%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO200+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 : n015.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 01:17:26 PM UTC 2026
% Result : Theorem 24.28s 8.59s
% Output : Proof 24.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO200+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/5.38 % Computer : n015.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Wed Sep 23 11:30:00 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.28/8.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.28/8.59 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.28/8.59 fof(sdef0, definition, (spl0 <=> (apart_point_and_line(sk0,line_connecting(sk0,sk1)))), introduced(definition, [new_symbols(naming, [spl0])], [avatar_definition])).
% 24.28/8.59 cnf(p292, plain, (apart_point_and_line(sk0,line_connecting(sk0,sk1)) | ~spl0), inference(avatar_component_clause, [status(thm)], [sdef0])).
% 24.28/8.59 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)).
% 24.28/8.59 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])).
% 24.28/8.59 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])).
% 24.28/8.59 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])).
% 24.28/8.59 fof(f12, conjecture, ! [X,Y] : ( distinct_points(X,Y) => ~ distinct_lines(line_connecting(X,Y),line_connecting(Y,X)) ), file('/export/starexec/sandbox/benchmark/theBenchmark.p', con)).
% 24.28/8.59 fof(f12_neg, negated_conjecture, ~(! [X,Y] : ( distinct_points(X,Y) => ~ distinct_lines(line_connecting(X,Y),line_connecting(Y,X)) )), inference(negated_conjecture, [status(cth)], [f12])).
% 24.28/8.59 fof(f12_nnf, plain, ? [X,Y] : ((distinct_points(X,Y) & distinct_lines(line_connecting(X,Y),line_connecting(Y,X)))), inference(nnf_transformation, [status(thm)], [f12_neg])).
% 24.28/8.59 fof(f12_sk, plain, (distinct_points(sk0,sk1) & distinct_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0))), inference(skolemisation, [status(esa), new_symbols(skolem, [sk0,sk1])], [f12_nnf])).
% 24.28/8.59 cnf(c14, plain, distinct_points(sk0,sk1), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 24.28/8.59 cnf(p35, plain, ~apart_point_and_line(X0,line_connecting(sk0,sk1)) | distinct_points(X0,sk0), inference(resolution, [status(thm)], [c6, c14])).
% 24.28/8.59 cnf(p319, plain, (distinct_points(sk0,sk0) | ~spl0), inference(resolution, [status(thm)], [p292, p35])).
% 24.28/8.59 fof(f0, axiom, ! [X] : ~ distinct_points(X,X), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apart1)).
% 24.28/8.59 fof(f0_nnf, plain, ! [X] : (~(distinct_points(X,X))), inference(nnf_transformation, [status(thm)], [f0])).
% 24.28/8.59 fof(f0_sk, plain, ! [X] : (~(distinct_points(X,X))), inference(skolemisation, [status(esa)], [f0_nnf])).
% 24.28/8.59 cnf(c0, plain, ~distinct_points(X0,X0), inference(cnf_transformation, [status(esa)], [f0_sk])).
% 24.28/8.59 cnf(p322, plain, ($false | ~spl0), inference(resolution, [status(thm)], [p319, c0])).
% 24.28/8.59 cnf(sct0, plain, (~spl0), inference(avatar_contradiction_clause, [status(thm)], [p322])).
% 24.28/8.59 fof(sdef1, definition, (spl1 <=> (apart_point_and_line(sk0,line_connecting(sk1,sk0)))), introduced(definition, [new_symbols(naming, [spl1])], [avatar_definition])).
% 24.28/8.59 cnf(p293, plain, (apart_point_and_line(sk0,line_connecting(sk1,sk0)) | ~spl1), inference(avatar_component_clause, [status(thm)], [sdef1])).
% 24.28/8.59 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])).
% 24.28/8.59 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)).
% 24.28/8.59 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])).
% 24.28/8.59 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])).
% 24.28/8.59 cnf(c3, plain, ~distinct_points(X0,X1) | distinct_points(X0,X2) | distinct_points(X1,X2), inference(cnf_transformation, [status(esa)], [f3_sk])).
% 24.28/8.59 cnf(p16, plain, distinct_points(sk0,X0) | distinct_points(sk1,X0), inference(resolution, [status(thm)], [c3, c14])).
