%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO076-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 : Thu Sep 24 12:23:59 PM UTC 2026
% Result : Unsatisfiable 0.11s 5.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 34
% Syntax : Number of formulae : 126 ( 9 unt; 20 def)
% Number of atoms : 426 ( 94 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 531 ( 231 ~; 280 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 21 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Z1,Z2] :
( ~ point(Z2)
| ~ point(Z1)
| Z1 = Z2
| on(Z1,line_from_to(Z1,Z2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Z2,Z1] :
( ~ point(Z2)
| ~ point(Z1)
| Z1 = Z2
| on(Z2,line_from_to(Z1,Z2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Z1,Z2] :
( ~ point(Z2)
| ~ point(Z1)
| Z1 = Z2
| line(line_from_to(Z1,Z2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Z1,Y3,Z2,Y4] :
( ~ line(Y4)
| ~ line(Y3)
| ~ point(Z2)
| ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| Y3 = Y4
| ~ on(Z2,Y3)
| Z1 = Z2
| ~ on(Z1,Y3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y1] :
( ~ line(Y1)
| on(point_1_on_line(Y1),Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Y1] :
( ~ line(Y1)
| on(point_2_on_line(Y1),Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Y1] :
( ~ line(Y1)
| point(point_1_on_line(Y1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Y1] :
( ~ line(Y1)
| point(point_2_on_line(Y1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Y1] :
( ~ line(Y1)
| point_1_on_line(Y1) != point_2_on_line(Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y1] :
( ~ line(Y1)
| ~ on(point_not_on_line(Y1),Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Y1] :
( ~ line(Y1)
| point(point_not_on_line(Y1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
line(at_least_one_line),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,hypothesis,
point(a_point),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
! [Line] :
( on(a_point,Line)
| ~ line(Line) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,plain,
! [Z2] :
( ~ point(Z2)
| ! [Z1] :
( ~ point(Z1)
| Z1 = Z2
| on(Z1,line_from_to(Z1,Z2)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f35,plain,
! [X0,X1] :
( ~ point(X1)
| ~ point(X0)
| X0 = X1
| on(X0,line_from_to(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [Z2] :
( ~ point(Z2)
| ! [Z1] :
( ~ point(Z1)
| Z1 = Z2
| on(Z2,line_from_to(Z1,Z2)) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1] :
( ~ point(X0)
| ~ point(X1)
| X1 = X0
| on(X0,line_from_to(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [Z2] :
( ~ point(Z2)
| ! [Z1] :
( ~ point(Z1)
| Z1 = Z2
| line(line_from_to(Z1,Z2)) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f39,plain,
! [X0,X1] :
( ~ point(X1)
| ~ point(X0)
| X0 = X1
| line(line_from_to(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [Y4] :
( ~ line(Y4)
| ! [Y3] :
( ~ line(Y3)
| ! [Z2] :
( ~ point(Z2)
| ! [Z1] :
( ~ point(Z1)
| ~ on(Z2,Y4)
| ~ on(Z1,Y4)
| Y3 = Y4
| ~ on(Z2,Y3)
| Z1 = Z2
| ~ on(Z1,Y3) ) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ~ line(X3)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X0,X3)
| X1 = X3
| ~ on(X2,X1)
| X0 = X2
| ~ on(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0] :
( ~ line(X0)
| on(point_1_on_line(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f43,plain,
! [X0] :
( ~ line(X0)
| on(point_2_on_line(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f44,plain,
! [X0] :
( ~ line(X0)
| point(point_1_on_line(X0)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f45,plain,
! [X0] :
( ~ line(X0)
| point(point_2_on_line(X0)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f46,plain,
! [X0] :
( ~ line(X0)
| point_1_on_line(X0) != point_2_on_line(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f47,plain,
! [X0] :
( ~ line(X0)
| ~ on(point_not_on_line(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f48,plain,
! [X0] :
( ~ line(X0)
| point(point_not_on_line(X0)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f49,plain,
line(at_least_one_line),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f76,plain,
point(a_point),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f77,plain,
! [X0] :
( on(a_point,X0)
| ~ line(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,at_least_one_line)
| ~ on(X0,at_least_one_line)
| X1 = at_least_one_line
| ~ on(X2,X1)
| X0 = X2
| ~ on(X0,X1) ),
inference(resolution,[status(thm)],[f49,f41]) ).
