%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS015-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:59:33 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.32s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 56 ( 4 unt; 6 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 189 ( 93 ~; 90 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X1] :
( ~ c(X1)
| t2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X1] :
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ t2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X1] :
( ~ d(X1)
| t1most(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X3,X2,X1] :
( ~ t(X1,X2)
| ~ t(X1,X3)
| ~ t1most(X1)
| equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X1] :
( ~ e(X1)
| r(X1,u4r4(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X1,X4] :
( ~ r(X1,X4)
| ~ e(X1)
| s(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X3,X1] :
( ~ s(X1,X3)
| ~ e(X1)
| d(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X2,X1] :
( ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,plain,
e(exist),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f28,plain,
! [X0] :
( ~ c(X0)
| t2least(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f30,plain,
! [X0] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ t2least(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
! [X0] :
( ~ t2least(X0)
| t(X0,u1r1(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f32,plain,
! [X0] :
( ~ t2least(X0)
| t(X0,u1r2(X0)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
! [X0] :
( ~ d(X0)
| t1most(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f37,plain,
! [X2,X1] :
( ~ t(X1,X2)
| ! [X3] :
( ~ t(X1,X3)
| ~ t1most(X1)
| equalish(X3,X2) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ t(X2,X1)
| ~ t(X2,X0)
| ~ t1most(X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f42,plain,
! [X0] :
( ~ e(X0)
| r(X0,u4r4(X0)) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f43,plain,
! [X0,X1] :
( ~ r(X0,X1)
| ~ e(X0)
| s(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
! [X0,X1] :
( ~ s(X1,X0)
| ~ e(X1)
| d(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
! [X0,X1] :
( ~ r(X1,X0)
| ~ e(X1)
| c(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ d(X2)
| ~ t(X2,X1)
| ~ t(X2,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f38,f35]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ~ s(X3,X2)
| ~ e(X3)
| ~ t(X2,X1)
| ~ t(X2,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f63,f45]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ s(exist,X2)
| ~ t(X2,X1)
| ~ t(X2,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f64,f27]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ r(exist,X2)
| ~ e(exist)
| ~ t(X2,X1)
| ~ t(X2,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f66,f43]) ).
fof(f68,definition,
! [X0,X1,X2] :
( sQ0_spl
<=> ( ~ r(exist,X2)
| ~ t(X2,X1)
| ~ t(X2,X0)
| equalish(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ r(exist,X2)
| ~ t(X2,X1)
| ~ t(X2,X0)
| equalish(X0,X1) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,definition,
( sQ1_spl
<=> e(exist) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( sQ1_spl
| ~ e(exist) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f68,f71]) ).
fof(f75,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ e(exist)
| ~ t(u4r4(exist),X1)
| ~ t(u4r4(exist),X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f69,f42]) ).
fof(f77,definition,
! [X0,X1] :
( sQ2_spl
<=> ( ~ t(u4r4(exist),X1)
| ~ t(u4r4(exist),X0)
| equalish(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ t(u4r4(exist),X1)
| ~ t(u4r4(exist),X0)
| equalish(X0,X1) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f75,f77,f71,f68]) ).
fof(f85,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f73,f27]) ).
fof(f86,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f85]) ).
fof(f92,plain,
! [X0] :
( ~ sQ2_spl
| ~ t2least(u4r4(exist))
| ~ t(u4r4(exist),X0)
| equalish(X0,u1r1(u4r4(exist))) ),
inference(resolution,[status(thm)],[f78,f31]) ).
fof(f96,definition,
( sQ5_spl
<=> t2least(u4r4(exist)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( sQ5_spl
| ~ t2least(u4r4(exist)) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f100,definition,
! [X0] :
( sQ6_spl
<=> ( ~ t(u4r4(exist),X0)
| equalish(X0,u1r1(u4r4(exist))) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f101,plain,
! [X0] :
( ~ sQ6_spl
| ~ t(u4r4(exist),X0)
| equalish(X0,u1r1(u4r4(exist))) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f92,f100,f96,f77]) ).
fof(f104,plain,
( sQ5_spl
| ~ c(u4r4(exist)) ),
inference(resolution,[status(thm)],[f98,f28]) ).
fof(f105,plain,
! [X0] :
( sQ5_spl
| ~ r(X0,u4r4(exist))
| ~ e(X0) ),
inference(resolution,[status(thm)],[f104,f46]) ).
fof(f107,plain,
( sQ5_spl
| ~ r(exist,u4r4(exist)) ),
inference(resolution,[status(thm)],[f105,f27]) ).
fof(f108,plain,
( sQ5_spl
| ~ e(exist) ),
inference(resolution,[status(thm)],[f107,f42]) ).
fof(f110,plain,
( sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f108,f71,f96]) ).
fof(f115,plain,
( ~ sQ6_spl
| ~ t2least(u4r4(exist))
| ~ t(u4r4(exist),u1r2(u4r4(exist))) ),
inference(resolution,[status(thm)],[f101,f30]) ).
fof(f116,definition,
( sQ8_spl
<=> t(u4r4(exist),u1r2(u4r4(exist))) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( sQ8_spl
| ~ t(u4r4(exist),u1r2(u4r4(exist))) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f115,f116,f96,f100]) ).
fof(f120,plain,
( sQ8_spl
| ~ t2least(u4r4(exist)) ),
inference(resolution,[status(thm)],[f118,f32]) ).
fof(f121,plain,
( sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f120,f96,f116]) ).
fof(f122,plain,
$false,
inference(sat_refutation,[status(thm)],[f74,f80,f86,f103,f110,f119,f121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KRS015-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 20 22:50:22 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.32 % Refutation found
% 0.03/0.32 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.06/0.33 % Elapsed time: 0.028880 seconds
% 0.06/0.33 % CPU time: 0.061979 seconds
% 0.06/0.33 % Total memory used: 17.273 MB
% 0.06/0.33 % Net memory used: 16.941 MB
%------------------------------------------------------------------------------