% 24.28/8.59 cnf(p17, plain, distinct_points(sk0,X0) | distinct_points(sk1,X1) | distinct_points(X0,X1), inference(resolution, [status(thm)], [p16, c3])).
% 24.28/8.59 cnf(p18, plain, distinct_points(sk0,X0) | distinct_points(X0,sk1), inference(resolution, [status(thm)], [p17, c0])).
% 24.28/8.59 cnf(p23, plain, distinct_points(X0,sk1) | distinct_points(sk0,X1) | distinct_points(X0,X1), inference(resolution, [status(thm)], [p18, c3])).
% 24.28/8.59 cnf(p25, plain, distinct_points(X0,sk1) | distinct_points(X0,sk0), inference(resolution, [status(thm)], [p23, c0])).
% 24.28/8.59 cnf(p28, plain, distinct_points(sk1,sk0), inference(resolution, [status(thm)], [p25, c0])).
% 24.28/8.59 cnf(p66, plain, ~apart_point_and_line(X0,line_connecting(sk1,sk0)) | distinct_points(X0,sk0), inference(resolution, [status(thm)], [c7, p28])).
% 24.28/8.59 cnf(p323, plain, (distinct_points(sk0,sk0) | ~spl1), inference(resolution, [status(thm)], [p293, p66])).
% 24.28/8.59 cnf(p326, plain, ($false | ~spl1), inference(resolution, [status(thm)], [p323, c0])).
% 24.28/8.59 cnf(sct1, plain, (~spl1), inference(avatar_contradiction_clause, [status(thm)], [p326])).
% 24.28/8.59 fof(sdef2, definition, (spl2 <=> (apart_point_and_line(sk1,line_connecting(sk0,sk1)))), introduced(definition, [new_symbols(naming, [spl2])], [avatar_definition])).
% 24.28/8.59 cnf(p294, plain, (apart_point_and_line(sk1,line_connecting(sk0,sk1)) | ~spl2), inference(avatar_component_clause, [status(thm)], [sdef2])).
% 24.28/8.59 cnf(p55, plain, ~apart_point_and_line(X0,line_connecting(sk0,sk1)) | distinct_points(X0,sk1), inference(resolution, [status(thm)], [c7, c14])).
% 24.28/8.59 cnf(p352, plain, (distinct_points(sk1,sk1) | ~spl2), inference(resolution, [status(thm)], [p294, p55])).
% 24.28/8.59 cnf(p355, plain, ($false | ~spl2), inference(resolution, [status(thm)], [p352, c0])).
% 24.28/8.59 cnf(sct2, plain, (~spl2), inference(avatar_contradiction_clause, [status(thm)], [p355])).
% 24.28/8.59 fof(sdef3, definition, (spl3 <=> (apart_point_and_line(sk1,line_connecting(sk1,sk0)))), introduced(definition, [new_symbols(naming, [spl3])], [avatar_definition])).
% 24.28/8.59 cnf(p295, plain, (apart_point_and_line(sk1,line_connecting(sk1,sk0)) | ~spl3), inference(avatar_component_clause, [status(thm)], [sdef3])).
% 24.28/8.59 cnf(p46, plain, ~apart_point_and_line(X0,line_connecting(sk1,sk0)) | distinct_points(X0,sk1), inference(resolution, [status(thm)], [c6, p28])).
% 24.28/8.59 cnf(p356, plain, (distinct_points(sk1,sk1) | ~spl3), inference(resolution, [status(thm)], [p295, p46])).
% 24.28/8.59 cnf(p359, plain, ($false | ~spl3), inference(resolution, [status(thm)], [p356, c0])).
% 24.28/8.59 cnf(sct3, plain, (~spl3), inference(avatar_contradiction_clause, [status(thm)], [p359])).
% 24.28/8.59 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)).
% 24.28/8.59 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])).
% 24.28/8.59 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])).
% 24.28/8.59 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])).
% 24.28/8.59 cnf(p78, 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])).
% 24.28/8.59 cnf(c15, plain, distinct_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0)), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 24.28/8.59 cnf(p291, 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)], [p78, c15])).
% 24.28/8.59 cnf(ssp0, plain, (spl0 | spl1 | spl2 | spl3), inference(avatar_split_clause, [status(thm)], [p291, sdef0, sdef1, sdef2, sdef3])).
