%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO048-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:23:54 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 55 ( 20 unt; 6 def)
% Number of atoms : 97 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 79 ( 37 ~; 36 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-5 aty)
% Number of variables : 64 ( 64 !; 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(u1,v1,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
between(u,x,u1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f29,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f34,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(f35,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(f46,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f47,plain,
between(u1,v1,w),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f48,plain,
between(u,x,u1),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f50,plain,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f51,plain,
! [X0,X1] :
( between(X1,inner_pasch(X0,X1,w,v,u),u)
| ~ between(X0,X1,w) ),
inference(resolution,[status(thm)],[f46,f34]) ).
fof(f52,plain,
! [X0,X1] :
( between(X1,inner_pasch(X0,X1,w,v1,u1),u1)
| ~ between(X0,X1,w) ),
inference(resolution,[status(thm)],[f47,f34]) ).
fof(f54,plain,
( ~ between(w,v,u)
| ~ between(v1,inner_pasch(u,x,u1,v1,w),u) ),
inference(resolution,[status(thm)],[f35,f50]) ).
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)],[f35,f33]) ).
fof(f57,definition,
( sQ0_spl
<=> between(v1,inner_pasch(u,x,u1,v1,w),u) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ0_spl
| ~ between(v1,inner_pasch(u,x,u1,v1,w),u) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,definition,
( sQ1_spl
<=> between(w,v,u) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f54,f57,f60]) ).
fof(f64,plain,
! [X0] :
( v1 = inner_pasch(v1,X0,w,v1,u1)
| ~ between(v1,X0,w) ),
inference(resolution,[status(thm)],[f56,f47]) ).
fof(f66,plain,
! [X0] :
( v = inner_pasch(v,X0,w,v,u)
| ~ between(v,X0,w) ),
inference(resolution,[status(thm)],[f56,f46]) ).
fof(f68,plain,
( sQ0_spl
| ~ between(w,v1,u1)
| ~ between(u,x,u1) ),
inference(resolution,[status(thm)],[f59,f35]) ).
fof(f69,definition,
( sQ2_spl
<=> between(u,x,u1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( sQ2_spl
| ~ between(u,x,u1) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,definition,
( sQ3_spl
<=> between(w,v1,u1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f68,f69,f72,f57]) ).
fof(f85,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f30,f28]) ).
fof(f133,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f85,f29]) ).
fof(f136,plain,
v1 = inner_pasch(v1,w,w,v1,u1),
inference(resolution,[status(thm)],[f133,f64]) ).
fof(f137,plain,
v = inner_pasch(v,w,w,v,u),
inference(resolution,[status(thm)],[f133,f66]) ).
fof(f179,plain,
( between(w,v1,u1)
| ~ between(v1,w,w) ),
inference(paramodulation,[status(thm)],[f136,f52]) ).
fof(f182,definition,
( sQ4_spl
<=> between(v1,w,w) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( sQ4_spl
| ~ between(v1,w,w) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f179,f182,f72]) ).
fof(f197,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f133]) ).
fof(f198,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f201,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f48]) ).
fof(f202,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f201]) ).
fof(f212,plain,
( between(w,v,u)
| ~ between(v,w,w) ),
inference(paramodulation,[status(thm)],[f137,f51]) ).
fof(f215,definition,
( sQ8_spl
<=> between(v,w,w) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( sQ8_spl
| ~ between(v,w,w) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( sQ1_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f212,f215,f60]) ).
fof(f230,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f217,f133]) ).
fof(f231,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f232,plain,
$false,
inference(sat_refutation,[status(thm)],[f63,f75,f185,f198,f202,f218,f231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 08:39:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.050539 seconds
% 0.10/0.42 % CPU time: 0.195708 seconds
% 0.10/0.42 % Total memory used: 82.418 MB
% 0.10/0.42 % Net memory used: 81.988 MB
%------------------------------------------------------------------------------