%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO036-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:23:51 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 16 unt; 3 def)
% Number of atoms : 55 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 24 ~; 18 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( lower_dimension_point_1 = lower_dimension_point_3
| lower_dimension_point_2 = lower_dimension_point_3
| lower_dimension_point_1 = lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f32,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( lower_dimension_point_1 = lower_dimension_point_3
| lower_dimension_point_2 = lower_dimension_point_3
| lower_dimension_point_1 = lower_dimension_point_2 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f43,definition,
( sQ0_spl
<=> lower_dimension_point_1 = lower_dimension_point_2 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ0_spl
| lower_dimension_point_1 = lower_dimension_point_2 ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,definition,
( sQ1_spl
<=> lower_dimension_point_2 = lower_dimension_point_3 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( ~ sQ1_spl
| lower_dimension_point_2 = lower_dimension_point_3 ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,definition,
( sQ2_spl
<=> lower_dimension_point_1 = lower_dimension_point_3 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ2_spl
| lower_dimension_point_1 = lower_dimension_point_3 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f43,f46,f49]) ).
fof(f54,plain,
( ~ sQ2_spl
| ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1) ),
inference(forward_demodulation,[status(thm)],[f50,f33]) ).
fof(f58,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f26,f24]) ).
fof(f61,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f58,f25]) ).
fof(f62,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f54,f61]) ).
fof(f64,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f62]) ).
fof(f65,plain,
( ~ sQ0_spl
| ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1) ),
inference(forward_demodulation,[status(thm)],[f44,f34]) ).
fof(f66,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f61]) ).
fof(f67,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f66]) ).
fof(f70,plain,
( ~ sQ1_spl
| ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2) ),
inference(forward_demodulation,[status(thm)],[f47,f32]) ).
fof(f71,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f61]) ).
fof(f72,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f71]) ).
fof(f73,plain,
$false,
inference(sat_refutation,[status(thm)],[f52,f64,f67,f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO036-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 08:28:57 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.050881 seconds
% 0.11/0.43 % CPU time: 0.153692 seconds
% 0.11/0.43 % Total memory used: 80.340 MB
% 0.11/0.43 % Net memory used: 79.921 MB
%------------------------------------------------------------------------------