%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO052-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:23:55 PM UTC 2026
% Result : Unsatisfiable 5.42s 1.25s
% Output : CNFRefutation 5.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 26
% Syntax : Number of formulae : 100 ( 19 unt; 16 def)
% Number of atoms : 240 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 243 ( 103 ~; 124 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 17 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 68 ( 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45,axiom,
! [U,V] : between(U,V,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [U,V,W] :
( V = W
| ~ between(U,W,V)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U,V,W,X] :
( V = W
| between(U,W,X)
| ~ between(V,W,X)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [U,V,W,X] :
( between(V,X,W)
| between(V,W,X)
| U = V
| ~ between(U,V,X)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U,V,X,W] :
( between(U,W,V)
| between(U,V,W)
| ~ between(U,W,X)
| ~ between(U,V,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,hypothesis,
between(u,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,hypothesis,
between(u,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,hypothesis,
~ between(v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,negated_conjecture,
~ between(w,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f138,plain,
! [X0,X1] : between(X0,X1,X1),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f141,plain,
! [X0,X1,X2] :
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f145,plain,
! [V,W] :
( V = W
| ! [U] :
( ~ between(U,W,V)
| ~ between(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f146,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ between(X0,X2,X1)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f155,plain,
! [V,W] :
( V = W
| ! [U,X] :
( between(U,W,X)
| ~ between(V,W,X)
| ~ between(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| between(X0,X2,X3)
| ~ between(X1,X2,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f191,plain,
! [V,W,X] :
( between(V,X,W)
| between(V,W,X)
| ! [U] :
( U = V
| ~ between(U,V,X)
| ~ between(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f192,plain,
! [X0,X1,X2,X3] :
( between(X1,X3,X2)
| between(X1,X2,X3)
| X0 = X1
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f195,plain,
! [U,V,W] :
( between(U,W,V)
| between(U,V,W)
| ! [X] :
( ~ between(U,W,X)
| ~ between(U,V,X) ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f196,plain,
! [X0,X1,X2,X3] :
( between(X0,X3,X1)
| between(X0,X1,X3)
| ~ between(X0,X3,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f197,plain,
between(u,v,x),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f198,plain,
between(u,w,x),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f199,plain,
~ between(v,w,x),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f200,plain,
~ between(w,v,x),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f384,plain,
! [X0] :
( between(u,X0,v)
| between(u,v,X0)
| ~ between(u,X0,x) ),
inference(resolution,[status(thm)],[f197,f196]) ).
fof(f388,plain,
! [X0] :
( between(v,X0,x)
| between(v,x,X0)
| u = v
| ~ between(u,v,X0) ),
inference(resolution,[status(thm)],[f197,f192]) ).
fof(f396,plain,
! [X0] :
( v = x
| between(u,x,X0)
| ~ between(v,x,X0) ),
inference(resolution,[status(thm)],[f197,f156]) ).
fof(f398,plain,
( v = x
| ~ between(u,x,v) ),
inference(resolution,[status(thm)],[f197,f146]) ).
fof(f400,plain,
between(x,v,u),
inference(resolution,[status(thm)],[f197,f141]) ).
fof(f404,definition,
( sQ1_spl
<=> u = v ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f405,plain,
( ~ sQ1_spl
| u = v ),
inference(component_clause,[status(thm)],[f404]) ).
fof(f415,definition,
( sQ4_spl
<=> v = x ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( ~ sQ4_spl
| v = x ),
inference(component_clause,[status(thm)],[f415]) ).
fof(f419,definition,
! [X0] :
( sQ5_spl
<=> ( between(v,X0,x)
| between(v,x,X0)
| ~ between(u,v,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f420,plain,
! [X0] :
( ~ sQ5_spl
| between(v,X0,x)
| between(v,x,X0)
| ~ between(u,v,X0) ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,plain,
( sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f388,f419,f404]) ).
fof(f431,definition,
! [X0] :
( sQ8_spl
<=> ( between(u,x,X0)
| ~ between(v,x,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f432,plain,
! [X0] :
( ~ sQ8_spl
| between(u,x,X0)
| ~ between(v,x,X0) ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f434,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f396,f431,f415]) ).
fof(f435,definition,
( sQ9_spl
<=> between(u,x,v) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( sQ9_spl
| ~ between(u,x,v) ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,plain,
( sQ4_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f398,f435,f415]) ).
fof(f469,plain,
( ~ sQ4_spl
| ~ between(w,v,v) ),
inference(backward_demodulation,[status(thm)],[f416,f200]) ).
fof(f470,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f469,f138]) ).
fof(f471,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f470]) ).
fof(f498,plain,
( ~ sQ1_spl
| ~ between(u,w,x) ),
inference(backward_demodulation,[status(thm)],[f405,f199]) ).
fof(f506,plain,
! [X0] :
( between(w,X0,x)
| between(w,x,X0)
| u = w
| ~ between(u,w,X0) ),
inference(resolution,[status(thm)],[f198,f192]) ).
fof(f514,plain,
! [X0] :
( w = x
| between(u,x,X0)
| ~ between(w,x,X0) ),
inference(resolution,[status(thm)],[f198,f156]) ).
fof(f516,plain,
( w = x
| ~ between(u,x,w) ),
inference(resolution,[status(thm)],[f198,f146]) ).
fof(f522,definition,
( sQ13_spl
<=> u = w ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f523,plain,
( ~ sQ13_spl
| u = w ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f537,definition,
( sQ17_spl
<=> w = x ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f538,plain,
( ~ sQ17_spl
| w = x ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f541,definition,
! [X0] :
( sQ18_spl
<=> ( between(w,X0,x)
| between(w,x,X0)
| ~ between(u,w,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f542,plain,
! [X0] :
( ~ sQ18_spl
| between(w,X0,x)
| between(w,x,X0)
| ~ between(u,w,X0) ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f544,plain,
( sQ13_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f506,f541,f522]) ).
