%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL099-2 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:08:46 PM UTC 2026
% Result : Unsatisfiable 21.42s 3.29s
% Output : CNFRefutation 21.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 9 unt; 3 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 106 ( 57 ~; 46 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f149,axiom,
! [A,B,R] :
( member(pair(A,B),trancl(R))
| ~ member(pair(A,B),R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f152,axiom,
! [R,X,Y,YP] :
( member(pair(YP,diamond_strip_lemmaD_sk1(X,Y,YP,R)),trancl(R))
| ~ member(pair(X,YP),R)
| ~ member(pair(X,Y),trancl(R))
| ~ diamond(R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f153,axiom,
! [R,X,Y,YP] :
( member(pair(Y,diamond_strip_lemmaD_sk1(X,Y,YP,R)),R)
| ~ member(pair(X,YP),R)
| ~ member(pair(X,Y),trancl(R))
| ~ diamond(R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f154,hypothesis,
diamond(r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f155,hypothesis,
member(pair(y,ya),r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f156,negated_conjecture,
member(pair(y,yp),trancl(r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f157,negated_conjecture,
! [Z] :
( ~ member(pair(yp,Z),trancl(r))
| ~ member(pair(ya,Z),trancl(r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f371,plain,
! [X0,X1,X2] :
( member(pair(X0,X1),trancl(X2))
| ~ member(pair(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f375,plain,
! [X0,X1,X2,X3] :
( member(pair(X3,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),trancl(X0))
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ~ diamond(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f376,plain,
! [X0,X1,X2,X3] :
( member(pair(X2,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),X0)
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ~ diamond(X0) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f377,plain,
diamond(r),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f378,plain,
member(pair(y,ya),r),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f379,plain,
member(pair(y,yp),trancl(r)),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f380,plain,
! [X0] :
( ~ member(pair(yp,X0),trancl(r))
| ~ member(pair(ya,X0),trancl(r)) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f388,plain,
! [X0] :
( ~ member(pair(ya,X0),trancl(r))
| ~ member(pair(yp,X0),r) ),
inference(resolution,[status(thm)],[f371,f380]) ).
fof(f8779,plain,
! [X0,X1] :
( ~ member(pair(yp,diamond_strip_lemmaD_sk1(X0,X1,ya,r)),r)
| ~ member(pair(X0,ya),r)
| ~ member(pair(X0,X1),trancl(r))
| ~ diamond(r) ),
inference(resolution,[status(thm)],[f375,f388]) ).
fof(f8792,definition,
( sQ36_spl
<=> diamond(r) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f8794,plain,
( sQ36_spl
| ~ diamond(r) ),
inference(component_clause,[status(thm)],[f8792]) ).
fof(f8795,definition,
! [X0,X1] :
( sQ37_spl
<=> ( ~ member(pair(yp,diamond_strip_lemmaD_sk1(X0,X1,ya,r)),r)
| ~ member(pair(X0,ya),r)
| ~ member(pair(X0,X1),trancl(r)) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f8796,plain,
! [X0,X1] :
( ~ sQ37_spl
| ~ member(pair(yp,diamond_strip_lemmaD_sk1(X0,X1,ya,r)),r)
| ~ member(pair(X0,ya),r)
| ~ member(pair(X0,X1),trancl(r)) ),
inference(component_clause,[status(thm)],[f8795]) ).
fof(f8798,plain,
( sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f8779,f8792,f8795]) ).
fof(f8804,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8794,f377]) ).
fof(f8805,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f8804]) ).
fof(f9410,plain,
! [X0] :
( ~ sQ37_spl
| ~ member(pair(X0,ya),r)
| ~ member(pair(X0,yp),trancl(r))
| ~ diamond(r)
| ~ member(pair(X0,ya),r)
| ~ member(pair(X0,yp),trancl(r)) ),
inference(resolution,[status(thm)],[f8796,f376]) ).
fof(f9411,definition,
! [X0] :
( sQ63_spl
<=> ( ~ member(pair(X0,ya),r)
| ~ member(pair(X0,yp),trancl(r))
| ~ member(pair(X0,ya),r)
| ~ member(pair(X0,yp),trancl(r)) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f9412,plain,
! [X0] :
( ~ sQ63_spl
| ~ member(pair(X0,ya),r)
| ~ member(pair(X0,yp),trancl(r))
| ~ member(pair(X0,ya),r)
| ~ member(pair(X0,yp),trancl(r)) ),
inference(component_clause,[status(thm)],[f9411]) ).
fof(f9414,plain,
( ~ sQ37_spl
| ~ sQ36_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f9410,f9411,f8792,f8795]) ).
fof(f9415,plain,
! [X0] :
( ~ sQ63_spl
| ~ member(pair(X0,ya),r)
| ~ member(pair(X0,yp),trancl(r)) ),
inference(duplicate_literals_removal,[status(thm)],[f9412]) ).
fof(f10083,plain,
( ~ sQ63_spl
| ~ member(pair(y,ya),r) ),
inference(resolution,[status(thm)],[f9415,f379]) ).
fof(f10099,plain,
( ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10083,f378]) ).
fof(f10100,plain,
~ sQ63_spl,
inference(contradiction_clause,[status(thm)],[f10099]) ).
fof(f10101,plain,
$false,
inference(sat_refutation,[status(thm)],[f8798,f8805,f9414,f10100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL099-2 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.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 : Mon Sep 21 14:12:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.02/0.38 % Drodi V4.1.1
% 21.42/3.29 % Refutation found
% 21.42/3.29 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 21.42/3.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.55/3.37 % Elapsed time: 2.987241 seconds
% 1.55/3.37 % CPU time: 23.177702 seconds
% 1.55/3.37 % Total memory used: 298.777 MB
% 1.55/3.37 % Net memory used: 261.530 MB
%------------------------------------------------------------------------------