%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO193+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 : n012
% 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 01:17:23 PM UTC 2026
% Result : Theorem 10.96s 31.97s
% Output : Proof 10.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO193+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.04/30.33 % Computer : n012
% 0.04/30.33 % Model : x86_64 x86_64
% 0.04/30.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/30.33 % Memory : 8046.5625MB
% 0.04/30.33 % OS : Linux 6.8.0-71-generic
% 0.04/30.33 % CPULimit : 300
% 0.04/30.33 % WCLimit : 300
% 0.04/30.33 % DateTime : Wed Sep 23 11:23:37 UTC 2026
% 0.04/30.33 % CPUTime :
% 0.04/30.33 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.96/31.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.96/31.97 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.96/31.97 fof(sdef0, definition, (spl0 <=> (distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1)))), introduced(definition, [new_symbols(naming, [spl0])], [avatar_definition])).
% 10.96/31.97 cnf(p312, plain, (distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1)) | ~spl0), inference(avatar_component_clause, [status(thm)], [sdef0])).
% 10.96/31.97 fof(f0, axiom, ! [X] : ~ distinct_points(X,X), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apart1)).
% 10.96/31.97 fof(f0_nnf, plain, ! [X] : (~(distinct_points(X,X))), inference(nnf_transformation, [status(thm)], [f0])).
% 10.96/31.97 fof(f0_sk, plain, ! [X] : (~(distinct_points(X,X))), inference(skolemisation, [status(esa)], [f0_nnf])).
% 10.96/31.97 cnf(c0, plain, ~distinct_points(X0,X0), inference(cnf_transformation, [status(esa)], [f0_sk])).
% 10.96/31.97 cnf(p314, plain, ($false | ~spl0), inference(resolution, [status(thm)], [p312, c0])).
% 10.96/31.97 cnf(sct0, plain, (~spl0), inference(avatar_contradiction_clause, [status(thm)], [p314])).
% 10.96/31.97 fof(sdef4, definition, (spl4 <=> (apart_point_and_line(intersection_point(sk2,sk1),sk0))), introduced(definition, [new_symbols(naming, [spl4])], [avatar_definition])).
% 10.96/31.97 cnf(p447, plain, (apart_point_and_line(intersection_point(sk2,sk1),sk0) | ~spl4), inference(avatar_component_clause, [status(thm)], [sdef4])).
% 10.96/31.97 fof(f12, conjecture, ! [X,Y,Z] : ( ( convergent_lines(X,Y) & convergent_lines(Z,Y) & convergent_lines(X,Z) ) => ( apart_point_and_line(intersection_point(X,Y),Z) => apart_point_and_line(intersection_point(Z,Y),X) ) ), file('/export/starexec/sandbox/benchmark/theBenchmark.p', con)).
% 10.96/31.97 fof(f12_neg, negated_conjecture, ~(! [X,Y,Z] : ( ( convergent_lines(X,Y) & convergent_lines(Z,Y) & convergent_lines(X,Z) ) => ( apart_point_and_line(intersection_point(X,Y),Z) => apart_point_and_line(intersection_point(Z,Y),X) ) )), inference(negated_conjecture, [status(cth)], [f12])).
% 10.96/31.97 fof(f12_nnf, plain, ? [X,Y,Z] : ((((convergent_lines(X,Y) & convergent_lines(Z,Y)) & convergent_lines(X,Z)) & (apart_point_and_line(intersection_point(X,Y),Z) & ~(apart_point_and_line(intersection_point(Z,Y),X))))), inference(nnf_transformation, [status(thm)], [f12_neg])).
% 10.96/31.97 fof(f12_sk, plain, (((convergent_lines(sk0,sk1) & convergent_lines(sk2,sk1)) & convergent_lines(sk0,sk2)) & (apart_point_and_line(intersection_point(sk0,sk1),sk2) & ~(apart_point_and_line(intersection_point(sk2,sk1),sk0)))), inference(skolemisation, [status(esa), new_symbols(skolem, [sk0,sk1,sk2])], [f12_nnf])).
% 10.96/31.97 cnf(c18, plain, ~apart_point_and_line(intersection_point(sk2,sk1),sk0), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 10.96/31.97 cnf(p504, plain, ($false | ~spl4), inference(resolution, [status(thm)], [p447, c18])).
