%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO043-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:23:53 PM UTC 2026
% Result : Unsatisfiable 0.14s 10.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 59 ( 20 unt; 7 def)
% Number of atoms : 114 ( 13 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 102 ( 47 ~; 48 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-5 aty)
% Number of variables : 66 ( 66 !; 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,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ between(v,w,x),
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,x),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
~ between(v,w,x),
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(f55,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(f56,plain,
! [X0,X1,X2,X3] :
( X0 = inner_pasch(X0,X1,X2,X0,X3)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f33,f31]) ).
fof(f62,plain,
! [X0,X1,X2] :
( X1 = inner_pasch(X0,X1,X2,X2,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f55,f51]) ).
fof(f63,plain,
w = inner_pasch(u,w,x,x,w),
inference(resolution,[status(thm)],[f62,f45]) ).
fof(f64,plain,
v = inner_pasch(u,v,w,w,v),
inference(resolution,[status(thm)],[f62,f44]) ).
fof(f75,plain,
( between(x,w,u)
| ~ between(w,x,x)
| ~ between(u,w,x) ),
inference(paramodulation,[status(thm)],[f63,f33]) ).
fof(f77,definition,
( sQ0_spl
<=> between(u,w,x) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( sQ0_spl
| ~ between(u,w,x) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,definition,
( sQ1_spl
<=> between(w,x,x) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( sQ1_spl
| ~ between(w,x,x) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ2_spl
<=> between(x,w,u) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ2_spl
| between(x,w,u) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f75,f77,f80,f83]) ).
fof(f91,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f51]) ).
fof(f92,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f91]) ).
fof(f93,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f45]) ).
fof(f94,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f93]) ).
fof(f95,plain,
! [X0] :
( ~ sQ2_spl
| w = inner_pasch(w,X0,u,w,x)
| ~ between(w,X0,u) ),
inference(resolution,[status(thm)],[f84,f56]) ).
fof(f98,plain,
( between(w,v,u)
| ~ between(v,w,w)
| ~ between(u,v,w) ),
inference(paramodulation,[status(thm)],[f64,f33]) ).
fof(f100,definition,
( sQ4_spl
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( sQ4_spl
| ~ between(u,v,w) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,definition,
( sQ5_spl
<=> between(v,w,w) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( sQ5_spl
| ~ between(v,w,w) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,definition,
( sQ6_spl
<=> between(w,v,u) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ6_spl
| between(w,v,u) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f98,f100,f103,f106]) ).
fof(f114,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f51]) ).
fof(f115,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f116,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f44]) ).
fof(f117,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f135,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| w = inner_pasch(w,v,u,w,x) ),
inference(resolution,[status(thm)],[f95,f107]) ).
fof(f140,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| between(v,w,x)
| ~ between(x,w,u)
| ~ between(w,v,u) ),
inference(paramodulation,[status(thm)],[f135,f32]) ).
fof(f142,definition,
( sQ8_spl
<=> between(v,w,x) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( ~ sQ8_spl
| between(v,w,x) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ8_spl
| ~ sQ2_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f140,f106,f83,f142]) ).
fof(f146,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f46]) ).
fof(f147,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f146]) ).
fof(f148,plain,
$false,
inference(sat_refutation,[status(thm)],[f86,f92,f94,f109,f115,f117,f145,f147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO043-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n010.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Sun Sep 20 08:36:21 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.14/10.40 % Drodi V4.1.1
% 0.14/10.46 % Refutation found
% 0.14/10.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/10.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.50 % Elapsed time: 0.096768 seconds
% 0.14/10.50 % CPU time: 0.525267 seconds
% 0.14/10.50 % Total memory used: 87.852 MB
% 0.14/10.50 % Net memory used: 86.919 MB
%------------------------------------------------------------------------------