fof(f80,plain,
! [X0,X1] :
( ~ line(X1)
| ~ point(X0)
| ~ on(a_point,at_least_one_line)
| ~ on(X0,at_least_one_line)
| X1 = at_least_one_line
| ~ on(a_point,X1)
| X0 = a_point
| ~ on(X0,X1) ),
inference(resolution,[status(thm)],[f79,f76]) ).
fof(f81,definition,
! [X0,X1] :
( sQ0_spl
<=> ( ~ line(X1)
| ~ point(X0)
| ~ on(X0,at_least_one_line)
| X1 = at_least_one_line
| ~ on(a_point,X1)
| X0 = a_point
| ~ on(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f82,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ line(X1)
| ~ point(X0)
| ~ on(X0,at_least_one_line)
| X1 = at_least_one_line
| ~ on(a_point,X1)
| X0 = a_point
| ~ on(X0,X1) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,definition,
( sQ1_spl
<=> on(a_point,at_least_one_line) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( sQ1_spl
| ~ on(a_point,at_least_one_line) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f80,f81,f84]) ).
fof(f88,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ line(X1)
| ~ point(X0)
| ~ on(X0,at_least_one_line)
| X1 = at_least_one_line
| X0 = a_point
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f77]) ).
fof(f97,plain,
( sQ1_spl
| ~ line(at_least_one_line) ),
inference(resolution,[status(thm)],[f86,f77]) ).
fof(f98,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f49]) ).
fof(f99,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f98]) ).
fof(f102,plain,
point_1_on_line(at_least_one_line) != point_2_on_line(at_least_one_line),
inference(resolution,[status(thm)],[f46,f49]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ point(X2)
| ~ point(X1)
| X1 = X2
| ~ point(X0)
| ~ on(X0,at_least_one_line)
| line_from_to(X1,X2) = at_least_one_line
| X0 = a_point
| ~ on(X0,line_from_to(X1,X2)) ),
inference(resolution,[status(thm)],[f88,f39]) ).
fof(f149,definition,
( sQ10_spl
<=> point_2_on_line(at_least_one_line) = a_point ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ10_spl
| point_2_on_line(at_least_one_line) = a_point ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,definition,
( sQ11_spl
<=> point(point_2_on_line(at_least_one_line)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( sQ11_spl
| ~ point(point_2_on_line(at_least_one_line)) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,definition,
( sQ12_spl
<=> line(at_least_one_line) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( sQ12_spl
| ~ line(at_least_one_line) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f159,definition,
( sQ13_spl
<=> point_1_on_line(at_least_one_line) = a_point ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ13_spl
| point_1_on_line(at_least_one_line) = a_point ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,definition,
( sQ14_spl
<=> point(point_1_on_line(at_least_one_line)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( sQ14_spl
| ~ point(point_1_on_line(at_least_one_line)) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f176,definition,
( sQ18_spl
<=> point(a_point) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( sQ18_spl
| ~ point(a_point) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f181,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f49]) ).
fof(f182,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f181]) ).
fof(f183,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f76]) ).
fof(f184,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f183]) ).
fof(f185,plain,
( ~ sQ10_spl
| point_1_on_line(at_least_one_line) != a_point ),
inference(backward_demodulation,[status(thm)],[f150,f102]) ).
fof(f194,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| a_point != a_point ),
inference(forward_demodulation,[status(thm)],[f160,f185]) ).
fof(f195,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f194]) ).
fof(f196,plain,
( ~ sQ10_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f195]) ).
fof(f197,plain,
( sQ11_spl
| ~ line(at_least_one_line) ),
inference(resolution,[status(thm)],[f154,f45]) ).
fof(f198,plain,
( sQ11_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f197,f155,f152]) ).
fof(f206,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ line(at_least_one_line)
| ~ point(X1)
| ~ point(X0)
| X0 = X1
| ~ point(point_2_on_line(at_least_one_line))
| line_from_to(X0,X1) = at_least_one_line
| point_2_on_line(at_least_one_line) = a_point
| ~ on(point_2_on_line(at_least_one_line),line_from_to(X0,X1)) ),
inference(resolution,[status(thm)],[f123,f43]) ).