% 24.28/8.59 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)).
% 24.28/8.59 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])).
% 24.28/8.59 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])).
% 24.28/8.59 cnf(c4, plain, ~distinct_lines(X0,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(cnf_transformation, [status(esa)], [f4_sk])).
% 24.28/8.59 cnf(p22, plain, distinct_lines(line_connecting(sk0,sk1),X0) | distinct_lines(line_connecting(sk1,sk0),X0), inference(resolution, [status(thm)], [c4, c15])).
% 24.28/8.59 cnf(p296, 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)], [p78, p22])).
% 24.28/8.59 fof(sdef4, definition, (spl4 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk0,sk1),X0))), introduced(definition, [new_symbols(naming, [spl4])], [avatar_definition])).
% 24.28/8.59 cnf(ssp1, plain, (spl1 | spl3 | spl4), inference(avatar_split_clause, [status(thm)], [p296, sdef1, sdef3, sdef4])).
% 24.28/8.59 cnf(p24, plain, distinct_lines(line_connecting(sk0,sk1),X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p22, c4])).
% 24.28/8.59 cnf(p298, plain, apart_point_and_line(sk0,line_connecting(sk0,sk1)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p78, p24])).
% 24.28/8.59 fof(sdef5, definition, (spl5 <=> (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, [spl5])], [avatar_definition])).
% 24.28/8.59 cnf(ssp2, plain, (spl0 | spl2 | spl5), inference(avatar_split_clause, [status(thm)], [p298, sdef0, sdef2, sdef5])).
% 24.28/8.59 cnf(p300, 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),X1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p78, p24])).
% 24.28/8.59 fof(sdef6, definition, (spl6 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk0,sk1),X1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl6])], [avatar_definition])).
% 24.28/8.59 cnf(ssp3, plain, (spl1 | spl3 | spl6), inference(avatar_split_clause, [status(thm)], [p300, sdef1, sdef3, sdef6])).
% 24.28/8.59 cnf(p302, 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,sk1),X0) | distinct_lines(line_connecting(sk1,sk0),X1), inference(resolution, [status(thm)], [p78, p24])).
% 24.28/8.59 fof(sdef7, definition, (spl7 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X0))), introduced(definition, [new_symbols(naming, [spl7])], [avatar_definition])).
% 24.28/8.59 cnf(ssp4, plain, (spl4 | spl7), inference(avatar_split_clause, [status(thm)], [p302, sdef4, sdef7])).
% 24.28/8.59 fof(f1, axiom, ! [X] : ~ distinct_lines(X,X), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apart2)).
% 24.28/8.59 fof(f1_nnf, plain, ! [X] : (~(distinct_lines(X,X))), inference(nnf_transformation, [status(thm)], [f1])).
% 24.28/8.59 fof(f1_sk, plain, ! [X] : (~(distinct_lines(X,X))), inference(skolemisation, [status(esa)], [f1_nnf])).
% 24.28/8.59 cnf(c1, plain, ~distinct_lines(X0,X0), inference(cnf_transformation, [status(esa)], [f1_sk])).
% 24.28/8.59 cnf(p142, plain, distinct_lines(line_connecting(sk0,sk1),X0) | distinct_lines(X0,line_connecting(sk1,sk0)), inference(resolution, [status(thm)], [p24, c1])).
% 24.28/8.59 cnf(p304, plain, apart_point_and_line(sk0,line_connecting(sk0,sk1)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,X0) | distinct_lines(X0,line_connecting(sk1,sk0)), inference(resolution, [status(thm)], [p78, p142])).
% 24.28/8.59 fof(sdef8, definition, (spl8 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(X0,line_connecting(sk1,sk0)))), introduced(definition, [new_symbols(naming, [spl8])], [avatar_definition])).
% 24.28/8.59 cnf(ssp5, plain, (spl0 | spl2 | spl8), inference(avatar_split_clause, [status(thm)], [p304, sdef0, sdef2, sdef8])).
% 24.28/8.59 cnf(p146, plain, distinct_lines(X0,line_connecting(sk1,sk0)) | distinct_lines(line_connecting(sk0,sk1),X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p142, c4])).
