%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS082+1 : TPTP v9.3.1. Released v3.1.0.
% 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 12:59:39 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 4 unt; 5 def)
% Number of atoms : 251 ( 0 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 327 ( 139 ~; 120 |; 48 &)
% ( 10 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 133 ( 117 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( cUnsatisfiable(X)
=> ? [Y] :
( ? [Z] :
( cowlThing(Z)
& rr(Y,Z) )
& ! [Z] :
( rp(Y,Z)
=> ! [W] :
( rr(Z,W)
=> cc(W) ) )
& ! [Z] :
( rp(Y,Z)
=> ? [W] :
( cowlThing(W)
& rp(Z,W) ) )
& ! [Z] :
( rp(Y,Z)
=> ? [W] :
( cowlThing(W)
& rr(Z,W) ) )
& ! [Z] :
( rr(Y,Z)
=> cc(Z) )
& ? [Z] :
( cowlThing(Z)
& rp(Y,Z) )
& rs(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( cUnsatisfiable(X)
=> ca(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( cc(X)
<=> ! [Y] :
( rinvR(X,Y)
=> ! [Z] :
( rinvP(Y,Z)
=> ! [W] :
( rinvS(Z,W)
=> ~ ca(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( rinvP(X,Y)
<=> rp(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
cUnsatisfiable(i2003_11_14_17_19_28752),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X] :
( ? [Y] :
( ? [Z] :
( cowlThing(Z)
& rr(Y,Z) )
& ! [Z] :
( ! [W] :
( cc(W)
| ~ rr(Z,W) )
| ~ rp(Y,Z) )
& ! [Z] :
( ? [W] :
( cowlThing(W)
& rp(Z,W) )
| ~ rp(Y,Z) )
& ! [Z] :
( ? [W] :
( cowlThing(W)
& rr(Z,W) )
| ~ rp(Y,Z) )
& ! [Z] :
( cc(Z)
| ~ rr(Y,Z) )
& ? [Z] :
( cowlThing(Z)
& rp(Y,Z) )
& rs(X,Y) )
| ~ cUnsatisfiable(X) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X] :
( ( cowlThing(sK4_skl(X))
& rr(sK0_skl(X),sK4_skl(X))
& ! [Z] :
( ! [W] :
( cc(W)
| ~ rr(Z,W) )
| ~ rp(sK0_skl(X),Z) )
& ! [Z] :
( ( cowlThing(sK3_skl(Z,X))
& rp(Z,sK3_skl(Z,X)) )
| ~ rp(sK0_skl(X),Z) )
& ! [Z] :
( ( cowlThing(sK2_skl(Z,X))
& rr(Z,sK2_skl(Z,X)) )
| ~ rp(sK0_skl(X),Z) )
& ! [Z] :
( cc(Z)
| ~ rr(sK0_skl(X),Z) )
& cowlThing(sK1_skl(X))
& rp(sK0_skl(X),sK1_skl(X))
& rs(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(Y,sK0_skl(X)),skolemize(Z,sK1_skl(X)),skolemize(W,sK2_skl(Z,X)),skolemize(W,sK3_skl(Z,X)),skolemize(Z,sK4_skl(X))],[f18]) ).