fof(f207,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ line(at_least_one_line)
| ~ point(X1)
| ~ point(X0)
| X0 = X1
| ~ point(point_1_on_line(at_least_one_line))
| line_from_to(X0,X1) = at_least_one_line
| point_1_on_line(at_least_one_line) = a_point
| ~ on(point_1_on_line(at_least_one_line),line_from_to(X0,X1)) ),
inference(resolution,[status(thm)],[f123,f42]) ).
fof(f215,definition,
! [X0,X1] :
( sQ20_spl
<=> ( ~ point(X1)
| ~ point(X0)
| X0 = X1
| line_from_to(X0,X1) = at_least_one_line
| ~ on(point_2_on_line(at_least_one_line),line_from_to(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f216,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ point(X1)
| ~ point(X0)
| X0 = X1
| line_from_to(X0,X1) = at_least_one_line
| ~ on(point_2_on_line(at_least_one_line),line_from_to(X0,X1)) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sQ10_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f206,f215,f149,f152,f155,f81]) ).
fof(f219,definition,
! [X0,X1] :
( sQ21_spl
<=> ( ~ point(X1)
| ~ point(X0)
| X0 = X1
| line_from_to(X0,X1) = at_least_one_line
| ~ on(point_1_on_line(at_least_one_line),line_from_to(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f220,plain,
! [X0,X1] :
( ~ sQ21_spl
| ~ point(X1)
| ~ point(X0)
| X0 = X1
| line_from_to(X0,X1) = at_least_one_line
| ~ on(point_1_on_line(at_least_one_line),line_from_to(X0,X1)) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| sQ13_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f207,f219,f159,f162,f155,f81]) ).
fof(f232,plain,
( sQ14_spl
| ~ line(at_least_one_line) ),
inference(resolution,[status(thm)],[f164,f44]) ).
fof(f233,plain,
( sQ14_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f232,f155,f162]) ).
fof(f234,plain,
! [X0] :
( ~ sQ20_spl
| ~ point(point_2_on_line(at_least_one_line))
| ~ point(X0)
| X0 = point_2_on_line(at_least_one_line)
| ~ point(point_2_on_line(at_least_one_line))
| ~ point(X0)
| X0 = point_2_on_line(at_least_one_line)
| line_from_to(X0,point_2_on_line(at_least_one_line)) = at_least_one_line ),
inference(resolution,[status(thm)],[f216,f37]) ).
fof(f236,definition,
! [X0] :
( sQ24_spl
<=> ( ~ point(X0)
| X0 = point_2_on_line(at_least_one_line)
| ~ point(X0)
| X0 = point_2_on_line(at_least_one_line)
| line_from_to(X0,point_2_on_line(at_least_one_line)) = at_least_one_line ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f237,plain,
! [X0] :
( ~ sQ24_spl
| ~ point(X0)
| X0 = point_2_on_line(at_least_one_line)
| ~ point(X0)
| X0 = point_2_on_line(at_least_one_line)
| line_from_to(X0,point_2_on_line(at_least_one_line)) = at_least_one_line ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f239,plain,
( ~ sQ20_spl
| ~ sQ11_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f234,f236,f152,f215]) ).
fof(f244,plain,
! [X0] :
( ~ sQ24_spl
| ~ point(X0)
| X0 = point_2_on_line(at_least_one_line)
| line_from_to(X0,point_2_on_line(at_least_one_line)) = at_least_one_line ),
inference(duplicate_literals_removal,[status(thm)],[f237]) ).
fof(f248,plain,
! [X0] :
( ~ sQ24_spl
| ~ line(X0)
| point_not_on_line(X0) = point_2_on_line(at_least_one_line)
| line_from_to(point_not_on_line(X0),point_2_on_line(at_least_one_line)) = at_least_one_line ),
inference(resolution,[status(thm)],[f244,f48]) ).
fof(f325,definition,
( sQ35_spl
<=> on(point_1_on_line(at_least_one_line),at_least_one_line) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( ~ sQ35_spl
| on(point_1_on_line(at_least_one_line),at_least_one_line) ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f383,plain,
( ~ sQ24_spl
| point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)
| line_from_to(point_not_on_line(at_least_one_line),point_2_on_line(at_least_one_line)) = at_least_one_line ),
inference(resolution,[status(thm)],[f248,f49]) ).