% 24.28/8.59 cnf(p306, plain, apart_point_and_line(sk0,X0) | apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | distinct_lines(line_connecting(sk0,sk1),X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p78, p146])).
% 24.28/8.59 fof(sdef9, definition, (spl9 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk0,sk1),X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl9])], [avatar_definition])).
% 24.28/8.59 cnf(ssp6, plain, (spl1 | spl3 | spl9), inference(avatar_split_clause, [status(thm)], [p306, sdef1, sdef3, sdef9])).
% 24.28/8.59 cnf(p308, plain, apart_point_and_line(sk0,line_connecting(sk0,sk1)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,X0) | distinct_lines(X1,line_connecting(sk1,sk0)) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p78, p146])).
% 24.28/8.59 fof(sdef10, definition, (spl10 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(X1,line_connecting(sk1,sk0)) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl10])], [avatar_definition])).
% 24.28/8.59 cnf(ssp7, plain, (spl0 | spl2 | spl10), inference(avatar_split_clause, [status(thm)], [p308, sdef0, sdef2, sdef10])).
% 24.28/8.59 cnf(p310, 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(X0,line_connecting(sk1,sk0)) | distinct_lines(line_connecting(sk0,sk1),X1), inference(resolution, [status(thm)], [p78, p146])).
% 24.28/8.59 cnf(ssp8, plain, (spl4 | spl8), inference(avatar_split_clause, [status(thm)], [p310, sdef4, sdef8])).
% 24.28/8.59 cnf(p245, plain, distinct_lines(X0,line_connecting(sk1,sk0)) | distinct_lines(X0,line_connecting(sk0,sk1)), inference(resolution, [status(thm)], [p146, c1])).
% 24.28/8.59 cnf(p311, plain, apart_point_and_line(sk0,X0) | apart_point_and_line(sk0,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | distinct_lines(X0,line_connecting(sk0,sk1)), inference(resolution, [status(thm)], [p78, p245])).
% 24.28/8.59 fof(sdef11, definition, (spl11 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(X0,line_connecting(sk0,sk1)))), introduced(definition, [new_symbols(naming, [spl11])], [avatar_definition])).
% 24.28/8.59 cnf(ssp9, plain, (spl1 | spl3 | spl11), inference(avatar_split_clause, [status(thm)], [p311, sdef1, sdef3, sdef11])).
% 24.28/8.59 cnf(p249, plain, distinct_lines(X0,line_connecting(sk0,sk1)) | distinct_lines(X0,X1) | distinct_lines(line_connecting(sk1,sk0),X1), inference(resolution, [status(thm)], [p245, c4])).
% 24.28/8.59 cnf(p313, 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(X0,line_connecting(sk0,sk1)) | distinct_lines(line_connecting(sk1,sk0),X1), inference(resolution, [status(thm)], [p78, p249])).
% 24.28/8.59 cnf(ssp10, plain, (spl7 | spl11), inference(avatar_split_clause, [status(thm)], [p313, sdef7, sdef11])).
% 24.28/8.59 cnf(p314, 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(X1,line_connecting(sk0,sk1)) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p78, p249])).
% 24.28/8.59 fof(sdef12, definition, (spl12 <=> (apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,X0) | distinct_lines(X1,line_connecting(sk0,sk1)) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl12])], [avatar_definition])).
% 24.28/8.59 cnf(ssp11, plain, (spl1 | spl3 | spl12), inference(avatar_split_clause, [status(thm)], [p314, sdef1, sdef3, sdef12])).
% 24.28/8.59 cnf(p274, plain, distinct_lines(X0,line_connecting(sk0,sk1)) | distinct_lines(line_connecting(sk1,sk0),X0), inference(resolution, [status(thm)], [p249, c1])).
% 24.28/8.59 cnf(p316, plain, apart_point_and_line(sk0,X0) | apart_point_and_line(sk0,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,line_connecting(sk0,sk1)) | distinct_lines(line_connecting(sk1,sk0),X0), inference(resolution, [status(thm)], [p78, p274])).
% 24.28/8.59 cnf(ssp12, plain, (spl0 | spl2 | spl7), inference(avatar_split_clause, [status(thm)], [p316, sdef0, sdef2, sdef7])).
