%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS002-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:59:31 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 52 ( 4 unt; 5 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 132 ( 64 ~; 63 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X1] :
( ~ c(X1)
| s2least(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X1] :
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ s2least(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X1] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X1] :
( ~ d(X1)
| s1most(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X3,X2,X1] :
( ~ s(X1,X2)
| ~ s(X1,X3)
| ~ s1most(X1)
| equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X1] :
( ~ e(X1)
| r(X1,u4r2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X2,X1] :
( ~ r(X1,X2)
| ~ e(X1)
| d(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X2,X1] :
( ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
e(exist),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0] :
( ~ c(X0)
| s2least(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
! [X0] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ s2least(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0] :
( ~ s2least(X0)
| s(X0,u1r1(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0] :
( ~ s2least(X0)
| s(X0,u1r2(X0)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0] :
( ~ d(X0)
| s1most(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
! [X2,X1] :
( ~ s(X1,X2)
| ! [X3] :
( ~ s(X1,X3)
| ~ s1most(X1)
| equalish(X3,X2) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ s(X2,X1)
| ~ s(X2,X0)
| ~ s1most(X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f34,plain,
! [X0] :
( ~ e(X0)
| r(X0,u4r2(X0)) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
! [X0,X1] :
( ~ r(X1,X0)
| ~ e(X1)
| d(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f36,plain,
! [X0,X1] :
( ~ r(X1,X0)
| ~ e(X1)
| c(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
! [X0] :
( ~ r(exist,X0)
| d(X0) ),
inference(resolution,[status(thm)],[f35,f19]) ).
fof(f43,plain,
( ~ e(exist)
| d(u4r2(exist)) ),
inference(resolution,[status(thm)],[f42,f34]) ).
fof(f44,definition,
( sQ0_spl
<=> d(u4r2(exist)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f45,plain,
( ~ sQ0_spl
| d(u4r2(exist)) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,definition,
( sQ1_spl
<=> e(exist) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ1_spl
| ~ e(exist) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f44,f47]) ).
fof(f51,plain,
( ~ sQ0_spl
| s1most(u4r2(exist)) ),
inference(resolution,[status(thm)],[f45,f27]) ).
fof(f52,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ s(u4r2(exist),X1)
| ~ s(u4r2(exist),X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f51,f30]) ).
fof(f54,plain,
! [X0] :
( ~ r(exist,X0)
| c(X0) ),
inference(resolution,[status(thm)],[f36,f19]) ).
fof(f55,plain,
( ~ e(exist)
| c(u4r2(exist)) ),
inference(resolution,[status(thm)],[f54,f34]) ).
fof(f56,definition,
( sQ2_spl
<=> c(u4r2(exist)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ2_spl
| c(u4r2(exist)) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f55,f56,f47]) ).
fof(f60,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f19]) ).
fof(f61,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f67,plain,
( ~ sQ2_spl
| s2least(u4r2(exist)) ),
inference(resolution,[status(thm)],[f57,f20]) ).
fof(f68,plain,
( ~ sQ2_spl
| s(u4r2(exist),u1r2(u4r2(exist))) ),
inference(resolution,[status(thm)],[f67,f24]) ).
fof(f69,plain,
( ~ sQ2_spl
| s(u4r2(exist),u1r1(u4r2(exist))) ),
inference(resolution,[status(thm)],[f67,f23]) ).
fof(f85,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ2_spl
| ~ s(u4r2(exist),X0)
| equalish(X0,u1r1(u4r2(exist))) ),
inference(resolution,[status(thm)],[f69,f52]) ).
fof(f86,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ s2least(u4r2(exist))
| ~ s(u4r2(exist),u1r2(u4r2(exist))) ),
inference(resolution,[status(thm)],[f85,f22]) ).
fof(f87,definition,
( sQ6_spl
<=> s(u4r2(exist),u1r2(u4r2(exist))) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( sQ6_spl
| ~ s(u4r2(exist),u1r2(u4r2(exist))) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,definition,
( sQ7_spl
<=> s2least(u4r2(exist)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( sQ7_spl
| ~ s2least(u4r2(exist)) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f86,f87,f90,f56,f44]) ).
fof(f94,plain,
( sQ6_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f68]) ).
fof(f95,plain,
( sQ6_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f96,plain,
( sQ7_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f67]) ).
fof(f97,plain,
( sQ7_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f96]) ).
fof(f98,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f59,f61,f93,f95,f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS002-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 22:49:27 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.047196 seconds
% 0.12/0.40 % CPU time: 0.122247 seconds
% 0.12/0.40 % Total memory used: 16.884 MB
% 0.12/0.40 % Net memory used: 16.479 MB
%------------------------------------------------------------------------------