% 10.96/31.97 cnf(sct1, plain, (~spl4), inference(avatar_contradiction_clause, [status(thm)], [p504])).
% 10.96/31.97 fof(sdef2, definition, (spl2 <=> (apart_point_and_line(intersection_point(sk0,sk1),sk0))), introduced(definition, [new_symbols(naming, [spl2])], [avatar_definition])).
% 10.96/31.97 cnf(p445, plain, (apart_point_and_line(intersection_point(sk0,sk1),sk0) | ~spl2), inference(avatar_component_clause, [status(thm)], [sdef2])).
% 10.96/31.97 fof(f7, axiom, ! [X,Y,Z] : ( convergent_lines(X,Y) => ( ( apart_point_and_line(Z,X) | apart_point_and_line(Z,Y) ) => distinct_points(Z,intersection_point(X,Y)) ) ), file('/export/starexec/sandbox/benchmark/theBenchmark.p', con2)).
% 10.96/31.97 fof(f7_nnf, plain, ! [X,Y,Z] : ((~(convergent_lines(X,Y)) | ((~(apart_point_and_line(Z,X)) & ~(apart_point_and_line(Z,Y))) | distinct_points(Z,intersection_point(X,Y))))), inference(nnf_transformation, [status(thm)], [f7])).
% 10.96/31.97 fof(f7_sk, plain, ! [X,Y,Z] : ((~(convergent_lines(X,Y)) | ((~(apart_point_and_line(Z,X)) & ~(apart_point_and_line(Z,Y))) | distinct_points(Z,intersection_point(X,Y))))), inference(skolemisation, [status(esa)], [f7_nnf])).
% 10.96/31.97 cnf(c8, plain, ~convergent_lines(X0,X1) | ~apart_point_and_line(X2,X0) | distinct_points(X2,intersection_point(X0,X1)), inference(cnf_transformation, [status(esa)], [f7_sk])).
% 10.96/31.97 cnf(c14, plain, convergent_lines(sk0,sk1), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 10.96/31.97 cnf(p44, plain, ~apart_point_and_line(X0,sk0) | distinct_points(X0,intersection_point(sk0,sk1)), inference(resolution, [status(thm)], [c8, c14])).
% 10.96/31.97 cnf(p492, plain, (distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1)) | ~spl2), inference(resolution, [status(thm)], [p445, p44])).
% 10.96/31.97 cnf(p515, plain, ($false | ~spl2), inference(resolution, [status(thm)], [p492, c0])).
% 10.96/31.97 cnf(sct2, plain, (~spl2), inference(avatar_contradiction_clause, [status(thm)], [p515])).
% 10.96/31.97 fof(sdef3, definition, (spl3 <=> (apart_point_and_line(intersection_point(sk0,sk1),sk1))), introduced(definition, [new_symbols(naming, [spl3])], [avatar_definition])).
% 10.96/31.97 cnf(p446, plain, (apart_point_and_line(intersection_point(sk0,sk1),sk1) | ~spl3), inference(avatar_component_clause, [status(thm)], [sdef3])).
% 10.96/31.97 cnf(c9, plain, ~convergent_lines(X0,X1) | ~apart_point_and_line(X2,X1) | distinct_points(X2,intersection_point(X0,X1)), inference(cnf_transformation, [status(esa)], [f7_sk])).
% 10.96/31.97 cnf(p58, plain, ~apart_point_and_line(X0,sk1) | distinct_points(X0,intersection_point(sk0,sk1)), inference(resolution, [status(thm)], [c9, c14])).
% 10.96/31.97 cnf(p498, plain, (distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1)) | ~spl3), inference(resolution, [status(thm)], [p446, p58])).
% 10.96/31.97 cnf(p516, plain, ($false | ~spl3), inference(resolution, [status(thm)], [p498, c0])).
% 10.96/31.97 cnf(sct3, plain, (~spl3), inference(avatar_contradiction_clause, [status(thm)], [p516])).
% 10.96/31.97 fof(sdef5, definition, (spl5 <=> (apart_point_and_line(intersection_point(sk2,sk1),sk1))), introduced(definition, [new_symbols(naming, [spl5])], [avatar_definition])).