fof(f384,definition,
( sQ38_spl
<=> line_from_to(point_not_on_line(at_least_one_line),point_2_on_line(at_least_one_line)) = at_least_one_line ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( ~ sQ38_spl
| line_from_to(point_not_on_line(at_least_one_line),point_2_on_line(at_least_one_line)) = at_least_one_line ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,definition,
( sQ39_spl
<=> point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f388,plain,
( ~ sQ39_spl
| point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line) ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,plain,
( ~ sQ24_spl
| sQ39_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f383,f384,f387,f236]) ).
fof(f394,plain,
( ~ sQ38_spl
| ~ point(point_2_on_line(at_least_one_line))
| ~ point(point_not_on_line(at_least_one_line))
| point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)
| on(point_not_on_line(at_least_one_line),at_least_one_line) ),
inference(paramodulation,[status(thm)],[f385,f35]) ).
fof(f395,definition,
( sQ40_spl
<=> point(point_not_on_line(at_least_one_line)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( ~ sQ40_spl
| point(point_not_on_line(at_least_one_line)) ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f397,plain,
( sQ40_spl
| ~ point(point_not_on_line(at_least_one_line)) ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f404,definition,
( sQ42_spl
<=> on(point_not_on_line(at_least_one_line),at_least_one_line) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f405,plain,
( ~ sQ42_spl
| on(point_not_on_line(at_least_one_line),at_least_one_line) ),
inference(component_clause,[status(thm)],[f404]) ).
fof(f407,plain,
( ~ sQ38_spl
| ~ sQ11_spl
| ~ sQ40_spl
| sQ39_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f394,f404,f387,f395,f152,f384]) ).
fof(f418,plain,
( ~ sQ39_spl
| ~ line(at_least_one_line)
| on(point_not_on_line(at_least_one_line),at_least_one_line) ),
inference(paramodulation,[status(thm)],[f388,f43]) ).
fof(f425,plain,
( ~ sQ39_spl
| ~ sQ12_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f418,f404,f155,f387]) ).
fof(f438,plain,
( sQ40_spl
| ~ line(at_least_one_line) ),
inference(resolution,[status(thm)],[f397,f48]) ).
fof(f439,plain,
( sQ40_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f438,f155,f395]) ).
fof(f524,plain,
( ~ sQ42_spl
| ~ line(at_least_one_line) ),
inference(resolution,[status(thm)],[f405,f47]) ).
fof(f527,plain,
( ~ sQ42_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f524,f155,f404]) ).
fof(f660,definition,
( sQ68_spl
<=> point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f661,plain,
( ~ sQ68_spl
| point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line) ),
inference(component_clause,[status(thm)],[f660]) ).
fof(f686,plain,
! [X0] :
( ~ sQ21_spl
| ~ point(point_1_on_line(at_least_one_line))
| ~ point(X0)
| X0 = point_1_on_line(at_least_one_line)
| ~ point(point_1_on_line(at_least_one_line))
| ~ point(X0)
| X0 = point_1_on_line(at_least_one_line)
| line_from_to(X0,point_1_on_line(at_least_one_line)) = at_least_one_line ),
inference(resolution,[status(thm)],[f220,f37]) ).
fof(f688,definition,
! [X0] :
( sQ72_spl
<=> ( ~ point(X0)
| X0 = point_1_on_line(at_least_one_line)
| ~ point(X0)
| X0 = point_1_on_line(at_least_one_line)
| line_from_to(X0,point_1_on_line(at_least_one_line)) = at_least_one_line ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f689,plain,
! [X0] :
( ~ sQ72_spl
| ~ point(X0)
| X0 = point_1_on_line(at_least_one_line)
| ~ point(X0)
| X0 = point_1_on_line(at_least_one_line)
| line_from_to(X0,point_1_on_line(at_least_one_line)) = at_least_one_line ),
inference(component_clause,[status(thm)],[f688]) ).
fof(f691,plain,
( ~ sQ21_spl
| ~ sQ14_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f686,f688,f162,f219]) ).
fof(f696,plain,
! [X0] :
( ~ sQ72_spl
| ~ point(X0)
| X0 = point_1_on_line(at_least_one_line)
| line_from_to(X0,point_1_on_line(at_least_one_line)) = at_least_one_line ),
inference(duplicate_literals_removal,[status(thm)],[f689]) ).