fof(f20,plain,
! [X0] :
( rs(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0] :
( rp(sK0_skl(X0),sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f24,plain,
! [X0,X1] :
( rr(X1,sK2_skl(X1,X0))
| ~ rp(sK0_skl(X0),X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f28,plain,
! [X0,X1,X2] :
( cc(X2)
| ~ rr(X1,X2)
| ~ rp(sK0_skl(X0),X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f31,plain,
! [X] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f32,plain,
! [X0] :
( ca(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X] :
( cc(X)
<=> ! [Y] :
( ! [Z] :
( ! [W] :
( ~ ca(W)
| ~ rinvS(Z,W) )
| ~ rinvP(Y,Z) )
| ~ rinvR(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
! [X] :
( ( ? [Y] :
( ? [Z] :
( ? [W] :
( ca(W)
& rinvS(Z,W) )
& rinvP(Y,Z) )
& rinvR(X,Y) )
| cc(X) )
& ( ! [Y] :
( ! [Z] :
( ! [W] :
( ~ ca(W)
| ~ rinvS(Z,W) )
| ~ rinvP(Y,Z) )
| ~ rinvR(X,Y) )
| ~ cc(X) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
( ! [X] :
( ? [Y] :
( ? [Z] :
( ? [W] :
( ca(W)
& rinvS(Z,W) )
& rinvP(Y,Z) )
& rinvR(X,Y) )
| cc(X) )
& ! [X] :
( ! [Y] :
( ! [Z] :
( ! [W] :
( ~ ca(W)
| ~ rinvS(Z,W) )
| ~ rinvP(Y,Z) )
| ~ rinvR(X,Y) )
| ~ cc(X) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
( ! [X] :
( ( ca(sK7_skl(X))
& rinvS(sK6_skl(X),sK7_skl(X))
& rinvP(sK5_skl(X),sK6_skl(X))
& rinvR(X,sK5_skl(X)) )
| cc(X) )
& ! [X] :
( ! [Y] :
( ! [Z] :
( ! [W] :
( ~ ca(W)
| ~ rinvS(Z,W) )
| ~ rinvP(Y,Z) )
| ~ rinvR(X,Y) )
| ~ cc(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(Y,sK5_skl(X)),skolemize(Z,sK6_skl(X)),skolemize(W,sK7_skl(X))],[f35]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( ~ ca(X3)
| ~ rinvS(X2,X3)
| ~ rinvP(X1,X2)
| ~ rinvR(X0,X1)
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f42,plain,
! [X,Y] :
( ( ~ rp(Y,X)
| rinvP(X,Y) )
& ( rp(Y,X)
| ~ rinvP(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
( ! [X,Y] :
( ~ rp(Y,X)
| rinvP(X,Y) )
& ! [X,Y] :
( rp(Y,X)
| ~ rinvP(X,Y) ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( ~ rp(X1,X0)
| rinvP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f47,plain,
( ! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) )
& ! [X,Y] :
( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f49,plain,
! [X0,X1] :
( ~ rr(X1,X0)
| rinvR(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f51,plain,
( ! [X,Y] :
( ~ rs(Y,X)
| rinvS(X,Y) )
& ! [X,Y] :
( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f53,plain,
! [X0,X1] :
( ~ rs(X1,X0)
| rinvS(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f57,plain,
cUnsatisfiable(i2003_11_14_17_19_28752),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ~ rp(X2,X1)
| ~ ca(X3)
| ~ rinvS(X2,X3)
| ~ rinvR(X0,X1)
| ~ cc(X0) ),
inference(resolution,[status(thm)],[f37,f45]) ).
fof(f61,plain,
! [X0,X1,X2,X3] :
( ~ rr(X3,X0)
| ~ rp(X1,X3)
| ~ ca(X2)
| ~ rinvS(X1,X2)
| ~ cc(X0) ),
inference(resolution,[status(thm)],[f60,f49]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( ~ cUnsatisfiable(X2)
| ~ rr(X3,X0)
| ~ rp(X1,X3)
| ~ rinvS(X1,X2)
| ~ cc(X0) ),
inference(resolution,[status(thm)],[f61,f32]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ rr(X2,X0)
| ~ rp(X1,X2)
| ~ rinvS(X1,i2003_11_14_17_19_28752)
| ~ cc(X0) ),
inference(resolution,[status(thm)],[f63,f57]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ rs(i2003_11_14_17_19_28752,X1)
| ~ rr(X2,X0)
| ~ rp(X1,X2)
| ~ cc(X0) ),
inference(resolution,[status(thm)],[f64,f53]) ).
fof(f66,plain,
! [X0,X1] :
( ~ cUnsatisfiable(i2003_11_14_17_19_28752)
| ~ rr(X1,X0)
| ~ rp(sK0_skl(i2003_11_14_17_19_28752),X1)
| ~ cc(X0) ),
inference(resolution,[status(thm)],[f65,f20]) ).
fof(f68,definition,
! [X0,X1] :
( sQ0_spl
<=> ( ~ rr(X1,X0)
| ~ rp(sK0_skl(i2003_11_14_17_19_28752),X1)
| ~ cc(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f69,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ rr(X1,X0)
| ~ rp(sK0_skl(i2003_11_14_17_19_28752),X1)
| ~ cc(X0) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,definition,
( sQ1_spl
<=> cUnsatisfiable(i2003_11_14_17_19_28752) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( sQ1_spl
| ~ cUnsatisfiable(i2003_11_14_17_19_28752) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f68,f71]) ).
fof(f76,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ rp(sK0_skl(X1),X0)
| ~ cUnsatisfiable(X1)
| ~ rp(sK0_skl(i2003_11_14_17_19_28752),X0)
| ~ cc(sK2_skl(X0,X1)) ),
inference(resolution,[status(thm)],[f69,f24]) ).
fof(f86,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f73,f57]) ).