% 10.96/31.97 cnf(p448, plain, (apart_point_and_line(intersection_point(sk2,sk1),sk1) | ~spl5), inference(avatar_component_clause, [status(thm)], [sdef5])).
% 10.96/31.97 cnf(c15, plain, convergent_lines(sk2,sk1), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 10.96/31.97 cnf(p59, plain, ~apart_point_and_line(X0,sk1) | distinct_points(X0,intersection_point(sk2,sk1)), inference(resolution, [status(thm)], [c9, c15])).
% 10.96/31.97 cnf(p507, plain, (distinct_points(intersection_point(sk2,sk1),intersection_point(sk2,sk1)) | ~spl5), inference(resolution, [status(thm)], [p448, p59])).
% 10.96/31.97 cnf(p523, plain, ($false | ~spl5), inference(resolution, [status(thm)], [p507, c0])).
% 10.96/31.97 cnf(sct4, plain, (~spl5), inference(avatar_contradiction_clause, [status(thm)], [p523])).
% 10.96/31.97 cnf(p45, plain, ~apart_point_and_line(X0,sk2) | distinct_points(X0,intersection_point(sk2,sk1)), inference(resolution, [status(thm)], [c8, c15])).
% 10.96/31.97 cnf(c17, plain, apart_point_and_line(intersection_point(sk0,sk1),sk2), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 10.96/31.97 cnf(p54, plain, distinct_points(intersection_point(sk0,sk1),intersection_point(sk2,sk1)), inference(resolution, [status(thm)], [p45, c17])).
% 10.96/31.97 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)).
% 10.96/31.97 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])).
% 10.96/31.97 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])).
% 10.96/31.97 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])).
% 10.96/31.97 cnf(p56, plain, ~apart_point_and_line(X0,line_connecting(intersection_point(sk0,sk1),intersection_point(sk2,sk1))) | distinct_points(X0,intersection_point(sk0,sk1)), inference(resolution, [status(thm)], [p54, c6])).
% 10.96/31.97 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)).
% 10.96/31.97 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])).
% 10.96/31.97 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])).
% 10.96/31.97 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])).
% 10.96/31.97 cnf(p93, plain, distinct_lines(sk2,X0) | apart_point_and_line(intersection_point(sk0,sk1),X0), inference(resolution, [status(thm)], [c12, c17])).
% 10.96/31.97 cnf(p311, plain, distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1)) | distinct_lines(sk2,line_connecting(intersection_point(sk0,sk1),intersection_point(sk2,sk1))), inference(resolution, [status(thm)], [p56, p93])).
% 10.96/31.97 fof(sdef1, definition, (spl1 <=> (distinct_lines(sk2,line_connecting(intersection_point(sk0,sk1),intersection_point(sk2,sk1))))), introduced(definition, [new_symbols(naming, [spl1])], [avatar_definition])).
% 10.96/31.97 cnf(ssp0, plain, (spl0 | spl1), inference(avatar_split_clause, [status(thm)], [p311, sdef0, sdef1])).
% 10.96/31.97 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)).
% 10.96/31.97 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])).
% 10.96/31.97 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])).
% 10.96/31.97 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])).
% 10.96/31.97 cnf(p68, plain, ~distinct_lines(X0,X1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X1), inference(resolution, [status(thm)], [c10, p54])).
% 10.96/31.97 fof(f11, axiom, ! [X,Y] : ( convergent_lines(X,Y) => distinct_lines(X,Y) ), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ceq3)).
% 10.96/31.97 fof(f11_nnf, plain, ! [X,Y] : ((~(convergent_lines(X,Y)) | distinct_lines(X,Y))), inference(nnf_transformation, [status(thm)], [f11])).
% 10.96/31.97 fof(f11_sk, plain, ! [X,Y] : ((~(convergent_lines(X,Y)) | distinct_lines(X,Y))), inference(skolemisation, [status(esa)], [f11_nnf])).
% 10.96/31.97 cnf(c13, plain, ~convergent_lines(X0,X1) | distinct_lines(X0,X1), inference(cnf_transformation, [status(esa)], [f11_sk])).