% 24.28/8.59 cnf(p277, plain, distinct_lines(line_connecting(sk1,sk0),X0) | distinct_lines(X0,X1) | distinct_lines(line_connecting(sk0,sk1),X1), inference(resolution, [status(thm)], [p274, c4])).
% 24.28/8.59 cnf(p317, plain, apart_point_and_line(sk0,line_connecting(sk0,sk1)) | apart_point_and_line(sk0,X0) | apart_point_and_line(sk1,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,X0) | distinct_lines(line_connecting(sk1,sk0),X1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p78, p277])).
% 24.28/8.59 fof(sdef13, definition, (spl13 <=> (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, [spl13])], [avatar_definition])).
% 24.28/8.59 cnf(ssp13, plain, (spl0 | spl2 | spl13), inference(avatar_split_clause, [status(thm)], [p317, sdef0, sdef2, sdef13])).
% 24.28/8.59 cnf(p79, plain, ~distinct_lines(X0,X1) | apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,X1) | apart_point_and_line(X2,X0) | apart_point_and_line(X2,X1) | distinct_points(sk0,X2), inference(resolution, [status(thm)], [c10, p16])).
% 24.28/8.59 cnf(p327, plain, apart_point_and_line(sk1,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(X0,line_connecting(sk0,sk1)) | apart_point_and_line(X0,line_connecting(sk1,sk0)) | distinct_points(sk0,X0), inference(resolution, [status(thm)], [p79, c15])).
% 24.28/8.59 fof(sdef14, definition, (spl14 <=> (apart_point_and_line(X0,line_connecting(sk0,sk1)) | apart_point_and_line(X0,line_connecting(sk1,sk0)) | distinct_points(sk0,X0))), introduced(definition, [new_symbols(naming, [spl14])], [avatar_definition])).
% 24.28/8.59 cnf(ssp14, plain, (spl2 | spl3 | spl14), inference(avatar_split_clause, [status(thm)], [p327, sdef2, sdef3, sdef14])).
% 24.28/8.59 cnf(p329, plain, apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk1,sk0)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk0,sk1),X0), inference(resolution, [status(thm)], [p79, p22])).
% 24.28/8.59 fof(sdef15, definition, (spl15 <=> (apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk1,sk0)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk0,sk1),X0))), introduced(definition, [new_symbols(naming, [spl15])], [avatar_definition])).
% 24.28/8.59 cnf(ssp15, plain, (spl3 | spl15), inference(avatar_split_clause, [status(thm)], [p329, sdef3, sdef15])).
% 24.28/8.59 cnf(p331, plain, apart_point_and_line(sk1,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk0,sk1)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk1,sk0),X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p79, p24])).
% 24.28/8.59 fof(sdef16, definition, (spl16 <=> (apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk0,sk1)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk1,sk0),X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl16])], [avatar_definition])).
% 24.28/8.59 cnf(ssp16, plain, (spl2 | spl16), inference(avatar_split_clause, [status(thm)], [p331, sdef2, sdef16])).
% 24.28/8.59 cnf(p333, plain, apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk1,sk0)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk0,sk1),X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p79, p24])).
% 24.28/8.59 fof(sdef17, definition, (spl17 <=> (apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk1,sk0)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk0,sk1),X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl17])], [avatar_definition])).
% 24.28/8.59 cnf(ssp17, plain, (spl3 | spl17), inference(avatar_split_clause, [status(thm)], [p333, sdef3, sdef17])).
% 24.28/8.59 cnf(p336, plain, apart_point_and_line(sk1,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk0,sk1)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(X0,line_connecting(sk1,sk0)), inference(resolution, [status(thm)], [p79, p142])).
% 24.28/8.59 fof(sdef18, definition, (spl18 <=> (apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk0,sk1)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(X0,line_connecting(sk1,sk0)))), introduced(definition, [new_symbols(naming, [spl18])], [avatar_definition])).
% 24.28/8.59 cnf(ssp18, plain, (spl2 | spl18), inference(avatar_split_clause, [status(thm)], [p336, sdef2, sdef18])).
% 24.28/8.59 cnf(p338, plain, apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,line_connecting(sk1,sk0)) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk0,sk1),X2) | distinct_lines(X0,X2), inference(resolution, [status(thm)], [p79, p146])).
