%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW425-1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 03:07:50 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 11 unt; 6 def)
% Number of atoms : 111 ( 44 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 107 ( 49 ~; 52 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [S,T,Sigma] : sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Sigma] : sep(lseg(X,X),Sigma) = Sigma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z,Sigma] :
( X = Z
| X = Y
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
x1 != x10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
x2 != x7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x10),sep(lseg(x2,x1),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x3,x10),sep(lseg(x6,x9),emp))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X0,X1,X2] : sep(X0,sep(X1,X2)) = sep(X1,sep(X0,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0,X1] : sep(lseg(X0,X0),X1) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f33,plain,
! [X,Z] :
( X = Z
| ! [Y] :
( X = Y
| ! [Sigma] : ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| X0 = X1
| ~ heap(sep(lseg(X0,X1),sep(lseg(X0,X2),X3))) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f45,plain,
x1 != x10,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f53,plain,
x2 != x7,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f54,plain,
heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x10),sep(lseg(x2,x1),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x3,x10),sep(lseg(x6,x9),emp))))))))),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f76,plain,
! [X0,X1,X2,X3,X4] :
( X0 = X3
| X0 = X1
| ~ heap(sep(lseg(X0,X1),sep(X2,sep(lseg(X0,X3),X4)))) ),
inference(paramodulation,[status(thm)],[f25,f34]) ).
fof(f83,plain,
! [X0,X1,X2,X3,X4] :
( X1 = X3
| X1 = X2
| ~ heap(sep(X0,sep(lseg(X1,X2),sep(lseg(X1,X3),X4)))) ),
inference(paramodulation,[status(thm)],[f25,f76]) ).
fof(f87,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = X4
| X0 = X1
| ~ heap(sep(lseg(X0,X1),sep(X2,sep(X3,sep(lseg(X0,X4),X5))))) ),
inference(paramodulation,[status(thm)],[f25,f76]) ).
fof(f89,plain,
( x2 = x10
| x2 = x5 ),
inference(resolution,[status(thm)],[f83,f54]) ).
fof(f96,definition,
( sQ2_spl
<=> x2 = x5 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ2_spl
| x2 = x5 ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,definition,
( sQ3_spl
<=> x2 = x10 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ3_spl
| x2 = x10 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f89,f96,f99]) ).
fof(f103,plain,
( ~ sQ2_spl
| heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x10),sep(lseg(x5,x1),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x3,x10),sep(lseg(x6,x9),emp))))))))) ),
inference(backward_demodulation,[status(thm)],[f97,f54]) ).
fof(f104,plain,
( ~ sQ2_spl
| heap(sep(lseg(x5,x7),sep(lseg(x5,x5),sep(lseg(x2,x10),sep(lseg(x5,x1),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x3,x10),sep(lseg(x6,x9),emp))))))))) ),
inference(forward_demodulation,[status(thm)],[f97,f103]) ).
fof(f105,plain,
( ~ sQ2_spl
| heap(sep(lseg(x5,x7),sep(lseg(x5,x5),sep(lseg(x5,x10),sep(lseg(x5,x1),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x3,x10),sep(lseg(x6,x9),emp))))))))) ),
inference(forward_demodulation,[status(thm)],[f97,f104]) ).
fof(f123,plain,
( ~ sQ2_spl
| x5 = x10
| x5 = x7 ),
inference(resolution,[status(thm)],[f105,f76]) ).
fof(f124,plain,
( ~ sQ2_spl
| x5 = x1
| x5 = x7 ),
inference(resolution,[status(thm)],[f105,f87]) ).
fof(f131,definition,
( sQ4_spl
<=> x5 = x7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ4_spl
| x5 = x7 ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f138,definition,
( sQ6_spl
<=> x5 = x10 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ6_spl
| x5 = x10 ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,plain,
( ~ sQ2_spl
| sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f123,f131,f138,f96]) ).
fof(f142,definition,
( sQ7_spl
<=> x5 = x1 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( ~ sQ7_spl
| x5 = x1 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( ~ sQ2_spl
| sQ7_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f124,f131,f142,f96]) ).
fof(f167,plain,
( ~ sQ2_spl
| x5 != x7 ),
inference(forward_demodulation,[status(thm)],[f97,f53]) ).
fof(f168,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f167]) ).
fof(f169,plain,
( ~ sQ4_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( ~ sQ3_spl
| x1 != x2 ),
inference(backward_demodulation,[status(thm)],[f100,f45]) ).
fof(f274,plain,
( ~ sQ7_spl
| x5 != x10 ),
inference(forward_demodulation,[status(thm)],[f143,f45]) ).
fof(f275,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| x5 != x5 ),
inference(forward_demodulation,[status(thm)],[f139,f274]) ).
fof(f276,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f275]) ).
fof(f277,plain,
( ~ sQ7_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f276]) ).
fof(f364,plain,
( ~ sQ3_spl
| heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x2),sep(lseg(x2,x1),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x3,x10),sep(lseg(x6,x9),emp))))))))) ),
inference(forward_demodulation,[status(thm)],[f100,f54]) ).
fof(f365,plain,
( ~ sQ3_spl
| heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x1),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x3,x10),sep(lseg(x6,x9),emp)))))))) ),
inference(forward_demodulation,[status(thm)],[f26,f364]) ).
fof(f366,plain,
( ~ sQ3_spl
| heap(sep(lseg(x5,x7),sep(lseg(x2,x5),sep(lseg(x2,x1),sep(lseg(x9,x1),sep(lseg(x7,x6),sep(lseg(x3,x2),sep(lseg(x6,x9),emp)))))))) ),
inference(forward_demodulation,[status(thm)],[f100,f365]) ).
fof(f367,plain,
( ~ sQ3_spl
| x2 = x1
| x2 = x5 ),
inference(resolution,[status(thm)],[f366,f83]) ).
fof(f370,definition,
( sQ12_spl
<=> x2 = x1 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f371,plain,
( ~ sQ12_spl
| x2 = x1 ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f373,plain,
( ~ sQ3_spl
| sQ12_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f367,f96,f370,f99]) ).
fof(f374,plain,
( ~ sQ12_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f371,f171]) ).
fof(f375,plain,
( ~ sQ12_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f376,plain,
$false,
inference(sat_refutation,[status(thm)],[f102,f141,f145,f169,f277,f373,f375]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW425-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 09:55:37 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.083227 seconds
% 0.14/0.45 % CPU time: 0.206249 seconds
% 0.14/0.45 % Total memory used: 53.175 MB
% 0.14/0.45 % Net memory used: 52.964 MB
%------------------------------------------------------------------------------