fof(f87,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f86]) ).
fof(f101,plain,
! [X0] :
( ~ sQ0_spl
| ~ rp(sK0_skl(i2003_11_14_17_19_28752),X0)
| ~ rp(sK0_skl(i2003_11_14_17_19_28752),X0)
| ~ cc(sK2_skl(X0,i2003_11_14_17_19_28752)) ),
inference(resolution,[status(thm)],[f76,f57]) ).
fof(f102,plain,
! [X0] :
( ~ sQ0_spl
| ~ rp(sK0_skl(i2003_11_14_17_19_28752),X0)
| ~ cc(sK2_skl(X0,i2003_11_14_17_19_28752)) ),
inference(duplicate_literals_removal,[status(thm)],[f101]) ).
fof(f106,plain,
( ~ sQ0_spl
| ~ cUnsatisfiable(i2003_11_14_17_19_28752)
| ~ cc(sK2_skl(sK1_skl(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752)) ),
inference(resolution,[status(thm)],[f102,f21]) ).
fof(f109,definition,
( sQ5_spl
<=> cc(sK2_skl(sK1_skl(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( sQ5_spl
| ~ cc(sK2_skl(sK1_skl(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752)) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f106,f109,f71,f68]) ).
fof(f114,plain,
! [X0,X1] :
( sQ5_spl
| ~ rr(X1,sK2_skl(sK1_skl(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752))
| ~ rp(sK0_skl(X0),X1)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f111,f28]) ).
fof(f133,plain,
! [X0] :
( sQ5_spl
| ~ rp(sK0_skl(i2003_11_14_17_19_28752),sK1_skl(i2003_11_14_17_19_28752))
| ~ cUnsatisfiable(i2003_11_14_17_19_28752)
| ~ rp(sK0_skl(X0),sK1_skl(i2003_11_14_17_19_28752))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f114,f24]) ).
fof(f134,definition,
! [X0] :
( sQ7_spl
<=> ( ~ rp(sK0_skl(X0),sK1_skl(i2003_11_14_17_19_28752))
| ~ cUnsatisfiable(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f135,plain,
! [X0] :
( ~ sQ7_spl
| ~ rp(sK0_skl(X0),sK1_skl(i2003_11_14_17_19_28752))
| ~ cUnsatisfiable(X0) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,definition,
( sQ8_spl
<=> rp(sK0_skl(i2003_11_14_17_19_28752),sK1_skl(i2003_11_14_17_19_28752)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( sQ8_spl
| ~ rp(sK0_skl(i2003_11_14_17_19_28752),sK1_skl(i2003_11_14_17_19_28752)) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ5_spl
| ~ sQ8_spl
| ~ sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f133,f134,f71,f137,f109]) ).
fof(f141,plain,
( ~ sQ7_spl
| ~ rp(sK0_skl(i2003_11_14_17_19_28752),sK1_skl(i2003_11_14_17_19_28752)) ),
inference(resolution,[status(thm)],[f135,f57]) ).
fof(f143,plain,
( ~ sQ7_spl
| ~ cUnsatisfiable(i2003_11_14_17_19_28752) ),
inference(resolution,[status(thm)],[f141,f21]) ).
fof(f145,plain,
( ~ sQ7_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f143,f71,f134]) ).
fof(f146,plain,
( sQ8_spl
| ~ cUnsatisfiable(i2003_11_14_17_19_28752) ),
inference(resolution,[status(thm)],[f139,f21]) ).
fof(f148,plain,
( sQ8_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f146,f71,f137]) ).
fof(f149,plain,
$false,
inference(sat_refutation,[status(thm)],[f74,f87,f112,f140,f145,f148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS082+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.46 % Computer : n006.cluster.edu
% 0.14/5.46 % Model : x86_64 x86_64
% 0.14/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.46 % Memory : 8046.5625MB
% 0.14/5.46 % OS : Linux 6.8.0-71-generic
% 0.14/5.46 % CPULimit : 300
% 0.14/5.46 % WCLimit : 300
% 0.14/5.46 % DateTime : Sun Sep 20 22:52:33 UTC 2026
% 0.14/5.46 % CPUTime :
% 0.14/5.46 % Drodi V4.1.1
% 0.14/5.47 % Refutation found
% 0.14/5.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.49 % Elapsed time: 0.023625 seconds
% 0.14/5.49 % CPU time: 0.036878 seconds
% 0.14/5.49 % Total memory used: 985.120 KB
% 0.14/5.49 % Net memory used: 946.432 KB
%------------------------------------------------------------------------------