%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO067-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:23:58 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.40s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 46 ( 15 unt; 5 def)
% Number of atoms : 91 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 84 ( 39 ~; 40 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 64 ( 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y,Z] :
( colinear(X,Y,Z)
| ~ between(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [Y,Z,X] :
( colinear(X,Y,Z)
| ~ between(Y,Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( colinear(X,Y,Z)
| ~ between(Z,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f47,plain,
! [X0,X1,X2] :
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
! [X0,X1,X2] :
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f49,plain,
! [X0,X1,X2] :
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f52,plain,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f53,definition,
( sQ0_spl
<=> colinear(x,x,y) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ0_spl
| ~ colinear(x,x,y) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ1_spl
<=> colinear(x,y,x) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( sQ1_spl
| ~ colinear(x,y,x) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,definition,
( sQ2_spl
<=> colinear(y,x,x) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( sQ2_spl
| ~ colinear(y,x,x) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,definition,
( sQ3_spl
<=> x = y ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( ~ sQ3_spl
| x = y ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,plain,
( sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f53,f56,f59,f62]) ).
fof(f66,definition,
( sQ4_spl
<=> colinear(x,z,y) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( sQ4_spl
| ~ colinear(x,z,y) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f53,f56,f59,f66]) ).
fof(f71,plain,
! [X0,X1,X2,X3] : colinear(X0,extension(X1,X0,X2,X3),X1),
inference(resolution,[status(thm)],[f30,f49]) ).
fof(f72,plain,
! [X0,X1,X2,X3] : colinear(extension(X0,X1,X2,X3),X0,X1),
inference(resolution,[status(thm)],[f30,f48]) ).
fof(f73,plain,
! [X0,X1,X2,X3] : colinear(X0,X1,extension(X0,X1,X2,X3)),
inference(resolution,[status(thm)],[f30,f47]) ).
fof(f77,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f31,f29]) ).
fof(f79,plain,
! [X0,X1] : colinear(X0,X1,X1),
inference(paramodulation,[status(thm)],[f77,f73]) ).
fof(f80,plain,
! [X0,X1] : colinear(X0,X1,X0),
inference(paramodulation,[status(thm)],[f77,f72]) ).
fof(f81,plain,
! [X0,X1] : colinear(X0,X0,X1),
inference(paramodulation,[status(thm)],[f77,f71]) ).
fof(f83,plain,
( sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f61,f79]) ).
fof(f85,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f83]) ).
fof(f93,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f80]) ).
fof(f94,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f93]) ).
fof(f95,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f81]) ).
fof(f96,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f95]) ).
fof(f97,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ colinear(y,z,y) ),
inference(forward_demodulation,[status(thm)],[f63,f68]) ).
fof(f98,plain,
( sQ4_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f80]) ).
fof(f99,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f98]) ).
fof(f100,plain,
$false,
inference(sat_refutation,[status(thm)],[f65,f69,f85,f94,f96,f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO067-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 09:28:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.16/0.38 % Drodi V4.1.1
% 0.16/0.40 % Refutation found
% 0.16/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.43 % Elapsed time: 0.052877 seconds
% 0.16/0.43 % CPU time: 0.152018 seconds
% 0.16/0.43 % Total memory used: 80.595 MB
% 0.16/0.43 % Net memory used: 80.304 MB
%------------------------------------------------------------------------------