%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS001-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 4 unt; 3 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 102 ( 51 ~; 48 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 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)
| r2least(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X1] :
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ r2least(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1] :
( ~ r2least(X1)
| r(X1,u1r1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X1] :
( ~ r2least(X1)
| r(X1,u1r2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X1] :
( ~ d(X1)
| r1most(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X3,X2,X1] :
( ~ r(X1,X2)
| ~ r(X1,X3)
| ~ r1most(X1)
| equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X1] :
( ~ e(X1)
| d(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X1] :
( ~ e(X1)
| c(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
e(exist),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] :
( ~ c(X0)
| r2least(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ r2least(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0] :
( ~ r2least(X0)
| r(X0,u1r1(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0] :
( ~ r2least(X0)
| r(X0,u1r2(X0)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0] :
( ~ d(X0)
| r1most(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X2,X1] :
( ~ r(X1,X2)
| ! [X3] :
( ~ r(X1,X3)
| ~ r1most(X1)
| equalish(X3,X2) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ r(X2,X1)
| ~ r(X2,X0)
| ~ r1most(X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f32,plain,
! [X0] :
( ~ e(X0)
| d(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f33,plain,
! [X0] :
( ~ e(X0)
| c(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ d(X2)
| ~ r(X2,X1)
| ~ r(X2,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f28,f25]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ e(X2)
| ~ r(X2,X1)
| ~ r(X2,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f35,f32]) ).
fof(f38,plain,
! [X0,X1] :
( ~ r(exist,X1)
| ~ r(exist,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f37,f17]) ).
fof(f41,plain,
! [X0] :
( ~ r2least(exist)
| ~ r(exist,X0)
| equalish(X0,u1r1(exist)) ),
inference(resolution,[status(thm)],[f38,f21]) ).
fof(f45,definition,
( sQ1_spl
<=> r2least(exist) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( sQ1_spl
| ~ r2least(exist) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f49,definition,
! [X0] :
( sQ2_spl
<=> ( ~ r(exist,X0)
| equalish(X0,u1r1(exist)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f50,plain,
! [X0] :
( ~ sQ2_spl
| ~ r(exist,X0)
| equalish(X0,u1r1(exist)) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f41,f49,f45]) ).
fof(f53,plain,
( sQ1_spl
| ~ c(exist) ),
inference(resolution,[status(thm)],[f47,f18]) ).
fof(f55,plain,
( sQ1_spl
| ~ e(exist) ),
inference(resolution,[status(thm)],[f53,f33]) ).
fof(f56,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f17]) ).
fof(f57,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f56]) ).
fof(f58,plain,
( ~ sQ2_spl
| ~ r2least(exist)
| ~ r(exist,u1r2(exist)) ),
inference(resolution,[status(thm)],[f50,f20]) ).
fof(f59,definition,
( sQ3_spl
<=> r(exist,u1r2(exist)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( sQ3_spl
| ~ r(exist,u1r2(exist)) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f58,f59,f45,f49]) ).
fof(f63,plain,
( sQ3_spl
| ~ r2least(exist) ),
inference(resolution,[status(thm)],[f61,f22]) ).
fof(f64,plain,
( sQ3_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f63,f45,f59]) ).
fof(f65,plain,
$false,
inference(sat_refutation,[status(thm)],[f52,f57,f62,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS001-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.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 : Sun Sep 20 22:44:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.036349 seconds
% 0.10/0.41 % CPU time: 0.085435 seconds
% 0.10/0.41 % Total memory used: 9.458 MB
% 0.10/0.41 % Net memory used: 9.238 MB
%------------------------------------------------------------------------------