fof(f702,plain,
( ~ sQ40_spl
| ~ sQ72_spl
| point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)
| line_from_to(point_not_on_line(at_least_one_line),point_1_on_line(at_least_one_line)) = at_least_one_line ),
inference(resolution,[status(thm)],[f696,f396]) ).
fof(f707,plain,
( ~ sQ72_spl
| a_point = point_1_on_line(at_least_one_line)
| line_from_to(a_point,point_1_on_line(at_least_one_line)) = at_least_one_line ),
inference(resolution,[status(thm)],[f696,f76]) ).
fof(f712,definition,
( sQ75_spl
<=> line_from_to(point_not_on_line(at_least_one_line),point_1_on_line(at_least_one_line)) = at_least_one_line ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f713,plain,
( ~ sQ75_spl
| line_from_to(point_not_on_line(at_least_one_line),point_1_on_line(at_least_one_line)) = at_least_one_line ),
inference(component_clause,[status(thm)],[f712]) ).
fof(f715,plain,
( ~ sQ40_spl
| ~ sQ72_spl
| sQ68_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f702,f712,f660,f688,f395]) ).
fof(f720,definition,
( sQ77_spl
<=> line_from_to(a_point,point_1_on_line(at_least_one_line)) = at_least_one_line ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f721,plain,
( ~ sQ77_spl
| line_from_to(a_point,point_1_on_line(at_least_one_line)) = at_least_one_line ),
inference(component_clause,[status(thm)],[f720]) ).
fof(f723,plain,
( ~ sQ72_spl
| sQ13_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f707,f720,f159,f688]) ).
fof(f727,plain,
( ~ sQ35_spl
| ~ sQ68_spl
| on(point_not_on_line(at_least_one_line),at_least_one_line) ),
inference(backward_demodulation,[status(thm)],[f661,f326]) ).
fof(f735,plain,
( ~ sQ35_spl
| ~ sQ68_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f727,f404,f660,f325]) ).
fof(f754,plain,
( ~ sQ77_spl
| ~ point(point_1_on_line(at_least_one_line))
| ~ point(a_point)
| a_point = point_1_on_line(at_least_one_line)
| on(point_1_on_line(at_least_one_line),at_least_one_line) ),
inference(paramodulation,[status(thm)],[f721,f37]) ).
fof(f766,plain,
( ~ sQ77_spl
| ~ sQ14_spl
| ~ sQ18_spl
| sQ13_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f754,f325,f159,f176,f162,f720]) ).
fof(f777,plain,
( ~ sQ75_spl
| ~ point(point_1_on_line(at_least_one_line))
| ~ point(point_not_on_line(at_least_one_line))
| point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)
| on(point_not_on_line(at_least_one_line),at_least_one_line) ),
inference(paramodulation,[status(thm)],[f713,f35]) ).
fof(f789,plain,
( ~ sQ75_spl
| ~ sQ14_spl
| ~ sQ40_spl
| sQ68_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f777,f404,f660,f395,f162,f712]) ).
fof(f790,plain,
$false,
inference(sat_refutation,[status(thm)],[f87,f99,f182,f184,f196,f198,f218,f222,f233,f239,f390,f407,f425,f439,f527,f691,f715,f723,f735,f766,f789]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO076-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.35 % Computer : n012.cluster.edu
% 0.08/5.35 % Model : x86_64 x86_64
% 0.08/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.35 % Memory : 8046.5625MB
% 0.08/5.35 % OS : Linux 6.8.0-71-generic
% 0.08/5.35 % CPULimit : 300
% 0.08/5.35 % WCLimit : 300
% 0.08/5.35 % DateTime : Sun Sep 20 09:52:12 UTC 2026
% 0.08/5.35 % CPUTime :
% 0.08/5.36 % Drodi V4.1.1
% 0.11/5.40 % Refutation found
% 0.11/5.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/5.41 % Elapsed time: 0.054293 seconds
% 0.11/5.41 % CPU time: 0.261494 seconds
% 0.11/5.41 % Total memory used: 87.853 MB
% 0.11/5.41 % Net memory used: 86.976 MB
%------------------------------------------------------------------------------