%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO180+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 : n010.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 12:24:19 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 61 ( 5 unt; 7 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 153 ( 57 ~; 73 |; 7 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 61 !; 6 ?)
% 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(f12,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
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,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(X,line_connecting(Z,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(X,line_connecting(Z,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(f39,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
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,Z] :
( ~ apart_point_and_line(X,line_connecting(Z,Y))
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
? [X,Y] :
( ? [Z] :
( ~ apart_point_and_line(X,line_connecting(Z,Y))
& apart_point_and_line(Z,line_connecting(X,Y)) )
& distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
( ~ apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK1_skl))
& apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))
& distinct_points(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f49]) ).
fof(f51,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
~ apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,plain,
! [X0] :
( apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| distinct_points(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f41,f52]) ).
fof(f59,plain,
! [X0,X1] :
( apart_point_and_line(sK1_skl,X1)
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK0_skl,X1)
| apart_point_and_line(sK0_skl,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f38,f51]) ).
fof(f60,plain,
! [X0] :
( apart_point_and_line(sK2_skl,X0)
| distinct_lines(line_connecting(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f44,f52]) ).
fof(f63,plain,
( ~ distinct_points(sK0_skl,sK1_skl)
| distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f55,f32]) ).
fof(f67,definition,
( sQ0_spl
<=> distinct_points(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ0_spl
| distinct_points(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,definition,
( sQ1_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( sQ1_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f67,f70]) ).
fof(f78,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f51]) ).
fof(f79,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0] :
( apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f60,f59]) ).
fof(f83,definition,
! [X0] :
( sQ3_spl
<=> ( apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK2_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f84,plain,
! [X0] :
( ~ sQ3_spl
| apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(sK2_skl,X0) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,definition,
( sQ4_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( ~ sQ4_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,definition,
( sQ5_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f80,f83,f86,f89]) ).
fof(f109,plain,
( ~ sQ5_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f90,f32]) ).
fof(f112,plain,
( ~ sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f109,f70,f89]) ).
fof(f159,plain,
( ~ sQ4_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f87,f30]) ).
fof(f162,plain,
( ~ sQ4_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f159,f70,f86]) ).
fof(f163,plain,
( ~ sQ3_spl
| apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl))
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f84,f53]) ).
fof(f173,definition,
( sQ13_spl
<=> apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ13_spl
| apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,definition,
( sQ14_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( ~ sQ14_spl
| apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,plain,
( ~ sQ3_spl
| sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f163,f173,f176,f83]) ).
fof(f256,plain,
( ~ sQ13_spl
| ~ distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f174,f30]) ).
fof(f259,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f68]) ).
fof(f260,plain,
( ~ sQ13_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f338,plain,
( ~ sQ14_spl
| ~ distinct_points(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f177,f32]) ).
fof(f341,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f68]) ).
fof(f342,plain,
( ~ sQ14_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f341]) ).
fof(f343,plain,
$false,
inference(sat_refutation,[status(thm)],[f73,f79,f92,f112,f162,f179,f260,f342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO180+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 13:07:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.074609 seconds
% 0.13/0.44 % CPU time: 0.382418 seconds
% 0.13/0.44 % Total memory used: 20.961 MB
% 0.13/0.44 % Net memory used: 19.945 MB
%------------------------------------------------------------------------------