%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO025-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:23:48 PM UTC 2026
% Result : Unsatisfiable 3.54s 0.90s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 79 ( 28 unt; 5 def)
% Number of atoms : 178 ( 22 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 200 ( 101 ~; 94 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 137 ( 137 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : equidistant(X,Y,Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
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(f6,axiom,
! [X,Y,X1,Y1,Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
between(u1,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ equidistant(u,w,u1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ! [X,Y] :
( ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
! [Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| ! [X,Y] :
( X = Y
| ! [X1,Y1] :
( ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( equidistant(X4,X6,X5,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f46,plain,
equidistant(u,v,u1,v1),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f47,plain,
equidistant(v,w,v1,w1),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f48,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f49,plain,
between(u1,v1,w1),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f50,plain,
~ equidistant(u,w,u1,w1),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( equidistant(X2,X3,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f26,f24]) ).
fof(f53,plain,
! [X0,X1] :
( equidistant(X0,X1,u1,v1)
| ~ equidistant(u,v,X0,X1) ),
inference(resolution,[status(thm)],[f46,f26]) ).
fof(f55,plain,
~ equidistant(w1,u1,u,w),
inference(resolution,[status(thm)],[f52,f50]) ).
fof(f57,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ equidistant(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f52,f28]) ).
fof(f60,plain,
~ equidistant(w,u,w1,u1),
inference(resolution,[status(thm)],[f55,f52]) ).
fof(f63,plain,
! [X0] :
( u1 = v1
| ~ equidistant(u,v,X0,X0) ),
inference(resolution,[status(thm)],[f53,f57]) ).
fof(f65,definition,
! [X0] :
( sQ0_spl
<=> ~ equidistant(u,v,X0,X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f66,plain,
! [X0] :
( ~ sQ0_spl
| ~ equidistant(u,v,X0,X0) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,definition,
( sQ1_spl
<=> u1 = v1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( ~ sQ1_spl
| u1 = v1 ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f65,f68]) ).
fof(f72,plain,
! [X0] :
( ~ sQ0_spl
| ~ equidistant(X0,X0,u,v) ),
inference(resolution,[status(thm)],[f66,f52]) ).
fof(f73,plain,
! [X0] :
( ~ sQ0_spl
| ~ equidistant(v,u,X0,X0) ),
inference(resolution,[status(thm)],[f72,f52]) ).
fof(f74,plain,
! [X0,X1,X2,X3,X4] :
( equidistant(X2,X3,w1,X4)
| X0 = X1
| ~ between(X0,X1,X2)
| ~ equidistant(X1,X3,v1,X4)
| ~ equidistant(X0,X3,u1,X4)
| ~ equidistant(X1,X2,v1,w1)
| ~ equidistant(X0,X1,u1,v1) ),
inference(resolution,[status(thm)],[f32,f49]) ).
fof(f86,plain,
! [X0] :
( ~ sQ0_spl
| ~ equidistant(X0,X0,v,u) ),
inference(resolution,[status(thm)],[f73,f52]) ).
fof(f89,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X4,X5,X2,X3)
| ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5) ),
inference(resolution,[status(thm)],[f30,f26]) ).
fof(f90,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f30,f28]) ).
fof(f104,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f89,f30]) ).
fof(f108,plain,
! [X0,X1,X2,X3] : equidistant(extension(X0,X1,X2,X3),X1,X2,X3),
inference(resolution,[status(thm)],[f89,f24]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f104,f26]) ).
fof(f115,plain,
! [X0,X1,X2,X3] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3),
inference(resolution,[status(thm)],[f111,f108]) ).
fof(f117,plain,
equidistant(u1,v1,u,v),
inference(resolution,[status(thm)],[f111,f46]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( ~ equidistant(X1,X0,X2,X3)
| equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f111,f52]) ).
fof(f154,plain,
equidistant(v1,u1,u,v),
inference(resolution,[status(thm)],[f122,f117]) ).
fof(f160,plain,
! [X0,X1,X2,X3] : equidistant(X0,X1,extension(X2,X3,X1,X0),X3),
inference(resolution,[status(thm)],[f122,f115]) ).
fof(f165,plain,
! [X0,X1,X2,X3] :
( ~ equidistant(X3,X2,X1,X0)
| equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f122,f52]) ).
fof(f177,definition,
( sQ8_spl
<=> u = v ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ8_spl
| u = v ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f201,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ equidistant(X0,X0,v,v) ),
inference(backward_demodulation,[status(thm)],[f178,f86]) ).
fof(f207,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(resolution,[status(thm)],[f201,f104]) ).
