%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS013-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:59:32 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 72 ( 6 unt; 5 def)
% Number of atoms : 177 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 187 ( 82 ~; 100 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ f(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X1] :
( ~ c(X1)
| t2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1] :
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ t2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X1] :
( ~ d(X1)
| t1most(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X3,X2,X1] :
( ~ t(X1,X2)
| ~ t(X1,X3)
| ~ t1most(X1)
| equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X3,X1] :
( ~ r(X1,X3)
| ~ e(X1)
| d(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X2,X1] :
( ~ s2least(X2)
| ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X1,X3,X2] :
( ~ s(X1,X2)
| ~ s(X1,X3)
| equalish(X3,X2)
| s2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X1] :
( ~ s1most(u6r1(X1))
| f(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X1] :
( r(X1,u6r1(X1))
| f(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X1] :
( ~ equalish(u7r2(X1),u7r1(X1))
| s1most(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X1] :
( s(X1,u7r1(X1))
| s1most(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X1] :
( s(X1,u7r2(X1))
| s1most(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,plain,
e(exist),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f35,plain,
~ f(exist),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f36,plain,
! [X0] :
( ~ c(X0)
| t2least(X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
! [X0] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ t2least(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f39,plain,
! [X0] :
( ~ t2least(X0)
| t(X0,u1r1(X0)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f40,plain,
! [X0] :
( ~ t2least(X0)
| t(X0,u1r2(X0)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f43,plain,
! [X0] :
( ~ d(X0)
| t1most(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f45,plain,
! [X2,X1] :
( ~ t(X1,X2)
| ! [X3] :
( ~ t(X1,X3)
| ~ t1most(X1)
| equalish(X3,X2) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ t(X2,X1)
| ~ t(X2,X0)
| ~ t1most(X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f50,plain,
! [X0,X1] :
( ~ r(X1,X0)
| ~ e(X1)
| d(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f51,plain,
! [X2] :
( ~ s2least(X2)
| ! [X1] :
( ~ r(X1,X2)
| ~ e(X1)
| c(X2) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f52,plain,
! [X0,X1] :
( ~ s2least(X0)
| ~ r(X1,X0)
| ~ e(X1)
| c(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f62,plain,
! [X1,X2] :
( ~ s(X1,X2)
| ! [X3] :
( ~ s(X1,X3)
| equalish(X3,X2)
| s2least(X1) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ s(X0,X2)
| ~ s(X0,X1)
| equalish(X1,X2)
| s2least(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f65,plain,
! [X0] :
( ~ s1most(u6r1(X0))
| f(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f66,plain,
! [X0] :
( r(X0,u6r1(X0))
| f(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f69,plain,
! [X0] :
( ~ equalish(u7r2(X0),u7r1(X0))
| s1most(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f70,plain,
! [X0] :
( s(X0,u7r1(X0))
| s1most(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f71,plain,
! [X0] :
( s(X0,u7r2(X0))
| s1most(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f74,plain,
! [X0] :
( ~ r(exist,X0)
| d(X0) ),
inference(resolution,[status(thm)],[f50,f34]) ).
fof(f75,plain,
( f(exist)
| d(u6r1(exist)) ),
inference(resolution,[status(thm)],[f74,f66]) ).
fof(f76,definition,
( sQ0_spl
<=> d(u6r1(exist)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ0_spl
| d(u6r1(exist)) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,definition,
( sQ1_spl
<=> f(exist) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ1_spl
| f(exist) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f75,f76,f79]) ).
fof(f83,plain,
( ~ sQ0_spl
| t1most(u6r1(exist)) ),
inference(resolution,[status(thm)],[f77,f43]) ).
fof(f84,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ t(u6r1(exist),X1)
| ~ t(u6r1(exist),X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f83,f46]) ).
fof(f124,plain,
! [X0,X1] :
( s1most(X0)
| ~ s(X0,X1)
| equalish(X1,u7r1(X0))
| s2least(X0) ),
inference(resolution,[status(thm)],[f63,f70]) ).
fof(f145,plain,
! [X0] :
( s1most(X0)
| s1most(X0)
| ~ s(X0,u7r2(X0))
| s2least(X0) ),
inference(resolution,[status(thm)],[f124,f69]) ).
fof(f146,plain,
! [X0] :
( s1most(X0)
| ~ s(X0,u7r2(X0))
| s2least(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0] :
( s1most(X0)
| s2least(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f71]) ).
fof(f148,plain,
! [X0] :
( f(X0)
| s2least(u6r1(X0)) ),
inference(resolution,[status(thm)],[f147,f65]) ).
fof(f150,plain,
! [X0,X1] :
( ~ r(X1,u6r1(X0))
| ~ e(X1)
| c(u6r1(X0))
| f(X0) ),
inference(resolution,[status(thm)],[f148,f52]) ).
fof(f155,plain,
! [X0] :
( ~ r(exist,u6r1(X0))
| c(u6r1(X0))
| f(X0) ),
inference(resolution,[status(thm)],[f150,f34]) ).
fof(f156,plain,
( f(exist)
| c(u6r1(exist))
| f(exist) ),
inference(resolution,[status(thm)],[f155,f66]) ).
fof(f157,definition,
( sQ12_spl
<=> c(u6r1(exist)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ12_spl
| c(u6r1(exist)) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ12_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f156,f79,f157]) ).
fof(f161,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f35]) ).
fof(f162,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f165,plain,
( ~ sQ12_spl
| t2least(u6r1(exist)) ),
inference(resolution,[status(thm)],[f158,f36]) ).
fof(f171,plain,
( ~ sQ12_spl
| t(u6r1(exist),u1r2(u6r1(exist))) ),
inference(resolution,[status(thm)],[f165,f40]) ).
fof(f172,plain,
( ~ sQ12_spl
| t(u6r1(exist),u1r1(u6r1(exist))) ),
inference(resolution,[status(thm)],[f165,f39]) ).
fof(f176,definition,
( sQ13_spl
<=> t2least(u6r1(exist)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( sQ13_spl
| ~ t2least(u6r1(exist)) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f183,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ12_spl
| ~ t(u6r1(exist),X0)
| equalish(X0,u1r1(u6r1(exist))) ),
inference(resolution,[status(thm)],[f172,f84]) ).
fof(f189,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ t2least(u6r1(exist))
| ~ t(u6r1(exist),u1r2(u6r1(exist))) ),
inference(resolution,[status(thm)],[f183,f38]) ).
fof(f190,definition,
( sQ16_spl
<=> t(u6r1(exist),u1r2(u6r1(exist))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ16_spl
| ~ t(u6r1(exist),u1r2(u6r1(exist))) ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f189,f190,f176,f157,f76]) ).
fof(f194,plain,
( sQ16_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f171]) ).
fof(f195,plain,
( sQ16_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f196,plain,
( sQ13_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f165]) ).
fof(f197,plain,
( sQ13_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f196]) ).
fof(f198,plain,
$false,
inference(sat_refutation,[status(thm)],[f82,f160,f162,f193,f195,f197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS013-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 22:50:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.035219 seconds
% 0.13/0.40 % CPU time: 0.102479 seconds
% 0.13/0.40 % Total memory used: 13.584 MB
% 0.13/0.40 % Net memory used: 13.446 MB
%------------------------------------------------------------------------------