%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO177+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 12:24:18 PM UTC 2026
% Result : Theorem 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 69 ( 9 unt; 10 def)
% Number of atoms : 190 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 184 ( 63 ~; 92 |; 11 &)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 54 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X,Y,U,V] :
( ( distinct_points(U,V)
& distinct_points(X,Y) )
=> ( ( apart_point_and_line(Y,line_connecting(U,V))
| apart_point_and_line(X,line_connecting(U,V)) )
=> ( apart_point_and_line(V,line_connecting(X,Y))
| apart_point_and_line(U,line_connecting(X,Y)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,U,V] :
( ( distinct_points(U,V)
& distinct_points(X,Y) )
=> ( ( apart_point_and_line(Y,line_connecting(U,V))
| apart_point_and_line(X,line_connecting(U,V)) )
=> ( apart_point_and_line(V,line_connecting(X,Y))
| apart_point_and_line(U,line_connecting(X,Y)) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f29,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f37,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f42,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f48,plain,
? [X,Y,U,V] :
( ~ apart_point_and_line(V,line_connecting(X,Y))
& ~ apart_point_and_line(U,line_connecting(X,Y))
& ( apart_point_and_line(Y,line_connecting(U,V))
| apart_point_and_line(X,line_connecting(U,V)) )
& distinct_points(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( ~ apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))
& ~ apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))
& ( apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)) )
& distinct_points(sK2_skl,sK3_skl)
& distinct_points(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(U,sK2_skl),skolemize(V,sK3_skl)],[f48]) ).
fof(f50,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
distinct_points(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
( apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
~ apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
~ apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f55,definition,
( sQ0_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,definition,
( sQ1_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ1_spl
| apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f55,f58]) ).
fof(f65,plain,
! [X0,X1] :
( apart_point_and_line(sK3_skl,X1)
| apart_point_and_line(sK3_skl,X0)
| apart_point_and_line(sK2_skl,X1)
| apart_point_and_line(sK2_skl,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f38,f51]) ).
fof(f67,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,X0)
| distinct_lines(line_connecting(sK2_skl,sK3_skl),X0) ),
inference(resolution,[status(thm)],[f44,f56]) ).
fof(f83,definition,
( sQ3_spl
<=> distinct_points(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( sQ3_spl
| ~ distinct_points(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f91,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f51]) ).
fof(f92,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f91]) ).
fof(f98,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(sK3_skl,X0)
| apart_point_and_line(sK3_skl,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f67,f65]) ).
fof(f105,definition,
! [X0] :
( sQ6_spl
<=> ( apart_point_and_line(sK3_skl,X0)
| apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f106,plain,
! [X0] :
( ~ sQ6_spl
| apart_point_and_line(sK3_skl,X0)
| apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,definition,
( sQ7_spl
<=> apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( ~ sQ7_spl
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,definition,
( sQ8_spl
<=> apart_point_and_line(sK3_skl,line_connecting(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ8_spl
| apart_point_and_line(sK3_skl,line_connecting(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( ~ sQ0_spl
| sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f98,f105,f108,f111,f55]) ).
fof(f115,plain,
! [X0] :
( ~ sQ1_spl
| apart_point_and_line(sK1_skl,X0)
| distinct_lines(line_connecting(sK2_skl,sK3_skl),X0) ),
inference(resolution,[status(thm)],[f59,f44]) ).
fof(f121,plain,
! [X0] :
( ~ sQ1_spl
| apart_point_and_line(sK3_skl,X0)
| apart_point_and_line(sK3_skl,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK3_skl))
| apart_point_and_line(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f115,f65]) ).
fof(f128,definition,
! [X0] :
( sQ10_spl
<=> ( apart_point_and_line(sK3_skl,X0)
| apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK1_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f129,plain,
! [X0] :
( ~ sQ10_spl
| apart_point_and_line(sK3_skl,X0)
| apart_point_and_line(sK2_skl,X0)
| apart_point_and_line(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,plain,
( ~ sQ1_spl
| sQ8_spl
| sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f121,f128,f108,f111,f58]) ).
fof(f184,plain,
( ~ sQ8_spl
| ~ distinct_points(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f112,f32]) ).
fof(f187,plain,
( ~ sQ8_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f184,f83,f111]) ).
fof(f225,plain,
( ~ sQ7_spl
| ~ distinct_points(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f109,f30]) ).
fof(f228,plain,
( ~ sQ7_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f225,f83,f108]) ).
fof(f253,plain,
( ~ sQ10_spl
| apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f129,f53]) ).
fof(f264,definition,
( sQ21_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( ~ sQ21_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f267,definition,
( sQ22_spl
<=> apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( ~ sQ22_spl
| apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( ~ sQ10_spl
| sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f253,f264,f267,f128]) ).
fof(f339,plain,
( ~ sQ21_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f265,f32]) ).
fof(f342,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f50]) ).
fof(f343,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f342]) ).
fof(f344,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f268,f54]) ).
fof(f345,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f378,plain,
( ~ sQ6_spl
| apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f106,f53]) ).
fof(f390,definition,
( sQ30_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( ~ sQ30_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,plain,
( ~ sQ6_spl
| sQ22_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f378,f390,f267,f105]) ).
fof(f464,plain,
( ~ sQ30_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f391,f30]) ).
fof(f467,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f50]) ).
fof(f468,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f467]) ).
fof(f469,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f92,f114,f131,f187,f228,f270,f343,f345,f393,f468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO177+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 13:02:34 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.43 % Refutation found
% 0.12/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.082161 seconds
% 0.12/0.44 % CPU time: 0.417829 seconds
% 0.12/0.44 % Total memory used: 21.651 MB
% 0.12/0.44 % Net memory used: 20.536 MB
%------------------------------------------------------------------------------