fof(f210,plain,
( ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f214,plain,
( ~ sQ1_spl
| equidistant(v1,v1,u,v) ),
inference(forward_demodulation,[status(thm)],[f69,f154]) ).
fof(f217,plain,
( ~ sQ1_spl
| u = v ),
inference(resolution,[status(thm)],[f214,f57]) ).
fof(f224,plain,
( ~ sQ1_spl
| ~ equidistant(u,w,v1,w1) ),
inference(forward_demodulation,[status(thm)],[f69,f50]) ).
fof(f227,plain,
( ~ sQ1_spl
| ~ equidistant(v,w,v1,w1) ),
inference(backward_demodulation,[status(thm)],[f217,f224]) ).
fof(f231,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f47]) ).
fof(f232,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f231]) ).
fof(f333,plain,
! [X0,X1,X2,X3] : equidistant(extension(X0,X1,X2,X3),X1,X3,X2),
inference(resolution,[status(thm)],[f160,f111]) ).
fof(f367,plain,
! [X0,X1,X2,X3] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f165,f111]) ).
fof(f734,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,w)
| ~ equidistant(X1,u,v1,u1)
| ~ equidistant(X0,u,u1,u1)
| ~ equidistant(X1,w,v1,w1)
| ~ equidistant(X0,X1,u1,v1) ),
inference(resolution,[status(thm)],[f74,f60]) ).
fof(f776,plain,
! [X0,X1] :
( extension(X0,u,u1,u1) = X1
| ~ between(extension(X0,u,u1,u1),X1,w)
| ~ equidistant(X1,u,v1,u1)
| ~ equidistant(X1,w,v1,w1)
| ~ equidistant(extension(X0,u,u1,u1),X1,u1,v1) ),
inference(resolution,[status(thm)],[f734,f333]) ).
fof(f792,plain,
! [X0,X1] :
( extension(X1,u,u1,u1) = X0
| ~ between(extension(X1,u,u1,u1),X0,w)
| ~ equidistant(X0,u,v1,u1)
| ~ equidistant(X0,w,v1,w1)
| ~ equidistant(u,X0,u1,v1) ),
inference(forward_demodulation,[status(thm)],[f90,f776]) ).
fof(f793,plain,
! [X0,X1] :
( extension(X1,u,u1,u1) = X0
| ~ between(u,X0,w)
| ~ equidistant(X0,u,v1,u1)
| ~ equidistant(X0,w,v1,w1)
| ~ equidistant(u,X0,u1,v1) ),
inference(forward_demodulation,[status(thm)],[f90,f792]) ).
fof(f794,plain,
! [X0] :
( u = X0
| ~ between(u,X0,w)
| ~ equidistant(X0,u,v1,u1)
| ~ equidistant(X0,w,v1,w1)
| ~ equidistant(u,X0,u1,v1) ),
inference(forward_demodulation,[status(thm)],[f90,f793]) ).
fof(f795,plain,
! [X0] :
( u = X0
| ~ between(u,X0,w)
| ~ equidistant(X0,w,v1,w1)
| ~ equidistant(u,X0,u1,v1) ),
inference(forward_subsumption_resolution,[status(thm)],[f794,f367]) ).
fof(f808,plain,
( u = v
| ~ between(u,v,w)
| ~ equidistant(u,v,u1,v1) ),
inference(resolution,[status(thm)],[f795,f47]) ).
fof(f816,definition,
( sQ23_spl
<=> equidistant(u,v,u1,v1) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f818,plain,
( sQ23_spl
| ~ equidistant(u,v,u1,v1) ),
inference(component_clause,[status(thm)],[f816]) ).
fof(f819,definition,
( sQ24_spl
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f821,plain,
( sQ24_spl
| ~ between(u,v,w) ),
inference(component_clause,[status(thm)],[f819]) ).
fof(f822,plain,
( sQ8_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f808,f816,f819,f177]) ).
fof(f823,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f818,f46]) ).
fof(f824,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f823]) ).
fof(f825,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f821,f48]) ).
fof(f826,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f825]) ).
fof(f827,plain,
$false,
inference(sat_refutation,[status(thm)],[f71,f210,f232,f822,f824,f826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO025-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 08:17:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 3.54/0.90 % Refutation found
% 3.54/0.90 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.54/0.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.92 % Elapsed time: 0.546411 seconds
% 0.27/0.92 % CPU time: 4.114828 seconds
% 0.27/0.92 % Total memory used: 111.209 MB
% 0.27/0.92 % Net memory used: 105.383 MB
%------------------------------------------------------------------------------