% 10.96/31.97 cnf(p19, plain, distinct_lines(sk0,sk1), inference(resolution, [status(thm)], [c13, c14])).
% 10.96/31.97 cnf(p444, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk2,sk1),sk0) | apart_point_and_line(intersection_point(sk2,sk1),sk1), inference(resolution, [status(thm)], [p68, p19])).
% 10.96/31.97 cnf(ssp1, plain, (spl2 | spl3 | spl4 | spl5), inference(avatar_split_clause, [status(thm)], [p444, sdef2, sdef3, sdef4, sdef5])).
% 10.96/31.97 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)).
% 10.96/31.97 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])).
% 10.96/31.97 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])).
% 10.96/31.97 cnf(c4, plain, ~distinct_lines(X0,X1) | distinct_lines(X0,X2) | distinct_lines(X1,X2), inference(cnf_transformation, [status(esa)], [f4_sk])).
% 10.96/31.97 cnf(p22, plain, distinct_lines(sk0,X0) | distinct_lines(sk1,X0), inference(resolution, [status(thm)], [c4, p19])).
% 10.96/31.97 cnf(p449, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk0,X0), inference(resolution, [status(thm)], [p68, p22])).
% 10.96/31.97 fof(sdef6, definition, (spl6 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk0,X0))), introduced(definition, [new_symbols(naming, [spl6])], [avatar_definition])).
% 10.96/31.97 cnf(ssp2, plain, (spl3 | spl5 | spl6), inference(avatar_split_clause, [status(thm)], [p449, sdef3, sdef5, sdef6])).
% 10.96/31.97 cnf(p28, plain, distinct_lines(sk0,X0) | distinct_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p22, c4])).
% 10.96/31.97 cnf(p451, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p68, p28])).
% 10.96/31.97 fof(sdef7, definition, (spl7 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk1,X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl7])], [avatar_definition])).
% 10.96/31.97 cnf(ssp3, plain, (spl2 | spl4 | spl7), inference(avatar_split_clause, [status(thm)], [p451, sdef2, sdef4, sdef7])).
% 10.96/31.97 cnf(p453, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk0,X1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p68, p28])).
% 10.96/31.97 fof(sdef8, definition, (spl8 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk0,X1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl8])], [avatar_definition])).
% 10.96/31.97 cnf(ssp4, plain, (spl3 | spl5 | spl8), inference(avatar_split_clause, [status(thm)], [p453, sdef3, sdef5, sdef8])).
% 10.96/31.97 cnf(p455, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X1) | distinct_lines(sk0,X0) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p68, p28])).
% 10.96/31.97 fof(sdef9, definition, (spl9 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk1,X0))), introduced(definition, [new_symbols(naming, [spl9])], [avatar_definition])).
% 10.96/31.97 cnf(ssp5, plain, (spl6 | spl9), inference(avatar_split_clause, [status(thm)], [p455, sdef6, sdef9])).
% 10.96/31.97 fof(f1, axiom, ! [X] : ~ distinct_lines(X,X), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apart2)).
% 10.96/31.97 fof(f1_nnf, plain, ! [X] : (~(distinct_lines(X,X))), inference(nnf_transformation, [status(thm)], [f1])).
% 10.96/31.97 fof(f1_sk, plain, ! [X] : (~(distinct_lines(X,X))), inference(skolemisation, [status(esa)], [f1_nnf])).
% 10.96/31.97 cnf(c1, plain, ~distinct_lines(X0,X0), inference(cnf_transformation, [status(esa)], [f1_sk])).
% 10.96/31.97 cnf(p84, plain, distinct_lines(sk0,X0) | distinct_lines(X0,sk1), inference(resolution, [status(thm)], [p28, c1])).
% 10.96/31.97 cnf(p457, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X0,sk1), inference(resolution, [status(thm)], [p68, p84])).
% 10.96/31.97 fof(sdef10, definition, (spl10 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X0,sk1))), introduced(definition, [new_symbols(naming, [spl10])], [avatar_definition])).
% 10.96/31.97 cnf(ssp6, plain, (spl2 | spl4 | spl10), inference(avatar_split_clause, [status(thm)], [p457, sdef2, sdef4, sdef10])).
% 10.96/31.97 cnf(p20, plain, distinct_lines(sk2,sk1), inference(resolution, [status(thm)], [c13, c15])).
