%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS003-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 0.16s 5.41s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 7 unt; 2 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 89 ( 45 ~; 42 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 31 ( 31 !; 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)
| s2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1] :
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ s2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X1] :
( ~ s2least(X1)
| s(X1,u1r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X1] :
( ~ s2least(X1)
| s(X1,u1r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X1] :
( ~ d(X1)
| s1most(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X3,X2,X1] :
( ~ s(X1,X2)
| ~ s(X1,X3)
| ~ s1most(X1)
| equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X1] :
( ~ e(X1)
| c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X1] :
( ~ f(X1)
| d(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
e(exist),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
f(exist),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] :
( ~ c(X0)
| s2least(X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ s2least(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0] :
( ~ s2least(X0)
| s(X0,u1r1(X0)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0] :
( ~ s2least(X0)
| s(X0,u1r2(X0)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0] :
( ~ d(X0)
| s1most(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
! [X2,X1] :
( ~ s(X1,X2)
| ! [X3] :
( ~ s(X1,X3)
| ~ s1most(X1)
| equalish(X3,X2) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ s(X2,X1)
| ~ s(X2,X0)
| ~ s1most(X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f33,plain,
! [X0] :
( ~ e(X0)
| c(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f34,plain,
! [X0] :
( ~ f(X0)
| d(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f35,plain,
! [X0] :
( ~ e(X0)
| s2least(X0) ),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f37,plain,
! [X0] :
( ~ f(X0)
| s1most(X0) ),
inference(resolution,[status(thm)],[f26,f34]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ f(X2)
| ~ s(X2,X1)
| ~ s(X2,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f29,f37]) ).
fof(f42,plain,
! [X0,X1] :
( ~ s(exist,X1)
| ~ s(exist,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f41,f18]) ).
fof(f44,plain,
! [X0] :
( ~ s2least(X0)
| ~ s(exist,u1r1(X0))
| ~ s(exist,u1r2(X0)) ),
inference(resolution,[status(thm)],[f42,f21]) ).
fof(f60,plain,
( ~ s2least(exist)
| ~ s2least(exist)
| ~ s(exist,u1r2(exist)) ),
inference(resolution,[status(thm)],[f44,f22]) ).
fof(f61,definition,
( sQ2_spl
<=> s(exist,u1r2(exist)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( sQ2_spl
| ~ s(exist,u1r2(exist)) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,definition,
( sQ3_spl
<=> s2least(exist) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( sQ3_spl
| ~ s2least(exist) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f60,f61,f64]) ).
fof(f68,plain,
( sQ2_spl
| ~ s2least(exist) ),
inference(resolution,[status(thm)],[f63,f23]) ).
fof(f69,plain,
( sQ2_spl
| ~ e(exist) ),
inference(resolution,[status(thm)],[f68,f35]) ).
fof(f70,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f17]) ).
fof(f71,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ3_spl
| ~ e(exist) ),
inference(resolution,[status(thm)],[f66,f35]) ).
fof(f73,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f17]) ).
fof(f74,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f73]) ).
fof(f75,plain,
$false,
inference(sat_refutation,[status(thm)],[f67,f71,f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS003-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.38 % Computer : n006.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Sun Sep 20 22:50:03 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 % Drodi V4.1.1
% 0.16/5.41 % Refutation found
% 0.16/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/5.44 % Elapsed time: 0.043649 seconds
% 0.16/5.44 % CPU time: 0.102289 seconds
% 0.16/5.44 % Total memory used: 8.939 MB
% 0.16/5.44 % Net memory used: 8.752 MB
%------------------------------------------------------------------------------