fof(f553,definition,
! [X0] :
( sQ21_spl
<=> ( between(u,x,X0)
| ~ between(w,x,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f554,plain,
! [X0] :
( ~ sQ21_spl
| between(u,x,X0)
| ~ between(w,x,X0) ),
inference(component_clause,[status(thm)],[f553]) ).
fof(f556,plain,
( sQ17_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f514,f553,f537]) ).
fof(f557,definition,
( sQ22_spl
<=> between(u,x,w) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f559,plain,
( sQ22_spl
| ~ between(u,x,w) ),
inference(component_clause,[status(thm)],[f557]) ).
fof(f560,plain,
( sQ17_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f516,f557,f537]) ).
fof(f612,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f198]) ).
fof(f613,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f612]) ).
fof(f616,plain,
( ~ sQ17_spl
| ~ between(v,w,w) ),
inference(forward_demodulation,[status(thm)],[f538,f199]) ).
fof(f617,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f616,f138]) ).
fof(f618,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f619,plain,
( ~ sQ13_spl
| ~ between(u,v,x) ),
inference(backward_demodulation,[status(thm)],[f523,f200]) ).
fof(f651,plain,
between(u,v,x),
inference(resolution,[status(thm)],[f400,f141]) ).
fof(f692,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f651,f619]) ).
fof(f693,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f692]) ).
fof(f1862,plain,
( between(u,w,v)
| between(u,v,w) ),
inference(resolution,[status(thm)],[f384,f198]) ).
fof(f1872,definition,
( sQ85_spl
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1873,plain,
( ~ sQ85_spl
| between(u,v,w) ),
inference(component_clause,[status(thm)],[f1872]) ).
fof(f1875,definition,
( sQ86_spl
<=> between(u,w,v) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1876,plain,
( ~ sQ86_spl
| between(u,w,v) ),
inference(component_clause,[status(thm)],[f1875]) ).
fof(f1878,plain,
( sQ86_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1862,f1872,f1875]) ).
fof(f3562,plain,
( ~ sQ86_spl
| ~ sQ18_spl
| between(w,v,x)
| between(w,x,v) ),
inference(resolution,[status(thm)],[f542,f1876]) ).
fof(f3569,definition,
( sQ200_spl
<=> between(w,x,v) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f3570,plain,
( ~ sQ200_spl
| between(w,x,v) ),
inference(component_clause,[status(thm)],[f3569]) ).
fof(f3572,definition,
( sQ201_spl
<=> between(w,v,x) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f3573,plain,
( ~ sQ201_spl
| between(w,v,x) ),
inference(component_clause,[status(thm)],[f3572]) ).
fof(f3575,plain,
( ~ sQ86_spl
| ~ sQ18_spl
| sQ201_spl
| sQ200_spl ),
inference(split_clause,[status(thm)],[f3562,f3569,f3572,f541,f1875]) ).
fof(f3661,plain,
( ~ sQ21_spl
| ~ sQ200_spl
| between(u,x,v) ),
inference(resolution,[status(thm)],[f3570,f554]) ).
fof(f3705,plain,
( ~ sQ21_spl
| ~ sQ200_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3661,f437]) ).
fof(f3706,plain,
( ~ sQ21_spl
| ~ sQ200_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f3705]) ).
fof(f3776,plain,
( ~ sQ5_spl
| ~ sQ85_spl
| between(v,w,x)
| between(v,x,w) ),
inference(resolution,[status(thm)],[f1873,f420]) ).
fof(f3822,definition,
( sQ209_spl
<=> between(v,x,w) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f3823,plain,
( ~ sQ209_spl
| between(v,x,w) ),
inference(component_clause,[status(thm)],[f3822]) ).
fof(f3825,definition,
( sQ210_spl
<=> between(v,w,x) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f3826,plain,
( ~ sQ210_spl
| between(v,w,x) ),
inference(component_clause,[status(thm)],[f3825]) ).
fof(f3828,plain,
( ~ sQ5_spl
| ~ sQ85_spl
| sQ210_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f3776,f3822,f3825,f1872,f419]) ).
fof(f4002,plain,
( ~ sQ8_spl
| ~ sQ209_spl
| between(u,x,w) ),
inference(resolution,[status(thm)],[f3823,f432]) ).
fof(f4048,plain,
( ~ sQ8_spl
| ~ sQ209_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4002,f559]) ).
fof(f4049,plain,
( ~ sQ8_spl
| ~ sQ209_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f4048]) ).
fof(f4050,plain,
( ~ sQ210_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3826,f199]) ).
fof(f4051,plain,
~ sQ210_spl,
inference(contradiction_clause,[status(thm)],[f4050]) ).
fof(f4052,plain,
( ~ sQ201_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3573,f200]) ).
fof(f4053,plain,
~ sQ201_spl,
inference(contradiction_clause,[status(thm)],[f4052]) ).
fof(f4054,plain,
$false,
inference(sat_refutation,[status(thm)],[f422,f434,f438,f471,f544,f556,f560,f613,f618,f693,f1878,f3575,f3706,f3828,f4049,f4051,f4053]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO052-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 08:45:36 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 5.42/1.25 % Refutation found
% 5.42/1.25 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.42/1.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.42/1.27 % Elapsed time: 0.895775 seconds
% 5.42/1.27 % CPU time: 6.775191 seconds
% 5.42/1.27 % Total memory used: 136.187 MB
% 5.42/1.27 % Net memory used: 130.003 MB
%------------------------------------------------------------------------------