% 10.96/31.97 cnf(p23, plain, distinct_lines(sk2,X0) | distinct_lines(sk1,X0), inference(resolution, [status(thm)], [c4, p20])).
% 10.96/31.97 cnf(p30, plain, distinct_lines(sk1,X0) | distinct_lines(sk2,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p23, c4])).
% 10.96/31.97 cnf(p459, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk2,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p68, p30])).
% 10.96/31.97 fof(sdef11, definition, (spl11 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk2,X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl11])], [avatar_definition])).
% 10.96/31.97 cnf(ssp7, plain, (spl3 | spl5 | spl11), inference(avatar_split_clause, [status(thm)], [p459, sdef3, sdef5, sdef11])).
% 10.96/31.97 cnf(p89, plain, distinct_lines(sk1,X0) | distinct_lines(X0,sk2), inference(resolution, [status(thm)], [p30, c1])).
% 10.96/31.97 cnf(p461, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X0,sk2), inference(resolution, [status(thm)], [p68, p89])).
% 10.96/31.97 fof(sdef12, definition, (spl12 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X0,sk2))), introduced(definition, [new_symbols(naming, [spl12])], [avatar_definition])).
% 10.96/31.97 cnf(ssp8, plain, (spl3 | spl5 | spl12), inference(avatar_split_clause, [status(thm)], [p461, sdef3, sdef5, sdef12])).
% 10.96/31.97 cnf(c16, plain, convergent_lines(sk0,sk2), inference(cnf_transformation, [status(esa)], [f12_sk])).
% 10.96/31.97 cnf(p21, plain, distinct_lines(sk0,sk2), inference(resolution, [status(thm)], [c13, c16])).
% 10.96/31.97 cnf(p24, plain, distinct_lines(sk0,X0) | distinct_lines(sk2,X0), inference(resolution, [status(thm)], [c4, p21])).
% 10.96/31.97 cnf(p31, plain, distinct_lines(sk0,X0) | distinct_lines(sk2,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p24, c4])).
% 10.96/31.97 cnf(p463, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk2,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p68, p31])).
% 10.96/31.97 cnf(ssp9, plain, (spl2 | spl4 | spl11), inference(avatar_split_clause, [status(thm)], [p463, sdef2, sdef4, sdef11])).
% 10.96/31.97 cnf(p97, plain, distinct_lines(sk0,X0) | distinct_lines(X0,sk2), inference(resolution, [status(thm)], [p31, c1])).
% 10.96/31.97 cnf(p464, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X0,sk2), inference(resolution, [status(thm)], [p68, p97])).
% 10.96/31.97 cnf(ssp10, plain, (spl2 | spl4 | spl12), inference(avatar_split_clause, [status(thm)], [p464, sdef2, sdef4, sdef12])).
% 10.96/31.97 fof(f5, axiom, ! [X,Y,Z] : ( convergent_lines(X,Y) => ( convergent_lines(X,Z) | convergent_lines(Y,Z) ) ), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apart6)).
% 10.96/31.97 fof(f5_nnf, plain, ! [X,Y,Z] : ((~(convergent_lines(X,Y)) | (convergent_lines(X,Z) | convergent_lines(Y,Z)))), inference(nnf_transformation, [status(thm)], [f5])).
% 10.96/31.97 fof(f5_sk, plain, ! [X,Y,Z] : ((~(convergent_lines(X,Y)) | (convergent_lines(X,Z) | convergent_lines(Y,Z)))), inference(skolemisation, [status(esa)], [f5_nnf])).
% 10.96/31.97 cnf(c5, plain, ~convergent_lines(X0,X1) | convergent_lines(X0,X2) | convergent_lines(X1,X2), inference(cnf_transformation, [status(esa)], [f5_sk])).
% 10.96/31.97 cnf(p25, plain, convergent_lines(sk0,X0) | convergent_lines(sk1,X0), inference(resolution, [status(thm)], [c5, c14])).
% 10.96/31.97 cnf(p32, plain, convergent_lines(sk0,X0) | distinct_lines(sk1,X0), inference(resolution, [status(thm)], [p25, c13])).
