%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO041-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:23:52 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 59 ( 20 unt; 7 def)
% Number of atoms : 113 ( 15 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 100 ( 46 ~; 47 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 62 ( 62 !; 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(f7,axiom,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
between(u,w,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
v != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
between(u,w,v),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
v != w,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f49,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f51,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f49,f27]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( X1 = inner_pasch(X0,X1,X2,X3,X1)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f32,f31]) ).
fof(f83,plain,
! [X0,X1,X2] :
( X1 = inner_pasch(X0,X1,X2,X2,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f75,f51]) ).
fof(f96,plain,
w = inner_pasch(u,w,v,v,w),
inference(resolution,[status(thm)],[f83,f45]) ).
fof(f97,plain,
v = inner_pasch(u,v,w,w,v),
inference(resolution,[status(thm)],[f83,f44]) ).
fof(f142,plain,
( between(v,w,u)
| ~ between(w,v,v)
| ~ between(u,w,v) ),
inference(paramodulation,[status(thm)],[f96,f33]) ).
fof(f144,definition,
( sQ0_spl
<=> between(u,w,v) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ0_spl
| ~ between(u,w,v) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
( sQ1_spl
<=> between(w,v,v) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( sQ1_spl
| ~ between(w,v,v) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,definition,
( sQ2_spl
<=> between(v,w,u) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ2_spl
| between(v,w,u) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f142,f144,f147,f150]) ).
fof(f158,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f51]) ).
fof(f159,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f160,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f45]) ).
fof(f161,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f164,plain,
! [X0] :
( ~ sQ2_spl
| v = inner_pasch(X0,v,u,w,v)
| ~ between(X0,v,u) ),
inference(resolution,[status(thm)],[f151,f75]) ).
fof(f166,plain,
( between(w,v,u)
| ~ between(v,w,w)
| ~ between(u,v,w) ),
inference(paramodulation,[status(thm)],[f97,f33]) ).
fof(f168,definition,
( sQ4_spl
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ4_spl
| ~ between(u,v,w) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ5_spl
<=> between(v,w,w) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( sQ5_spl
| ~ between(v,w,w) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
( sQ6_spl
<=> between(w,v,u) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ6_spl
| between(w,v,u) ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f166,f168,f171,f174]) ).
fof(f182,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f51]) ).
fof(f183,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f184,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f44]) ).
fof(f185,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f184]) ).
fof(f385,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| v = inner_pasch(w,v,u,w,v) ),
inference(resolution,[status(thm)],[f164,f175]) ).
fof(f387,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| between(w,v,w)
| ~ between(v,w,u)
| ~ between(w,v,u) ),
inference(paramodulation,[status(thm)],[f385,f33]) ).
fof(f389,definition,
( sQ21_spl
<=> between(w,v,w) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( ~ sQ21_spl
| between(w,v,w) ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f392,plain,
( sQ21_spl
| ~ sQ2_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f387,f174,f150,f389]) ).
fof(f401,plain,
( ~ sQ21_spl
| w = v ),
inference(resolution,[status(thm)],[f390,f31]) ).
fof(f403,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f46]) ).
fof(f404,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f403]) ).
fof(f405,plain,
$false,
inference(sat_refutation,[status(thm)],[f153,f159,f161,f177,f183,f185,f392,f404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO041-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n026.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sun Sep 20 08:37:13 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.38 % Drodi V4.1.1
% 0.13/5.42 % Refutation found
% 0.13/5.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.44 % Elapsed time: 0.071039 seconds
% 0.13/5.44 % CPU time: 0.295950 seconds
% 0.13/5.44 % Total memory used: 82.821 MB
% 0.13/5.44 % Net memory used: 82.208 MB
%------------------------------------------------------------------------------