk0),X0))), introduced(definition, [new_symbols(naming, [spl22])], [avatar_definition])).
% 25.41/8.71 cnf(ssp20, plain, (spl1 | spl22), inference(avatar_split_clause, [status(thm)], [p549, sdef1, sdef22])).
% 25.41/8.71 cnf(p552, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(sk2,sk2) | distinct_points(sk0,X1), inference(resolution, [status(thm)], [p202, p49])).
% 25.41/8.71 fof(sdef23, definition, (spl23 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(sk0,X1))), introduced(definition, [new_symbols(naming, [spl23])], [avatar_definition])).
% 25.41/8.71 cnf(ssp21, plain, (spl1 | spl23), inference(avatar_split_clause, [status(thm)], [p552, sdef1, sdef23])).
% 25.41/8.71 cnf(p554, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(sk2,sk2) | distinct_points(sk1,X1), inference(resolution, [status(thm)], [p202, p50])).
% 25.41/8.71 fof(sdef24, definition, (spl24 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(sk1,X1))), introduced(definition, [new_symbols(naming, [spl24])], [avatar_definition])).
% 25.41/8.71 cnf(ssp22, plain, (spl1 | spl24), inference(avatar_split_clause, [status(thm)], [p554, sdef1, sdef24])).
% 25.41/8.71 cnf(p557, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(X1,sk2),X0) | distinct_points(sk2,sk2) | distinct_points(sk0,X1), inference(resolution, [status(thm)], [p202, p87])).
% 25.41/8.71 fof(sdef25, definition, (spl25 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(X1,sk2),X0) | distinct_points(sk0,X1))), introduced(definition, [new_symbols(naming, [spl25])], [avatar_definition])).
% 25.41/8.71 cnf(ssp23, plain, (spl1 | spl25), inference(avatar_split_clause, [status(thm)], [p557, sdef1, sdef25])).
% 25.41/8.71 cnf(p560, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(X1,sk2),X0) | distinct_points(sk2,sk2) | distinct_points(sk1,X1), inference(resolution, [status(thm)], [p202, p92])).
% 25.41/8.71 fof(sdef26, definition, (spl26 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(X1,sk2),X0) | distinct_points(sk1,X1))), introduced(definition, [new_symbols(naming, [spl26])], [avatar_definition])).
% 25.41/8.71 cnf(ssp24, plain, (spl1 | spl26), inference(avatar_split_clause, [status(thm)], [p560, sdef1, sdef26])).
% 25.41/8.71 cnf(p562, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(X1,sk2),X0) | distinct_points(X1,sk0) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p202, p114])).
% 25.41/8.71 fof(sdef27, definition, (spl27 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(X1,sk2),X0) | distinct_points(X1,sk0))), introduced(definition, [new_symbols(naming, [spl27])], [avatar_definition])).
% 25.41/8.71 cnf(ssp25, plain, (spl1 | spl27), inference(avatar_split_clause, [status(thm)], [p562, sdef1, sdef27])).
% 25.41/8.71 cnf(p564, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(X1,sk2),X0) | distinct_points(X1,sk1) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p202, p155])).
% 25.41/8.71 fof(sdef28, definition, (spl28 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(X1,sk2),X0) | distinct_points(X1,sk1))), introduced(definition, [new_symbols(naming, [spl28])], [avatar_definition])).
% 25.41/8.71 cnf(ssp26, plain, (spl1 | spl28), inference(avatar_split_clause, [status(thm)], [p564, sdef1, sdef28])).
% 25.41/8.71 cnf(p566, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(X1,sk1) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p202, p179])).
% 25.41/8.71 fof(sdef29, definition, (spl29 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(X1,sk1))), introduced(definition, [new_symbols(naming, [spl29])], [avatar_definition])).
% 25.41/8.71 cnf(ssp27, plain, (spl1 | spl29), inference(avatar_split_clause, [status(thm)], [p566, sdef1, sdef29])).
% 25.41/8.71 cnf(p570, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(X1,sk0) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p202, p185])).
% 25.41/8.71 fof(sdef30, definition, (spl30 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(X1,sk0))), introduced(definition, [new_symbols(naming, [spl30])], [avatar_definition])).
% 25.41/8.71 cnf(ssp28, plain, (spl1 | spl30), inference(avatar_split_clause, [status(thm)], [p570, sdef1, sdef30])).
% 25.41/8.71 cnf(p574, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(sk2,sk2) | distinct_points(sk0,X2) | distinct_points(X2,X1), inference(resolution, [status(thm)], [p202, p57])).
% 25.41/8.71 fof(sdef31, definition, (spl31 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(sk0,X2) | distinct_points(X2,X1))), introduced(definition, [new_symbols(naming, [spl31])], [avatar_definition])).
% 25.41/8.71 cnf(ssp29, plain, (spl1 | spl31), inference(avatar_split_clause, [status(thm)], [p574, sdef1, sdef31])).
% 25.41/8.71 cnf(p576, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(sk2,sk2) | distinct_points(sk1,X2) | distinct_points(X2,X1), inference(resolution, [status(thm)], [p202, p62])).
% 25.41/8.71 fof(sdef32, definition, (spl32 <=> (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(sk1,X2) | distinct_points(X2,X1))), introduced(definition, [new_symbols(naming, [spl32])], [avatar_definition])).
% 25.41/8.71 cnf(ssp30, plain, (spl1 | spl32), inference(avatar_split_clause, [status(thm)], [p576, sdef1, sdef32])).
% 25.41/8.71 cnf(p83, plain, ~apart_point_and_line(X0,line_connecting(sk0,X1)) | distinct_points(X0,X1) | distinct_points(sk2,X2) | distinct_points(X1,X2), inference(resolution, [status(thm)], [c7, p23])).
% 25.41/8.71 cnf(p662, plain, ~apart_point_and_line(sk2,line_connecting(sk0,X0)) | distinct_points(sk2,X0) | distinct_points(X0,X0), inference(factoring, [status(thm)], [p83])).
% 25.41/8.71 cnf(p666, plain, distinct_points(sk2,X0) | distinct_points(X0,X0) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk0,X0)) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p662, p201])).
% 25.41/8.71 fof(sdef33, definition, (spl33 <=> (distinct_points(sk2,X0) | distinct_points(X0,X0) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk0,X0)))), introduced(definition, [new_symbols(naming, [spl33])], [avatar_definition])).
% 25.41/8.71 cnf(ssp31, plain, (spl1 | spl33), inference(avatar_split_clause, [status(thm)], [p666, sdef1, sdef33])).
% 25.41/8.71 cnf(p85, plain, ~apart_point_and_line(X0,line_connecting(X1,X2)) | distinct_points(X0,X2) | distinct_points(sk0,X1) | distinct_points(sk2,X2), inference(resolution, [status(thm)], [c7, p23])).
% 25.41/8.71 cnf(p724, plain, ~apart_point_and_line(sk2,line_connecting(X0,X1)) | distinct_points(sk2,X1) | distinct_points(sk0,X0), inference(factoring, [status(thm)], [p85])).
% 25.41/8.71 cnf(p727, plain, distinct_points(sk2,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk1,sk0),line_connecting(X1,X0)) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p724, p201])).
% 25.41/8.71 fof(sdef34, definition, (spl34 <=> (distinct_points(sk2,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk1,sk0),line_connecting(X1,X0)))), introduced(definition, [new_symbols(naming, [spl34])], [avatar_definition])).
% 25.41/8.71 cnf(ssp32, plain, (spl1 | spl34), inference(avatar_split_clause, [status(thm)], [p727, sdef1, sdef34])).