% 10.96/31.97 cnf(p40, plain, distinct_lines(sk1,X0) | convergent_lines(sk0,X1) | convergent_lines(X0,X1), inference(resolution, [status(thm)], [p32, c5])).
% 10.96/31.97 fof(f2, axiom, ! [X] : ~ convergent_lines(X,X), file('/export/starexec/sandbox/benchmark/theBenchmark.p', apart3)).
% 10.96/31.97 fof(f2_nnf, plain, ! [X] : (~(convergent_lines(X,X))), inference(nnf_transformation, [status(thm)], [f2])).
% 10.96/31.97 fof(f2_sk, plain, ! [X] : (~(convergent_lines(X,X))), inference(skolemisation, [status(esa)], [f2_nnf])).
% 10.96/31.97 cnf(c2, plain, ~convergent_lines(X0,X0), inference(cnf_transformation, [status(esa)], [f2_sk])).
% 10.96/31.97 cnf(p172, plain, distinct_lines(sk1,X0) | convergent_lines(X0,sk0), inference(resolution, [status(thm)], [p40, c2])).
% 10.96/31.97 cnf(p186, plain, distinct_lines(sk1,X0) | distinct_lines(X0,sk0), inference(resolution, [status(thm)], [p172, c13])).
% 10.96/31.97 cnf(p465, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X0,sk0), inference(resolution, [status(thm)], [p68, p186])).
% 10.96/31.97 fof(sdef13, definition, (spl13 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X0,sk0))), introduced(definition, [new_symbols(naming, [spl13])], [avatar_definition])).
% 10.96/31.97 cnf(ssp11, plain, (spl3 | spl5 | spl13), inference(avatar_split_clause, [status(thm)], [p465, sdef3, sdef5, sdef13])).
% 10.96/31.97 cnf(p467, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk0) | distinct_lines(sk1,X0), inference(resolution, [status(thm)], [p68, p186])).
% 10.96/31.97 cnf(ssp12, plain, (spl2 | spl4 | spl9), inference(avatar_split_clause, [status(thm)], [p467, sdef2, sdef4, sdef9])).
% 10.96/31.97 cnf(p88, plain, distinct_lines(X0,sk1) | distinct_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p84, c4])).
% 10.96/31.97 cnf(p468, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk1) | distinct_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p68, p88])).
% 10.96/31.97 fof(sdef14, definition, (spl14 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk0,X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl14])], [avatar_definition])).
% 10.96/31.97 cnf(ssp13, plain, (spl3 | spl5 | spl14), inference(avatar_split_clause, [status(thm)], [p468, sdef3, sdef5, sdef14])).
% 10.96/31.97 cnf(p470, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X1,sk1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p68, p88])).
% 10.96/31.97 fof(sdef15, definition, (spl15 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X1,sk1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl15])], [avatar_definition])).
% 10.96/31.97 cnf(ssp14, plain, (spl2 | spl4 | spl15), inference(avatar_split_clause, [status(thm)], [p470, sdef2, sdef4, sdef15])).
% 10.96/31.97 cnf(p472, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X1) | distinct_lines(X0,sk1) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p68, p88])).
% 10.96/31.97 cnf(ssp15, plain, (spl6 | spl10), inference(avatar_split_clause, [status(thm)], [p472, sdef6, sdef10])).
% 10.96/31.97 cnf(p94, plain, distinct_lines(X0,sk2) | distinct_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p89, c4])).
% 10.96/31.97 cnf(p473, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X1,sk2) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p68, p94])).
% 10.96/31.97 fof(sdef16, definition, (spl16 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X1,sk2) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl16])], [avatar_definition])).
% 10.96/31.97 cnf(ssp16, plain, (spl3 | spl5 | spl16), inference(avatar_split_clause, [status(thm)], [p473, sdef3, sdef5, sdef16])).
% 10.96/31.97 cnf(p475, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X1) | distinct_lines(X0,sk2) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p68, p94])).
% 10.96/31.97 cnf(ssp17, plain, (spl9 | spl12), inference(avatar_split_clause, [status(thm)], [p475, sdef9, sdef12])).
% 10.96/31.97 cnf(p101, plain, distinct_lines(X0,sk2) | distinct_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p97, c4])).
