%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO011-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:23:45 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 55 ( 18 unt; 4 def)
% Number of atoms : 104 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 95 ( 46 ~; 45 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 76 ( 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,W,V,Y,Z] :
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,W,V,Y,Z] :
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,Z] :
( between(X,Z,Y)
| between(Y,X,Z)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f32,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f33,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4] :
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f44,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f45,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f46,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f47,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
! [X0,X1,X2] :
( between(X0,X2,X1)
| between(X1,X0,X2)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f57,plain,
( between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolution,[status(thm)],[f52,f56]) ).
fof(f58,definition,
( sQ0_spl
<=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ0_spl
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,definition,
( sQ1_spl
<=> between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ1_spl
| between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,definition,
( sQ2_spl
<=> between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ2_spl
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f58,f61,f64]) ).
fof(f88,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f44,f33]) ).
fof(f93,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f88,f43]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( between(X0,outer_pasch(X1,X0,X3,X2,X2),X3)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f36,f93]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( between(X2,X1,outer_pasch(X1,X0,X3,X2,X2))
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f37,f93]) ).
fof(f136,plain,
! [X0,X1] :
( ~ sQ1_spl
| between(lower_dimension_point_3,X1,outer_pasch(X1,X0,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1))
| ~ between(X0,X1,lower_dimension_point_1) ),
inference(resolution,[status(thm)],[f62,f37]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sQ1_spl
| between(X0,outer_pasch(X1,X0,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),lower_dimension_point_2)
| ~ between(X0,X1,lower_dimension_point_1) ),
inference(resolution,[status(thm)],[f62,f36]) ).
fof(f160,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f45]) ).
fof(f161,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f194,definition,
( sQ13_spl
<=> between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( ~ sQ13_spl
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f283,plain,
! [X0] :
( ~ sQ1_spl
| between(lower_dimension_point_3,lower_dimension_point_1,outer_pasch(lower_dimension_point_1,X0,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)) ),
inference(resolution,[status(thm)],[f136,f93]) ).
fof(f300,plain,
! [X0] :
( ~ sQ1_spl
| between(X0,outer_pasch(lower_dimension_point_1,X0,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),lower_dimension_point_2) ),
inference(resolution,[status(thm)],[f137,f93]) ).
fof(f547,plain,
( ~ sQ1_spl
| lower_dimension_point_2 = outer_pasch(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
inference(resolution,[status(thm)],[f300,f26]) ).
fof(f553,plain,
( ~ sQ1_spl
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
inference(paramodulation,[status(thm)],[f547,f283]) ).
fof(f554,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f553,f47]) ).
fof(f555,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f556,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f46]) ).
fof(f557,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f556]) ).
fof(f560,plain,
! [X0] :
( ~ sQ2_spl
| between(lower_dimension_point_2,lower_dimension_point_3,outer_pasch(lower_dimension_point_3,lower_dimension_point_1,X0,lower_dimension_point_2,lower_dimension_point_2)) ),
inference(resolution,[status(thm)],[f65,f129]) ).
fof(f561,plain,
! [X0] :
( ~ sQ2_spl
| between(lower_dimension_point_1,outer_pasch(lower_dimension_point_3,lower_dimension_point_1,X0,lower_dimension_point_2,lower_dimension_point_2),X0) ),
inference(resolution,[status(thm)],[f65,f127]) ).
fof(f637,plain,
( ~ sQ2_spl
| lower_dimension_point_1 = outer_pasch(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2) ),
inference(resolution,[status(thm)],[f561,f26]) ).
fof(f903,plain,
( ~ sQ2_spl
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
inference(paramodulation,[status(thm)],[f637,f560]) ).
fof(f920,plain,
( ~ sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f903,f194,f64]) ).
fof(f921,plain,
$false,
inference(sat_refutation,[status(thm)],[f67,f161,f555,f557,f920]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO011-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n003.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sun Sep 20 08:18:20 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.13/5.44 % Refutation found
% 0.13/5.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.46 % Elapsed time: 0.093444 seconds
% 0.13/5.46 % CPU time: 0.526315 seconds
% 0.13/5.46 % Total memory used: 87.845 MB
% 0.13/5.46 % Net memory used: 86.795 MB
%------------------------------------------------------------------------------