% 25.41/8.71 cnf(p88, plain, ~apart_point_and_line(X0,line_connecting(sk1,X1)) | distinct_points(X0,X1) | distinct_points(sk2,X2) | distinct_points(X1,X2), inference(resolution, [status(thm)], [c7, p24])).
% 25.41/8.71 cnf(p762, plain, ~apart_point_and_line(sk2,line_connecting(sk1,X0)) | distinct_points(sk2,X0) | distinct_points(X0,X0), inference(factoring, [status(thm)], [p88])).
% 25.41/8.71 cnf(p766, plain, distinct_points(sk2,X0) | distinct_points(X0,X0) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk1,X0)) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p762, p201])).
% 25.41/8.71 fof(sdef35, definition, (spl35 <=> (distinct_points(sk2,X0) | distinct_points(X0,X0) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk1,X0)))), introduced(definition, [new_symbols(naming, [spl35])], [avatar_definition])).
% 25.41/8.71 cnf(ssp33, plain, (spl1 | spl35), inference(avatar_split_clause, [status(thm)], [p766, sdef1, sdef35])).
% 25.41/8.71 cnf(p90, plain, ~apart_point_and_line(X0,line_connecting(X1,X2)) | distinct_points(X0,X2) | distinct_points(sk1,X1) | distinct_points(sk2,X2), inference(resolution, [status(thm)], [c7, p24])).
% 25.41/8.71 cnf(p819, plain, ~apart_point_and_line(sk2,line_connecting(X0,X1)) | distinct_points(sk2,X1) | distinct_points(sk1,X0), inference(factoring, [status(thm)], [p90])).
% 25.41/8.71 cnf(p822, plain, distinct_points(sk2,X0) | distinct_points(sk1,X1) | distinct_lines(line_connecting(sk1,sk0),line_connecting(X1,X0)) | distinct_points(sk2,sk2), inference(resolution, [status(thm)], [p819, p201])).
% 25.41/8.71 fof(sdef36, definition, (spl36 <=> (distinct_points(sk2,X0) | distinct_points(sk1,X1) | distinct_lines(line_connecting(sk1,sk0),line_connecting(X1,X0)))), introduced(definition, [new_symbols(naming, [spl36])], [avatar_definition])).
% 25.41/8.71 cnf(ssp34, plain, (spl1 | spl36), inference(avatar_split_clause, [status(thm)], [p822, sdef1, sdef36])).
% 25.41/8.71 cnf(p515, plain, (distinct_points(sk0,X0) | distinct_points(X0,X1) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X1)) | ~spl17), inference(avatar_component_clause, [status(thm)], [sdef17])).
% 25.41/8.71 cnf(p910, plain, (distinct_points(sk0,sk0) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,sk0)) | ~spl17), inference(factoring, [status(thm)], [p515])).
% 25.41/8.71 cnf(ssp35, plain, (~spl17 | spl6 | spl37), inference(avatar_split_clause, [status(thm)], [p910, sdef6, sdef37])).
% 25.41/8.71 cnf(p530, plain, (distinct_points(sk1,X0) | distinct_points(X0,X1) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X1)) | ~spl18), inference(avatar_component_clause, [status(thm)], [sdef18])).
% 25.41/8.71 cnf(p943, plain, (distinct_points(sk1,sk1) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,sk1)) | ~spl18), inference(factoring, [status(thm)], [p530])).
% 25.41/8.71 cnf(ssp36, plain, (~spl18 | spl5 | spl38), inference(avatar_split_clause, [status(thm)], [p943, sdef5, sdef38])).
% 25.41/8.71 cnf(p109, plain, distinct_points(sk0,X0) | distinct_points(X1,X0) | ~apart_point_and_line(X2,line_connecting(X1,sk2)) | distinct_points(X2,sk2), inference(resolution, [status(thm)], [p34, c7])).
% 25.41/8.71 cnf(p957, plain, distinct_points(sk0,X0) | distinct_points(X1,X0) | distinct_points(X2,sk2) | distinct_lines(line_connecting(sk1,sk0),line_connecting(X1,sk2)) | distinct_points(sk2,X2), inference(resolution, [status(thm)], [p109, p201])).
% 25.41/8.71 fof(sdef39, definition, (spl39 <=> (distinct_points(sk0,X0) | distinct_points(X1,X0) | distinct_lines(line_connecting(sk1,sk0),line_connecting(X1,sk2)))), introduced(definition, [new_symbols(naming, [spl39])], [avatar_definition])).
% 25.41/8.71 cnf(ssp37, plain, (spl3 | spl39), inference(avatar_split_clause, [status(thm)], [p957, sdef3, sdef39])).
% 25.41/8.71 cnf(p959, plain, distinct_points(sk0,X0) | distinct_points(X1,X0) | distinct_points(sk2,sk2) | distinct_lines(line_connecting(sk1,sk0),X2) | distinct_lines(line_connecting(X1,sk2),X2), inference(resolution, [status(thm)], [p109, p202])).
% 25.41/8.71 fof(sdef40, definition, (spl40 <=> (distinct_points(sk0,X0) | distinct_points(X1,X0) | distinct_lines(line_connecting(sk1,sk0),X2) | distinct_lines(line_connecting(X1,sk2),X2))), introduced(definition, [new_symbols(naming, [spl40])], [avatar_definition])).
% 25.41/8.71 cnf(ssp38, plain, (spl1 | spl40), inference(avatar_split_clause, [status(thm)], [p959, sdef1, sdef40])).
% 25.41/8.71 cnf(p110, plain, distinct_points(X0,sk2) | distinct_points(X0,X1) | ~apart_point_and_line(X2,line_connecting(sk0,X1)) | distinct_points(X2,X1), inference(resolution, [status(thm)], [p34, c7])).
% 25.41/8.71 cnf(p971, plain, distinct_points(X0,sk2) | distinct_points(X0,X1) | ~apart_point_and_line(X0,line_connecting(sk0,X1)), inference(factoring, [status(thm)], [p110])).
% 25.41/8.71 cnf(p975, plain, distinct_points(sk2,sk2) | distinct_points(sk2,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(line_connecting(sk0,X0),X1), inference(resolution, [status(thm)], [p971, p202])).
% 25.41/8.71 fof(sdef41, definition, (spl41 <=> (distinct_points(sk2,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(line_connecting(sk0,X0),X1))), introduced(definition, [new_symbols(naming, [spl41])], [avatar_definition])).
% 25.41/8.71 cnf(ssp39, plain, (spl1 | spl41), inference(avatar_split_clause, [status(thm)], [p975, sdef1, sdef41])).
% 25.41/8.71 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/sandbox/benchmark/theBenchmark.p', cu1)).
% 25.41/8.71 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])).
% 25.41/8.71 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])).
% 25.41/8.71 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])).
% 25.41/8.71 cnf(p115, plain, ~distinct_lines(X0,X1) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,X1), inference(resolution, [status(thm)], [c10, c14])).
% 25.41/8.71 cnf(p990, plain, apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk2,X0), inference(resolution, [status(thm)], [p115, p200])).
% 25.41/8.71 fof(sdef43, definition, (spl43 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk2,X0))), introduced(definition, [new_symbols(naming, [spl43])], [avatar_definition])).
% 25.41/8.71 cnf(ssp40, plain, (spl42 | spl43 | spl44), inference(avatar_split_clause, [status(thm)], [p990, sdef42, sdef43, sdef44])).
% 25.41/8.71 cnf(p994, plain, apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | apart_point_and_line(X1,X0) | distinct_points(sk2,X1), inference(resolution, [status(thm)], [p115, p201])).