% 10.96/31.97 cnf(p476, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X1,sk2) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p68, p101])).
% 10.96/31.97 cnf(ssp18, plain, (spl2 | spl4 | spl16), inference(avatar_split_clause, [status(thm)], [p476, sdef2, sdef4, sdef16])).
% 10.96/31.97 cnf(p477, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X1) | distinct_lines(X0,sk2) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p68, p101])).
% 10.96/31.97 cnf(ssp19, plain, (spl6 | spl12), inference(avatar_split_clause, [status(thm)], [p477, sdef6, sdef12])).
% 10.96/31.97 cnf(p33, plain, convergent_lines(sk0,X0) | convergent_lines(sk1,X1) | convergent_lines(X0,X1), inference(resolution, [status(thm)], [p25, c5])).
% 10.96/31.97 cnf(p105, plain, convergent_lines(sk0,X0) | convergent_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p33, c13])).
% 10.96/31.97 cnf(p478, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X1) | convergent_lines(sk0,X0) | convergent_lines(sk1,X1), inference(resolution, [status(thm)], [p68, p105])).
% 10.96/31.97 fof(sdef17, definition, (spl17 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | convergent_lines(sk0,X0))), introduced(definition, [new_symbols(naming, [spl17])], [avatar_definition])).
% 10.96/31.97 fof(sdef18, definition, (spl18 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | convergent_lines(sk1,X0))), introduced(definition, [new_symbols(naming, [spl18])], [avatar_definition])).
% 10.96/31.97 cnf(ssp20, plain, (spl17 | spl18), inference(avatar_split_clause, [status(thm)], [p478, sdef17, sdef18])).
% 10.96/31.97 cnf(p26, plain, convergent_lines(sk2,X0) | convergent_lines(sk1,X0), inference(resolution, [status(thm)], [c5, c15])).
% 10.96/31.97 cnf(p36, plain, convergent_lines(sk1,X0) | convergent_lines(sk2,X1) | convergent_lines(X0,X1), inference(resolution, [status(thm)], [p26, c5])).
% 10.96/31.97 cnf(p130, plain, convergent_lines(sk1,X0) | convergent_lines(sk2,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p36, c13])).
% 10.96/31.97 cnf(p481, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X1) | convergent_lines(sk1,X0) | convergent_lines(sk2,X1), inference(resolution, [status(thm)], [p68, p130])).
% 10.96/31.97 fof(sdef19, definition, (spl19 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | convergent_lines(sk2,X0))), introduced(definition, [new_symbols(naming, [spl19])], [avatar_definition])).
% 10.96/31.97 cnf(ssp21, plain, (spl18 | spl19), inference(avatar_split_clause, [status(thm)], [p481, sdef18, sdef19])).
% 10.96/31.97 cnf(p27, plain, convergent_lines(sk0,X0) | convergent_lines(sk2,X0), inference(resolution, [status(thm)], [c5, c16])).
% 10.96/31.97 cnf(p38, plain, convergent_lines(sk0,X0) | convergent_lines(sk2,X1) | convergent_lines(X0,X1), inference(resolution, [status(thm)], [p27, c5])).
% 10.96/31.97 cnf(p143, plain, convergent_lines(sk0,X0) | convergent_lines(sk2,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p38, c13])).
% 10.96/31.97 cnf(p483, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X1) | convergent_lines(sk0,X0) | convergent_lines(sk2,X1), inference(resolution, [status(thm)], [p68, p143])).
% 10.96/31.97 cnf(ssp22, plain, (spl17 | spl19), inference(avatar_split_clause, [status(thm)], [p483, sdef17, sdef19])).
% 10.96/31.97 cnf(p174, plain, distinct_lines(sk1,X0) | convergent_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p40, c13])).
% 10.96/31.97 cnf(p484, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | convergent_lines(sk0,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p68, p174])).
% 10.96/31.97 fof(sdef20, definition, (spl20 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | convergent_lines(sk0,X1) | distinct_lines(X0,X1))), introduced(definition, [new_symbols(naming, [spl20])], [avatar_definition])).
% 10.96/31.97 cnf(ssp23, plain, (spl3 | spl5 | spl20), inference(avatar_split_clause, [status(thm)], [p484, sdef3, sdef5, sdef20])).