% 24.28/8.59 fof(sdef19, definition, (spl19 <=> (apart_point_and_line(sk1,X0) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,line_connecting(sk1,sk0)) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk0,sk1),X2) | distinct_lines(X0,X2))), introduced(definition, [new_symbols(naming, [spl19])], [avatar_definition])).
% 24.28/8.59 cnf(ssp19, plain, (spl3 | spl19), inference(avatar_split_clause, [status(thm)], [p338, sdef3, sdef19])).
% 24.28/8.59 cnf(p340, plain, apart_point_and_line(sk1,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk0,sk1)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(X2,line_connecting(sk1,sk0)) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p79, p146])).
% 24.28/8.59 fof(sdef20, definition, (spl20 <=> (apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk0,sk1)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(X2,line_connecting(sk1,sk0)) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl20])], [avatar_definition])).
% 24.28/8.59 cnf(ssp20, plain, (spl2 | spl20), inference(avatar_split_clause, [status(thm)], [p340, sdef2, sdef20])).
% 24.28/8.59 cnf(p343, plain, apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,line_connecting(sk1,sk0)) | distinct_points(sk0,X1) | distinct_lines(X0,line_connecting(sk0,sk1)), inference(resolution, [status(thm)], [p79, p245])).
% 24.28/8.59 fof(sdef21, definition, (spl21 <=> (apart_point_and_line(sk1,X0) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,line_connecting(sk1,sk0)) | distinct_points(sk0,X1) | distinct_lines(X0,line_connecting(sk0,sk1)))), introduced(definition, [new_symbols(naming, [spl21])], [avatar_definition])).
% 24.28/8.59 cnf(ssp21, plain, (spl3 | spl21), inference(avatar_split_clause, [status(thm)], [p343, sdef3, sdef21])).
% 24.28/8.59 cnf(p346, plain, apart_point_and_line(sk1,line_connecting(sk1,sk0)) | apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk1,sk0)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(X2,line_connecting(sk0,sk1)) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p79, p249])).
% 24.28/8.59 fof(sdef22, definition, (spl22 <=> (apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk1,sk0)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(X2,line_connecting(sk0,sk1)) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl22])], [avatar_definition])).
% 24.28/8.59 cnf(ssp22, plain, (spl3 | spl22), inference(avatar_split_clause, [status(thm)], [p346, sdef3, sdef22])).
% 24.28/8.59 cnf(p348, plain, apart_point_and_line(sk1,X0) | apart_point_and_line(sk1,line_connecting(sk0,sk1)) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,line_connecting(sk0,sk1)) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk1,sk0),X0), inference(resolution, [status(thm)], [p79, p274])).
% 24.28/8.59 fof(sdef23, definition, (spl23 <=> (apart_point_and_line(sk1,X0) | apart_point_and_line(X1,X0) | apart_point_and_line(X1,line_connecting(sk0,sk1)) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk1,sk0),X0))), introduced(definition, [new_symbols(naming, [spl23])], [avatar_definition])).
% 24.28/8.59 cnf(ssp23, plain, (spl2 | spl23), inference(avatar_split_clause, [status(thm)], [p348, sdef2, sdef23])).
% 24.28/8.59 cnf(p350, plain, apart_point_and_line(sk1,line_connecting(sk0,sk1)) | apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk0,sk1)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk1,sk0),X2) | distinct_lines(X2,X0), inference(resolution, [status(thm)], [p79, p277])).
% 24.28/8.59 fof(sdef24, definition, (spl24 <=> (apart_point_and_line(sk1,X0) | apart_point_and_line(X1,line_connecting(sk0,sk1)) | apart_point_and_line(X1,X0) | distinct_points(sk0,X1) | distinct_lines(line_connecting(sk1,sk0),X2) | distinct_lines(X2,X0))), introduced(definition, [new_symbols(naming, [spl24])], [avatar_definition])).
% 24.28/8.59 cnf(ssp24, plain, (spl2 | spl24), inference(avatar_split_clause, [status(thm)], [p350, sdef2, sdef24])).
% 24.28/8.59 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, sct0, sct1, sct2, sct3])).
% 24.28/8.59 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------