% 25.41/8.71 fof(sdef45, definition, (spl45 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | apart_point_and_line(X1,X0) | distinct_points(sk2,X1))), introduced(definition, [new_symbols(naming, [spl45])], [avatar_definition])).
% 25.41/8.71 cnf(ssp41, plain, (spl42 | spl44 | spl45), inference(avatar_split_clause, [status(thm)], [p994, sdef42, sdef44, sdef45])).
% 25.41/8.71 cnf(p463, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk0,sk1)) | ~spl0), inference(avatar_component_clause, [status(thm)], [sdef0])).
% 25.41/8.71 cnf(p996, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk0,sk1)) | ~spl0), inference(resolution, [status(thm)], [p115, p463])).
% 25.41/8.71 cnf(ssp42, plain, (~spl0 | spl42 | spl44 | spl46 | spl47), inference(avatar_split_clause, [status(thm)], [p996, sdef42, sdef44, sdef46, sdef47])).
% 25.41/8.71 cnf(p467, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk0,sk2)) | ~spl2), inference(avatar_component_clause, [status(thm)], [sdef2])).
% 25.41/8.71 cnf(p999, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk0,sk2)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk0,sk2)) | ~spl2), inference(resolution, [status(thm)], [p115, p467])).
% 25.41/8.71 fof(sdef48, definition, (spl48 <=> (apart_point_and_line(sk0,line_connecting(sk0,sk2)))), introduced(definition, [new_symbols(naming, [spl48])], [avatar_definition])).
% 25.41/8.71 fof(sdef49, definition, (spl49 <=> (apart_point_and_line(sk1,line_connecting(sk0,sk2)))), introduced(definition, [new_symbols(naming, [spl49])], [avatar_definition])).
% 25.41/8.71 cnf(ssp43, plain, (~spl2 | spl42 | spl44 | spl48 | spl49), inference(avatar_split_clause, [status(thm)], [p999, sdef42, sdef44, sdef48, sdef49])).
% 25.41/8.71 cnf(p470, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk1,sk2)) | ~spl4), inference(avatar_component_clause, [status(thm)], [sdef4])).
% 25.41/8.71 cnf(p1002, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk1,sk2)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk1,sk2)) | ~spl4), inference(resolution, [status(thm)], [p115, p470])).
% 25.41/8.71 fof(sdef50, definition, (spl50 <=> (apart_point_and_line(sk0,line_connecting(sk1,sk2)))), introduced(definition, [new_symbols(naming, [spl50])], [avatar_definition])).
% 25.41/8.71 fof(sdef51, definition, (spl51 <=> (apart_point_and_line(sk1,line_connecting(sk1,sk2)))), introduced(definition, [new_symbols(naming, [spl51])], [avatar_definition])).
% 25.41/8.71 cnf(ssp44, plain, (~spl4 | spl42 | spl44 | spl50 | spl51), inference(avatar_split_clause, [status(thm)], [p1002, sdef42, sdef44, sdef50, sdef51])).
% 25.41/8.71 cnf(p472, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,sk1)) | ~spl5), inference(avatar_component_clause, [status(thm)], [sdef5])).
% 25.41/8.71 cnf(p1005, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,sk1)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,sk1)) | ~spl5), inference(resolution, [status(thm)], [p115, p472])).
% 25.41/8.71 fof(sdef52, definition, (spl52 <=> (apart_point_and_line(sk0,line_connecting(sk2,sk1)))), introduced(definition, [new_symbols(naming, [spl52])], [avatar_definition])).
% 25.41/8.71 fof(sdef53, definition, (spl53 <=> (apart_point_and_line(sk1,line_connecting(sk2,sk1)))), introduced(definition, [new_symbols(naming, [spl53])], [avatar_definition])).
% 25.41/8.71 cnf(ssp45, plain, (~spl5 | spl42 | spl44 | spl52 | spl53), inference(avatar_split_clause, [status(thm)], [p1005, sdef42, sdef44, sdef52, sdef53])).
% 25.41/8.71 cnf(p474, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,sk0)) | ~spl6), inference(avatar_component_clause, [status(thm)], [sdef6])).
% 25.41/8.71 cnf(p1008, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,sk0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,sk0)) | ~spl6), inference(resolution, [status(thm)], [p115, p474])).
% 25.41/8.71 fof(sdef54, definition, (spl54 <=> (apart_point_and_line(sk0,line_connecting(sk2,sk0)))), introduced(definition, [new_symbols(naming, [spl54])], [avatar_definition])).
% 25.41/8.71 fof(sdef55, definition, (spl55 <=> (apart_point_and_line(sk1,line_connecting(sk2,sk0)))), introduced(definition, [new_symbols(naming, [spl55])], [avatar_definition])).
% 25.41/8.71 cnf(ssp46, plain, (~spl6 | spl42 | spl44 | spl54 | spl55), inference(avatar_split_clause, [status(thm)], [p1008, sdef42, sdef44, sdef54, sdef55])).
% 25.41/8.71 cnf(p477, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(sk0,X0) | ~spl7), inference(avatar_component_clause, [status(thm)], [sdef7])).
% 25.41/8.71 cnf(p1011, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(sk0,X0) | ~spl7), inference(resolution, [status(thm)], [p115, p477])).
% 25.41/8.71 fof(sdef56, definition, (spl56 <=> (apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(sk0,X0))), introduced(definition, [new_symbols(naming, [spl56])], [avatar_definition])).
% 25.41/8.71 cnf(ssp47, plain, (~spl7 | spl42 | spl44 | spl56), inference(avatar_split_clause, [status(thm)], [p1011, sdef42, sdef44, sdef56])).
% 25.41/8.71 cnf(p479, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(sk1,X0) | ~spl8), inference(avatar_component_clause, [status(thm)], [sdef8])).
% 25.41/8.71 cnf(p1013, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(sk1,X0) | ~spl8), inference(resolution, [status(thm)], [p115, p479])).
% 25.41/8.71 fof(sdef57, definition, (spl57 <=> (apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(sk1,X0))), introduced(definition, [new_symbols(naming, [spl57])], [avatar_definition])).
% 25.41/8.71 cnf(ssp48, plain, (~spl8 | spl42 | spl44 | spl57), inference(avatar_split_clause, [status(thm)], [p1013, sdef42, sdef44, sdef57])).
% 25.41/8.71 cnf(p482, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(sk0,X0) | ~spl9), inference(avatar_component_clause, [status(thm)], [sdef9])).
% 25.41/8.71 cnf(p1015, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | distinct_points(sk0,X0) | ~spl9), inference(resolution, [status(thm)], [p115, p482])).
% 25.41/8.71 fof(sdef58, definition, (spl58 <=> (apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | distinct_points(sk0,X0))), introduced(definition, [new_symbols(naming, [spl58])], [avatar_definition])).
% 25.41/8.71 cnf(ssp49, plain, (~spl9 | spl42 | spl44 | spl58), inference(avatar_split_clause, [status(thm)], [p1015, sdef42, sdef44, sdef58])).
% 25.41/8.71 cnf(p485, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(sk1,X0) | ~spl10), inference(avatar_component_clause, [status(thm)], [sdef10])).
% 25.41/8.71 cnf(p1017, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | distinct_points(sk1,X0) | ~spl10), inference(resolution, [status(thm)], [p115, p485])).
% 25.41/8.71 fof(sdef59, definition, (spl59 <=> (apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | distinct_points(sk1,X0))), introduced(definition, [new_symbols(naming, [spl59])], [avatar_definition])).
% 25.41/8.71 cnf(ssp50, plain, (~spl10 | spl42 | spl44 | spl59), inference(avatar_split_clause, [status(thm)], [p1017, sdef42, sdef44, sdef59])).