% 10.96/31.97 cnf(p486, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X1) | distinct_lines(sk1,X0) | convergent_lines(sk0,X1), inference(resolution, [status(thm)], [p68, p174])).
% 10.96/31.97 cnf(ssp24, plain, (spl9 | spl17), inference(avatar_split_clause, [status(thm)], [p486, sdef9, sdef17])).
% 10.96/31.97 cnf(p189, plain, distinct_lines(X0,sk0) | distinct_lines(sk1,X1) | distinct_lines(X0,X1), inference(resolution, [status(thm)], [p186, c4])).
% 10.96/31.97 cnf(p487, plain, apart_point_and_line(intersection_point(sk0,sk1),sk1) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X1,sk0) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p68, p189])).
% 10.96/31.97 fof(sdef21, definition, (spl21 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(X1,sk0) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl21])], [avatar_definition])).
% 10.96/31.97 cnf(ssp25, plain, (spl3 | spl5 | spl21), inference(avatar_split_clause, [status(thm)], [p487, sdef3, sdef5, sdef21])).
% 10.96/31.97 cnf(p489, plain, apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk0,sk1),X1) | apart_point_and_line(intersection_point(sk2,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X1) | distinct_lines(X0,sk0) | distinct_lines(sk1,X1), inference(resolution, [status(thm)], [p68, p189])).
% 10.96/31.97 cnf(ssp26, plain, (spl9 | spl13), inference(avatar_split_clause, [status(thm)], [p489, sdef9, sdef13])).
% 10.96/31.97 cnf(p190, plain, distinct_lines(sk1,X0) | distinct_lines(X0,X1) | distinct_lines(sk0,X1), inference(resolution, [status(thm)], [p186, c4])).
% 10.96/31.97 cnf(p490, plain, apart_point_and_line(intersection_point(sk0,sk1),sk0) | apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),sk0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk1,X1) | distinct_lines(X1,X0), inference(resolution, [status(thm)], [p68, p190])).
% 10.96/31.97 fof(sdef22, definition, (spl22 <=> (apart_point_and_line(intersection_point(sk0,sk1),X0) | apart_point_and_line(intersection_point(sk2,sk1),X0) | distinct_lines(sk1,X1) | distinct_lines(X1,X0))), introduced(definition, [new_symbols(naming, [spl22])], [avatar_definition])).
% 10.96/31.97 cnf(ssp27, plain, (spl2 | spl4 | spl22), inference(avatar_split_clause, [status(thm)], [p490, sdef2, sdef4, sdef22])).
% 10.96/31.97 cnf(p60, plain, ~apart_point_and_line(X0,sk2) | distinct_points(X0,intersection_point(sk0,sk2)), inference(resolution, [status(thm)], [c9, c16])).
% 10.96/31.97 cnf(p69, plain, distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)), inference(resolution, [status(thm)], [p60, c17])).
% 10.96/31.97 cnf(p71, plain, ~apart_point_and_line(X0,line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))) | distinct_points(X0,intersection_point(sk0,sk1)), inference(resolution, [status(thm)], [p69, c6])).
% 10.96/31.97 cnf(p513, plain, distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk1)) | distinct_lines(sk2,line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))), inference(resolution, [status(thm)], [p71, p93])).
% 10.96/31.97 fof(sdef23, definition, (spl23 <=> (distinct_lines(sk2,line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))))), introduced(definition, [new_symbols(naming, [spl23])], [avatar_definition])).
% 10.96/31.97 cnf(ssp28, plain, (spl0 | spl23), inference(avatar_split_clause, [status(thm)], [p513, sdef0, sdef23])).
% 10.96/31.97 cnf(sat_ref, plain, $false, inference(avatar_sat_refutation, [status(thm)], [ssp0, ssp1, ssp2, ssp3, ssp4, ssp5, ssp6, ssp7, ssp8, ssp9, ssp10, ssp11, ssp12, ssp13, ssp14, ssp15, ssp16, ssp17, ssp18, ssp19, ssp20, ssp21, ssp22, ssp23, ssp24, ssp25, ssp26, ssp27, ssp28, sct0, sct1, sct2, sct3, sct4])).
% 10.96/31.97 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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