% 25.41/8.71 cnf(p487, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(X0,sk0) | ~spl11), inference(avatar_component_clause, [status(thm)], [sdef11])).
% 25.41/8.71 cnf(p1019, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | distinct_points(X0,sk0) | ~spl11), inference(resolution, [status(thm)], [p115, p487])).
% 25.41/8.71 fof(sdef60, definition, (spl60 <=> (apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | distinct_points(X0,sk0))), introduced(definition, [new_symbols(naming, [spl60])], [avatar_definition])).
% 25.41/8.71 cnf(ssp51, plain, (~spl11 | spl42 | spl44 | spl60), inference(avatar_split_clause, [status(thm)], [p1019, sdef42, sdef44, sdef60])).
% 25.41/8.71 cnf(p489, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk2)) | distinct_points(X0,sk1) | ~spl12), inference(avatar_component_clause, [status(thm)], [sdef12])).
% 25.41/8.71 cnf(p1021, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | distinct_points(X0,sk1) | ~spl12), inference(resolution, [status(thm)], [p115, p489])).
% 25.41/8.71 fof(sdef61, definition, (spl61 <=> (apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | distinct_points(X0,sk1))), introduced(definition, [new_symbols(naming, [spl61])], [avatar_definition])).
% 25.41/8.71 cnf(ssp52, plain, (~spl12 | spl42 | spl44 | spl61), inference(avatar_split_clause, [status(thm)], [p1021, sdef42, sdef44, sdef61])).
% 25.41/8.71 cnf(p491, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(X0,sk1) | ~spl13), inference(avatar_component_clause, [status(thm)], [sdef13])).
% 25.41/8.71 cnf(p1023, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(X0,sk1) | ~spl13), inference(resolution, [status(thm)], [p115, p491])).
% 25.41/8.71 fof(sdef62, definition, (spl62 <=> (apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(X0,sk1))), introduced(definition, [new_symbols(naming, [spl62])], [avatar_definition])).
% 25.41/8.71 cnf(ssp53, plain, (~spl13 | spl42 | spl44 | spl62), inference(avatar_split_clause, [status(thm)], [p1023, sdef42, sdef44, sdef62])).
% 25.41/8.71 cnf(p494, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk1)) | distinct_points(sk2,X0) | ~spl14), inference(avatar_component_clause, [status(thm)], [sdef14])).
% 25.41/8.71 cnf(p1025, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(X0,sk1)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(X0,sk1)) | distinct_points(sk2,X0) | ~spl14), inference(resolution, [status(thm)], [p115, p494])).
% 25.41/8.71 fof(sdef63, definition, (spl63 <=> (apart_point_and_line(sk0,line_connecting(X0,sk1)) | apart_point_and_line(sk1,line_connecting(X0,sk1)) | distinct_points(sk2,X0))), introduced(definition, [new_symbols(naming, [spl63])], [avatar_definition])).
% 25.41/8.71 cnf(ssp54, plain, (~spl14 | spl42 | spl44 | spl63), inference(avatar_split_clause, [status(thm)], [p1025, sdef42, sdef44, sdef63])).
% 25.41/8.71 cnf(p496, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(X0,sk0) | ~spl15), inference(avatar_component_clause, [status(thm)], [sdef15])).
% 25.41/8.71 cnf(p1027, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(X0,sk0) | ~spl15), inference(resolution, [status(thm)], [p115, p496])).
% 25.41/8.71 fof(sdef64, definition, (spl64 <=> (apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(X0,sk0))), introduced(definition, [new_symbols(naming, [spl64])], [avatar_definition])).
% 25.41/8.71 cnf(ssp55, plain, (~spl15 | spl42 | spl44 | spl64), inference(avatar_split_clause, [status(thm)], [p1027, sdef42, sdef44, sdef64])).
% 25.41/8.71 cnf(p499, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(X0,sk0)) | distinct_points(sk2,X0) | ~spl16), inference(avatar_component_clause, [status(thm)], [sdef16])).
% 25.41/8.71 cnf(p1029, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(X0,sk0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(X0,sk0)) | distinct_points(sk2,X0) | ~spl16), inference(resolution, [status(thm)], [p115, p499])).
% 25.41/8.71 fof(sdef65, definition, (spl65 <=> (apart_point_and_line(sk0,line_connecting(X0,sk0)) | apart_point_and_line(sk1,line_connecting(X0,sk0)) | distinct_points(sk2,X0))), introduced(definition, [new_symbols(naming, [spl65])], [avatar_definition])).
% 25.41/8.71 cnf(ssp56, plain, (~spl16 | spl42 | spl44 | spl65), inference(avatar_split_clause, [status(thm)], [p1029, sdef42, sdef44, sdef65])).
% 25.41/8.71 cnf(p502, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk0,sk2),X0) | ~spl2), inference(resolution, [status(thm)], [p467, c4])).
% 25.41/8.71 cnf(p1031, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk0,sk2),X0) | ~spl2), inference(resolution, [status(thm)], [p115, p502])).
% 25.41/8.71 fof(sdef66, definition, (spl66 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk0,sk2),X0))), introduced(definition, [new_symbols(naming, [spl66])], [avatar_definition])).
% 25.41/8.71 cnf(ssp57, plain, (~spl2 | spl42 | spl44 | spl66), inference(avatar_split_clause, [status(thm)], [p1031, sdef42, sdef44, sdef66])).
% 25.41/8.71 cnf(p513, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk1,sk2),X0) | ~spl4), inference(resolution, [status(thm)], [p470, c4])).
% 25.41/8.71 cnf(p1033, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk2)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk2)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X0) | ~spl4), inference(resolution, [status(thm)], [p115, p513])).
% 25.41/8.71 fof(sdef67, definition, (spl67 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X0))), introduced(definition, [new_symbols(naming, [spl67])], [avatar_definition])).
% 25.41/8.71 cnf(ssp58, plain, (~spl4 | spl50 | spl51 | spl67), inference(avatar_split_clause, [status(thm)], [p1033, sdef50, sdef51, sdef67])).
% 25.41/8.71 cnf(p516, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk1),X0) | ~spl5), inference(resolution, [status(thm)], [p472, c4])).
% 25.41/8.71 cnf(p1035, plain, (apart_point_and_line(sk0,line_connecting(sk2,sk1)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk2,sk1)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X0) | ~spl5), inference(resolution, [status(thm)], [p115, p516])).
% 25.41/8.71 cnf(ssp59, plain, (~spl5 | spl52 | spl53 | spl67), inference(avatar_split_clause, [status(thm)], [p1035, sdef52, sdef53, sdef67])).
% 25.41/8.71 cnf(p517, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk0),X0) | ~spl6), inference(resolution, [status(thm)], [p474, c4])).
% 25.41/8.71 cnf(p1036, plain, (apart_point_and_line(sk0,line_connecting(sk2,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk2,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X0) | ~spl6), inference(resolution, [status(thm)], [p115, p517])).
% 25.41/8.71 cnf(ssp60, plain, (~spl6 | spl54 | spl55 | spl67), inference(avatar_split_clause, [status(thm)], [p1036, sdef54, sdef55, sdef67])).
% 25.41/8.71 cnf(p1037, plain, apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk2,X1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p115, p202])).
% 25.41/8.71 fof(sdef68, definition, (spl68 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk2,X1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl68])], [avatar_definition])).
% 25.41/8.71 cnf(ssp61, plain, (spl42 | spl44 | spl68), inference(avatar_split_clause, [status(thm)], [p1037, sdef42, sdef44, sdef68])).
% 25.41/8.71 cnf(p1039, plain, apart_point_and_line(sk0,X0) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,X1) | apart_point_and_line(sk2,X0) | distinct_lines(line_connecting(sk1,sk0),X1), inference(resolution, [status(thm)], [p115, p202])).
% 25.41/8.71 cnf(ssp62, plain, (spl43 | spl67), inference(avatar_split_clause, [status(thm)], [p1039, sdef43, sdef67])).
% 25.41/8.71 cnf(p539, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk0,sk1),X0), inference(resolution, [status(thm)], [p202, c17])).
% 25.41/8.71 cnf(p1040, plain, apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk0,sk1),X0), inference(resolution, [status(thm)], [p115, p539])).
% 25.41/8.71 fof(sdef69, definition, (spl69 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk0,sk1),X0))), introduced(definition, [new_symbols(naming, [spl69])], [avatar_definition])).
% 25.41/8.71 cnf(ssp63, plain, (spl42 | spl44 | spl69), inference(avatar_split_clause, [status(thm)], [p1040, sdef42, sdef44, sdef69])).
% 25.41/8.71 fof(f1, axiom, ! [X] : ~ distinct_lines(X,X), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apart2)).
% 25.41/8.71 fof(f1_nnf, plain, ! [X] : (~(distinct_lines(X,X))), inference(nnf_transformation, [status(thm)], [f1])).
% 25.41/8.71 fof(f1_sk, plain, ! [X] : (~(distinct_lines(X,X))), inference(skolemisation, [status(esa)], [f1_nnf])).
% 25.41/8.71 cnf(c1, plain, ~distinct_lines(X0,X0), inference(cnf_transformation, [status(esa)], [f1_sk])).
% 25.41/8.71 cnf(p578, plain, distinct_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0)), inference(resolution, [status(thm)], [p539, c1])).
% 25.41/8.71 cnf(p1042, plain, apart_point_and_line(sk0,line_connecting(sk0,sk1)) | apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)), inference(resolution, [status(thm)], [p115, p578])).
% 25.41/8.71 cnf(ssp64, plain, (spl42 | spl44 | spl46 | spl47), inference(avatar_split_clause, [status(thm)], [p1042, sdef42, sdef44, sdef46, sdef47])).
% 25.41/8.71 cnf(p544, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk0,sk2),X0) | ~spl19), inference(avatar_component_clause, [status(thm)], [sdef19])).
% 25.41/8.71 cnf(p1043, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk0,sk2),X0) | ~spl19), inference(resolution, [status(thm)], [p115, p544])).
% 25.41/8.71 cnf(ssp65, plain, (~spl19 | spl42 | spl44 | spl66), inference(avatar_split_clause, [status(thm)], [p1043, sdef42, sdef44, sdef66])).
% 25.41/8.71 cnf(p580, plain, (distinct_lines(line_connecting(sk0,sk2),line_connecting(sk1,sk0)) | ~spl19), inference(resolution, [status(thm)], [p544, c1])).
% 25.41/8.71 cnf(p1044, plain, (apart_point_and_line(sk0,line_connecting(sk0,sk2)) | apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk0,sk2)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | ~spl19), inference(resolution, [status(thm)], [p115, p580])).
% 25.41/8.71 cnf(ssp66, plain, (~spl19 | spl42 | spl44 | spl48 | spl49), inference(avatar_split_clause, [status(thm)], [p1044, sdef42, sdef44, sdef48, sdef49])).
% 25.41/8.71 cnf(p546, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk1,sk2),X0) | ~spl20), inference(avatar_component_clause, [status(thm)], [sdef20])).
% 25.41/8.71 cnf(p1045, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk2)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk2)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X0) | ~spl20), inference(resolution, [status(thm)], [p115, p546])).
% 25.41/8.71 cnf(ssp67, plain, (~spl20 | spl50 | spl51 | spl67), inference(avatar_split_clause, [status(thm)], [p1045, sdef50, sdef51, sdef67])).
% 25.41/8.71 cnf(p582, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk1,sk2)) | ~spl20), inference(resolution, [status(thm)], [p546, c1])).
% 25.41/8.71 cnf(p1046, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk1,sk2)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk1,sk2)) | ~spl20), inference(resolution, [status(thm)], [p115, p582])).
% 25.41/8.71 cnf(ssp68, plain, (~spl20 | spl42 | spl44 | spl50 | spl51), inference(avatar_split_clause, [status(thm)], [p1046, sdef42, sdef44, sdef50, sdef51])).
% 25.41/8.71 cnf(p548, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk1),X0) | ~spl21), inference(avatar_component_clause, [status(thm)], [sdef21])).
% 25.41/8.71 cnf(p1047, plain, (apart_point_and_line(sk0,line_connecting(sk2,sk1)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk2,sk1)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X0) | ~spl21), inference(resolution, [status(thm)], [p115, p548])).
% 25.41/8.71 cnf(ssp69, plain, (~spl21 | spl52 | spl53 | spl67), inference(avatar_split_clause, [status(thm)], [p1047, sdef52, sdef53, sdef67])).
% 25.41/8.71 cnf(p584, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,sk1)) | ~spl21), inference(resolution, [status(thm)], [p548, c1])).
% 25.41/8.71 cnf(p1048, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,sk1)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,sk1)) | ~spl21), inference(resolution, [status(thm)], [p115, p584])).
% 25.41/8.71 cnf(ssp70, plain, (~spl21 | spl42 | spl44 | spl52 | spl53), inference(avatar_split_clause, [status(thm)], [p1048, sdef42, sdef44, sdef52, sdef53])).
% 25.41/8.71 cnf(p550, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk0),X0) | ~spl22), inference(avatar_component_clause, [status(thm)], [sdef22])).
% 25.41/8.71 cnf(p1049, plain, (apart_point_and_line(sk0,line_connecting(sk2,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk2,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X0) | ~spl22), inference(resolution, [status(thm)], [p115, p550])).
% 25.41/8.71 cnf(ssp71, plain, (~spl22 | spl54 | spl55 | spl67), inference(avatar_split_clause, [status(thm)], [p1049, sdef54, sdef55, sdef67])).
% 25.41/8.71 cnf(p586, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,sk0)) | ~spl22), inference(resolution, [status(thm)], [p550, c1])).
% 25.41/8.71 cnf(p1050, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,sk0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,sk0)) | ~spl22), inference(resolution, [status(thm)], [p115, p586])).
% 25.41/8.71 cnf(ssp72, plain, (~spl22 | spl42 | spl44 | spl54 | spl55), inference(avatar_split_clause, [status(thm)], [p1050, sdef42, sdef44, sdef54, sdef55])).
% 25.41/8.71 cnf(p1051, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(sk0,X1) | distinct_points(X1,X0) | ~spl17), inference(resolution, [status(thm)], [p115, p515])).
% 25.41/8.71 fof(sdef70, definition, (spl70 <=> (apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(sk0,X1) | distinct_points(X1,X0))), introduced(definition, [new_symbols(naming, [spl70])], [avatar_definition])).
% 25.41/8.71 cnf(ssp73, plain, (~spl17 | spl42 | spl44 | spl70), inference(avatar_split_clause, [status(thm)], [p1051, sdef42, sdef44, sdef70])).
% 25.41/8.71 cnf(p912, plain, (distinct_points(sk0,X0) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | ~spl17), inference(resolution, [status(thm)], [p515, c0])).
% 25.41/8.71 cnf(p1053, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(sk0,X0) | ~spl17), inference(resolution, [status(thm)], [p115, p912])).
% 25.41/8.71 cnf(ssp74, plain, (~spl17 | spl42 | spl44 | spl56), inference(avatar_split_clause, [status(thm)], [p1053, sdef42, sdef44, sdef56])).
% 25.41/8.71 cnf(p518, plain, (distinct_points(sk0,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(line_connecting(sk2,X0),X1) | ~spl7), inference(resolution, [status(thm)], [p477, c4])).
% 25.41/8.71 cnf(p1054, plain, (apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | apart_point_and_line(sk1,X1) | distinct_points(sk0,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | ~spl7), inference(resolution, [status(thm)], [p115, p518])).
% 25.41/8.71 cnf(ssp75, plain, (~spl7 | spl56 | spl67), inference(avatar_split_clause, [status(thm)], [p1054, sdef56, sdef67])).
% 25.41/8.71 cnf(p519, plain, (distinct_points(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(line_connecting(sk2,X0),X1) | ~spl8), inference(resolution, [status(thm)], [p479, c4])).
% 25.41/8.71 cnf(p1055, plain, (apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | apart_point_and_line(sk1,X1) | distinct_points(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | ~spl8), inference(resolution, [status(thm)], [p115, p519])).
% 25.41/8.71 cnf(ssp76, plain, (~spl8 | spl57 | spl67), inference(avatar_split_clause, [status(thm)], [p1055, sdef57, sdef67])).
% 25.41/8.71 cnf(p521, plain, (distinct_points(sk0,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(line_connecting(X0,sk2),X1) | ~spl9), inference(resolution, [status(thm)], [p482, c4])).
% 25.41/8.71 cnf(p1056, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(X1,sk2),X0) | ~spl9), inference(resolution, [status(thm)], [p115, p521])).
% 25.41/8.71 fof(sdef71, definition, (spl71 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(X1,sk2),X0))), introduced(definition, [new_symbols(naming, [spl71])], [avatar_definition])).
% 25.41/8.71 cnf(ssp77, plain, (~spl9 | spl42 | spl44 | spl71), inference(avatar_split_clause, [status(thm)], [p1056, sdef42, sdef44, sdef71])).
% 25.41/8.71 cnf(p1058, plain, (apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | apart_point_and_line(sk1,X1) | distinct_points(sk0,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | ~spl9), inference(resolution, [status(thm)], [p115, p521])).
% 25.41/8.71 cnf(ssp78, plain, (~spl9 | spl58 | spl67), inference(avatar_split_clause, [status(thm)], [p1058, sdef58, sdef67])).
% 25.41/8.71 cnf(p522, plain, (distinct_points(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(line_connecting(X0,sk2),X1) | ~spl10), inference(resolution, [status(thm)], [p485, c4])).
% 25.41/8.71 cnf(p1059, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_points(sk1,X1) | distinct_lines(line_connecting(X1,sk2),X0) | ~spl10), inference(resolution, [status(thm)], [p115, p522])).
% 25.41/8.71 fof(sdef72, definition, (spl72 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_points(sk1,X1) | distinct_lines(line_connecting(X1,sk2),X0))), introduced(definition, [new_symbols(naming, [spl72])], [avatar_definition])).
% 25.41/8.71 cnf(ssp79, plain, (~spl10 | spl42 | spl44 | spl72), inference(avatar_split_clause, [status(thm)], [p1059, sdef42, sdef44, sdef72])).
% 25.41/8.71 cnf(p1061, plain, (apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | apart_point_and_line(sk1,X1) | distinct_points(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | ~spl10), inference(resolution, [status(thm)], [p115, p522])).
% 25.41/8.71 cnf(ssp80, plain, (~spl10 | spl59 | spl67), inference(avatar_split_clause, [status(thm)], [p1061, sdef59, sdef67])).
% 25.41/8.71 cnf(p523, plain, (distinct_points(X0,sk0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(line_connecting(X0,sk2),X1) | ~spl11), inference(resolution, [status(thm)], [p487, c4])).
% 25.41/8.71 cnf(p1062, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_points(X1,sk0) | distinct_lines(line_connecting(X1,sk2),X0) | ~spl11), inference(resolution, [status(thm)], [p115, p523])).
% 25.41/8.71 fof(sdef73, definition, (spl73 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_points(X1,sk0) | distinct_lines(line_connecting(X1,sk2),X0))), introduced(definition, [new_symbols(naming, [spl73])], [avatar_definition])).
% 25.41/8.71 cnf(ssp81, plain, (~spl11 | spl42 | spl44 | spl73), inference(avatar_split_clause, [status(thm)], [p1062, sdef42, sdef44, sdef73])).
% 25.41/8.71 cnf(p1064, plain, (apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | apart_point_and_line(sk1,X1) | distinct_points(X0,sk0) | distinct_lines(line_connecting(sk1,sk0),X1) | ~spl11), inference(resolution, [status(thm)], [p115, p523])).
% 25.41/8.71 cnf(ssp82, plain, (~spl11 | spl60 | spl67), inference(avatar_split_clause, [status(thm)], [p1064, sdef60, sdef67])).
% 25.41/8.71 cnf(p524, plain, (distinct_points(X0,sk1) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(line_connecting(X0,sk2),X1) | ~spl12), inference(resolution, [status(thm)], [p489, c4])).
% 25.41/8.71 cnf(p1065, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_points(X1,sk1) | distinct_lines(line_connecting(X1,sk2),X0) | ~spl12), inference(resolution, [status(thm)], [p115, p524])).
% 25.41/8.71 fof(sdef74, definition, (spl74 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_points(X1,sk1) | distinct_lines(line_connecting(X1,sk2),X0))), introduced(definition, [new_symbols(naming, [spl74])], [avatar_definition])).
% 25.41/8.71 cnf(ssp83, plain, (~spl12 | spl42 | spl44 | spl74), inference(avatar_split_clause, [status(thm)], [p1065, sdef42, sdef44, sdef74])).
% 25.41/8.71 cnf(p1067, plain, (apart_point_and_line(sk0,line_connecting(X0,sk2)) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,line_connecting(X0,sk2)) | apart_point_and_line(sk1,X1) | distinct_points(X0,sk1) | distinct_lines(line_connecting(sk1,sk0),X1) | ~spl12), inference(resolution, [status(thm)], [p115, p524])).
% 25.41/8.71 cnf(ssp84, plain, (~spl12 | spl61 | spl67), inference(avatar_split_clause, [status(thm)], [p1067, sdef61, sdef67])).
% 25.41/8.71 cnf(p525, plain, (distinct_points(X0,sk1) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(line_connecting(sk2,X0),X1) | ~spl13), inference(resolution, [status(thm)], [p491, c4])).
% 25.41/8.71 cnf(p1068, plain, (apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | apart_point_and_line(sk1,X1) | distinct_points(X0,sk1) | distinct_lines(line_connecting(sk1,sk0),X1) | ~spl13), inference(resolution, [status(thm)], [p115, p525])).
% 25.41/8.71 cnf(ssp85, plain, (~spl13 | spl62 | spl67), inference(avatar_split_clause, [status(thm)], [p1068, sdef62, sdef67])).
% 25.41/8.71 cnf(p527, plain, (distinct_points(X0,sk0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(line_connecting(sk2,X0),X1) | ~spl15), inference(resolution, [status(thm)], [p496, c4])).
% 25.41/8.71 cnf(p1069, plain, (apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | apart_point_and_line(sk1,X1) | distinct_points(X0,sk0) | distinct_lines(line_connecting(sk1,sk0),X1) | ~spl15), inference(resolution, [status(thm)], [p115, p527])).
% 25.41/8.71 cnf(ssp86, plain, (~spl15 | spl64 | spl67), inference(avatar_split_clause, [status(thm)], [p1069, sdef64, sdef67])).
% 25.41/8.71 cnf(p1070, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(sk1,X1) | distinct_points(X1,X0) | ~spl18), inference(resolution, [status(thm)], [p115, p530])).
% 25.41/8.71 fof(sdef75, definition, (spl75 <=> (apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(sk1,X1) | distinct_points(X1,X0))), introduced(definition, [new_symbols(naming, [spl75])], [avatar_definition])).
% 25.41/8.71 cnf(ssp87, plain, (~spl18 | spl42 | spl44 | spl75), inference(avatar_split_clause, [status(thm)], [p1070, sdef42, sdef44, sdef75])).
% 25.41/8.71 cnf(p945, plain, (distinct_points(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | ~spl18), inference(resolution, [status(thm)], [p530, c0])).
% 25.41/8.71 cnf(p1072, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(sk1,X0) | ~spl18), inference(resolution, [status(thm)], [p115, p945])).
% 25.41/8.71 cnf(ssp88, plain, (~spl18 | spl42 | spl44 | spl57), inference(avatar_split_clause, [status(thm)], [p1072, sdef42, sdef44, sdef57])).
% 25.41/8.71 cnf(p534, plain, (distinct_lines(line_connecting(sk0,sk2),X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X0,X1) | ~spl2), inference(resolution, [status(thm)], [p502, c4])).
% 25.41/8.71 cnf(p1073, plain, (apart_point_and_line(sk0,line_connecting(sk0,sk2)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk0,sk2)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X0,X1) | ~spl2), inference(resolution, [status(thm)], [p115, p534])).
% 25.41/8.71 fof(sdef76, definition, (spl76 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl76])], [avatar_definition])).
% 25.41/8.71 cnf(ssp89, plain, (~spl2 | spl48 | spl49 | spl76), inference(avatar_split_clause, [status(thm)], [p1073, sdef48, sdef49, sdef76])).
% 25.41/8.71 cnf(p1075, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk0,sk2),X1) | distinct_lines(X1,X0) | ~spl2), inference(resolution, [status(thm)], [p115, p534])).
% 25.41/8.71 fof(sdef77, definition, (spl77 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk0,sk2),X1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl77])], [avatar_definition])).
% 25.41/8.71 cnf(ssp90, plain, (~spl2 | spl42 | spl44 | spl77), inference(avatar_split_clause, [status(thm)], [p1075, sdef42, sdef44, sdef77])).
% 25.41/8.71 cnf(p1077, plain, (apart_point_and_line(sk0,X0) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,X1) | distinct_lines(line_connecting(sk0,sk2),X0) | distinct_lines(line_connecting(sk1,sk0),X1) | ~spl2), inference(resolution, [status(thm)], [p115, p534])).
% 25.41/8.71 cnf(ssp91, plain, (~spl2 | spl66 | spl67), inference(avatar_split_clause, [status(thm)], [p1077, sdef66, sdef67])).
% 25.41/8.71 cnf(p961, plain, (distinct_lines(line_connecting(sk0,sk2),X0) | distinct_lines(X0,line_connecting(sk1,sk0)) | ~spl2), inference(resolution, [status(thm)], [p534, c1])).
% 25.41/8.71 cnf(p1078, plain, (apart_point_and_line(sk0,line_connecting(sk0,sk2)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk0,sk2)) | apart_point_and_line(sk1,X0) | distinct_lines(X0,line_connecting(sk1,sk0)) | ~spl2), inference(resolution, [status(thm)], [p115, p961])).
% 25.41/8.71 fof(sdef78, definition, (spl78 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(X0,line_connecting(sk1,sk0)))), introduced(definition, [new_symbols(naming, [spl78])], [avatar_definition])).
% 25.41/8.71 cnf(ssp92, plain, (~spl2 | spl48 | spl49 | spl78), inference(avatar_split_clause, [status(thm)], [p1078, sdef48, sdef49, sdef78])).
% 25.41/8.71 cnf(p536, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk1,sk2),X1) | distinct_lines(X0,X1) | ~spl4), inference(resolution, [status(thm)], [p513, c4])).
% 25.41/8.71 cnf(p1080, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk2),X1) | distinct_lines(X0,X1) | ~spl4), inference(resolution, [status(thm)], [p115, p536])).
% 25.41/8.71 fof(sdef79, definition, (spl79 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk2),X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl79])], [avatar_definition])).
% 25.41/8.71 cnf(ssp93, plain, (~spl4 | spl42 | spl44 | spl79), inference(avatar_split_clause, [status(thm)], [p1080, sdef42, sdef44, sdef79])).
% 25.41/8.71 cnf(p1082, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk2)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk2)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X1,X0) | ~spl4), inference(resolution, [status(thm)], [p115, p536])).
% 25.41/8.71 fof(sdef80, definition, (spl80 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl80])], [avatar_definition])).
% 25.41/8.71 cnf(ssp94, plain, (~spl4 | spl50 | spl51 | spl80), inference(avatar_split_clause, [status(thm)], [p1082, sdef50, sdef51, sdef80])).
% 25.41/8.71 cnf(p1084, plain, (apart_point_and_line(sk0,X0) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,X1) | distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk1,sk2),X1) | ~spl4), inference(resolution, [status(thm)], [p115, p536])).
% 25.41/8.71 fof(sdef81, definition, (spl81 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk2),X0))), introduced(definition, [new_symbols(naming, [spl81])], [avatar_definition])).
% 25.41/8.71 cnf(ssp95, plain, (~spl4 | spl67 | spl81), inference(avatar_split_clause, [status(thm)], [p1084, sdef67, sdef81])).
% 25.41/8.71 cnf(p966, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(X0,line_connecting(sk1,sk2)) | ~spl4), inference(resolution, [status(thm)], [p536, c1])).
% 25.41/8.71 cnf(p1086, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(X0,line_connecting(sk1,sk2)) | ~spl4), inference(resolution, [status(thm)], [p115, p966])).
% 25.41/8.71 fof(sdef82, definition, (spl82 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(X0,line_connecting(sk1,sk2)))), introduced(definition, [new_symbols(naming, [spl82])], [avatar_definition])).
% 25.41/8.71 cnf(ssp96, plain, (~spl4 | spl42 | spl44 | spl82), inference(avatar_split_clause, [status(thm)], [p1086, sdef42, sdef44, sdef82])).
% 25.41/8.71 cnf(p537, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk1),X1) | distinct_lines(X0,X1) | ~spl5), inference(resolution, [status(thm)], [p516, c4])).
% 25.41/8.71 cnf(p1088, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk2,sk1),X1) | distinct_lines(X0,X1) | ~spl5), inference(resolution, [status(thm)], [p115, p537])).
% 25.41/8.71 fof(sdef83, definition, (spl83 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk2,sk1),X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl83])], [avatar_definition])).
% 25.41/8.71 cnf(ssp97, plain, (~spl5 | spl42 | spl44 | spl83), inference(avatar_split_clause, [status(thm)], [p1088, sdef42, sdef44, sdef83])).
% 25.41/8.71 cnf(p1090, plain, (apart_point_and_line(sk0,line_connecting(sk2,sk1)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk2,sk1)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X1,X0) | ~spl5), inference(resolution, [status(thm)], [p115, p537])).
% 25.41/8.71 cnf(ssp98, plain, (~spl5 | spl52 | spl53 | spl80), inference(avatar_split_clause, [status(thm)], [p1090, sdef52, sdef53, sdef80])).
% 25.41/8.71 cnf(p1091, plain, (apart_point_and_line(sk0,X0) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,X1) | distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk1),X1) | ~spl5), inference(resolution, [status(thm)], [p115, p537])).
% 25.41/8.71 fof(sdef84, definition, (spl84 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk2,sk1),X0))), introduced(definition, [new_symbols(naming, [spl84])], [avatar_definition])).
% 25.41/8.71 cnf(ssp99, plain, (~spl5 | spl67 | spl84), inference(avatar_split_clause, [status(thm)], [p1091, sdef67, sdef84])).
% 25.41/8.71 cnf(p977, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(X0,line_connecting(sk2,sk1)) | ~spl5), inference(resolution, [status(thm)], [p537, c1])).
% 25.41/8.71 cnf(p1093, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(X0,line_connecting(sk2,sk1)) | ~spl5), inference(resolution, [status(thm)], [p115, p977])).
% 25.41/8.71 fof(sdef85, definition, (spl85 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(X0,line_connecting(sk2,sk1)))), introduced(definition, [new_symbols(naming, [spl85])], [avatar_definition])).
% 25.41/8.71 cnf(ssp100, plain, (~spl5 | spl42 | spl44 | spl85), inference(avatar_split_clause, [status(thm)], [p1093, sdef42, sdef44, sdef85])).
% 25.41/8.71 cnf(p538, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk0),X1) | distinct_lines(X0,X1) | ~spl6), inference(resolution, [status(thm)], [p517, c4])).
% 25.41/8.71 cnf(p1095, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk2,sk0),X1) | distinct_lines(X0,X1) | ~spl6), inference(resolution, [status(thm)], [p115, p538])).
% 25.41/8.71 fof(sdef86, definition, (spl86 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk2,sk0),X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl86])], [avatar_definition])).
% 25.41/8.71 cnf(ssp101, plain, (~spl6 | spl42 | spl44 | spl86), inference(avatar_split_clause, [status(thm)], [p1095, sdef42, sdef44, sdef86])).
% 25.41/8.71 cnf(p1097, plain, (apart_point_and_line(sk0,line_connecting(sk2,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk2,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X1,X0) | ~spl6), inference(resolution, [status(thm)], [p115, p538])).
% 25.41/8.71 cnf(ssp102, plain, (~spl6 | spl54 | spl55 | spl80), inference(avatar_split_clause, [status(thm)], [p1097, sdef54, sdef55, sdef80])).
% 25.41/8.71 cnf(p1098, plain, (apart_point_and_line(sk0,X0) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,X1) | distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,sk0),X1) | ~spl6), inference(resolution, [status(thm)], [p115, p538])).
% 25.41/8.71 fof(sdef87, definition, (spl87 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk2,sk0),X0))), introduced(definition, [new_symbols(naming, [spl87])], [avatar_definition])).
% 25.41/8.71 cnf(ssp103, plain, (~spl6 | spl67 | spl87), inference(avatar_split_clause, [status(thm)], [p1098, sdef67, sdef87])).
% 25.41/8.71 cnf(p982, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(X0,line_connecting(sk2,sk0)) | ~spl6), inference(resolution, [status(thm)], [p538, c1])).
% 25.41/8.71 cnf(p1100, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | distinct_lines(X0,line_connecting(sk2,sk0)) | ~spl6), inference(resolution, [status(thm)], [p115, p982])).
% 25.41/8.71 fof(sdef88, definition, (spl88 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(X0,line_connecting(sk2,sk0)))), introduced(definition, [new_symbols(naming, [spl88])], [avatar_definition])).
% 25.41/8.71 cnf(ssp104, plain, (~spl6 | spl42 | spl44 | spl88), inference(avatar_split_clause, [status(thm)], [p1100, sdef42, sdef44, sdef88])).
% 25.41/8.71 cnf(p553, plain, (distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(line_connecting(sk2,X1),X0) | distinct_points(sk0,X1) | ~spl23), inference(avatar_component_clause, [status(thm)], [sdef23])).
% 25.41/8.71 cnf(p1102, plain, (apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | apart_point_and_line(sk1,X1) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_points(sk0,X0) | ~spl23), inference(resolution, [status(thm)], [p115, p553])).
% 25.41/8.71 cnf(ssp105, plain, (~spl23 | spl56 | spl67), inference(avatar_split_clause, [status(thm)], [p1102, sdef56, sdef67])).
% 25.41/8.71 cnf(p988, plain, (distinct_lines(line_connecting(sk1,sk0),line_connecting(sk2,X0)) | distinct_points(sk0,X0) | ~spl23), inference(resolution, [status(thm)], [p553, c1])).
% 25.41/8.71 cnf(p1103, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk0,line_connecting(sk2,X0)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,line_connecting(sk2,X0)) | distinct_points(sk0,X0) | ~spl23), inference(resolution, [status(thm)], [p115, p988])).
% 25.41/8.71 cnf(ssp106, plain, (~spl23 | spl42 | spl44 | spl56), inference(avatar_split_clause, [status(thm)], [p1103, sdef42, sdef44, sdef56])).
% 25.41/8.71 cnf(p116, plain, ~distinct_lines(X0,X1) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk0,X1) | apart_point_and_line(sk2,X0) | apart_point_and_line(sk2,X1), inference(resolution, [status(thm)], [c10, c15])).
% 25.41/8.71 cnf(p1112, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk2)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk2,line_connecting(sk1,sk2)) | apart_point_and_line(sk2,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X1,X0) | ~spl4), inference(resolution, [status(thm)], [p116, p536])).
% 25.41/8.71 fof(sdef89, definition, (spl89 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk2,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl89])], [avatar_definition])).
% 25.41/8.71 fof(sdef90, definition, (spl90 <=> (apart_point_and_line(sk2,line_connecting(sk1,sk2)))), introduced(definition, [new_symbols(naming, [spl90])], [avatar_definition])).
% 25.41/8.71 cnf(ssp107, plain, (~spl4 | spl50 | spl89 | spl90), inference(avatar_split_clause, [status(thm)], [p1112, sdef50, sdef89, sdef90])).
% 25.41/8.71 cnf(p1115, plain, (apart_point_and_line(sk0,line_connecting(sk2,sk1)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk2,line_connecting(sk2,sk1)) | apart_point_and_line(sk2,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X1,X0) | ~spl5), inference(resolution, [status(thm)], [p116, p537])).
% 25.41/8.71 fof(sdef91, definition, (spl91 <=> (apart_point_and_line(sk2,line_connecting(sk2,sk1)))), introduced(definition, [new_symbols(naming, [spl91])], [avatar_definition])).
% 25.41/8.71 cnf(ssp108, plain, (~spl5 | spl52 | spl89 | spl91), inference(avatar_split_clause, [status(thm)], [p1115, sdef52, sdef89, sdef91])).
% 25.41/8.71 cnf(p1117, plain, (apart_point_and_line(sk0,line_connecting(sk2,sk0)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk2,line_connecting(sk2,sk0)) | apart_point_and_line(sk2,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X1,X0) | ~spl6), inference(resolution, [status(thm)], [p116, p538])).
% 25.41/8.71 fof(sdef92, definition, (spl92 <=> (apart_point_and_line(sk2,line_connecting(sk2,sk0)))), introduced(definition, [new_symbols(naming, [spl92])], [avatar_definition])).
% 25.41/8.71 cnf(ssp109, plain, (~spl6 | spl54 | spl89 | spl92), inference(avatar_split_clause, [status(thm)], [p1117, sdef54, sdef89, sdef92])).
% 25.41/8.71 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, sct0, sct1, sct2, sct3, sct4, sct5, sct6, sct7])).
% 25.41/8.71 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------