%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS078+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:59:38 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.58s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 6 unt; 5 def)
% Number of atoms : 192 ( 18 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 238 ( 92 ~; 83 |; 52 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 96 ( 75 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ cp(Y)
& ~ cq(Y)
& rs(X,Y) )
& ? [Y] :
( ! [Z0,Z1] :
( ( rinvR(Y,Z1)
& rinvR(Y,Z0) )
=> Z0 = Z1 )
& ? [Z] :
( ! [W] :
( rs(Z,W)
=> cp(W) )
& rinvR(Y,Z) )
& rr(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
cUnsatisfiable(i2003_11_14_17_19_13721),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ cp(Y)
& ~ cq(Y)
& rs(X,Y) )
& ? [Y] :
( ! [Z0,Z1] :
( Z0 = Z1
| ~ rinvR(Y,Z1)
| ~ rinvR(Y,Z0) )
& ? [Z] :
( ! [W] :
( cp(W)
| ~ rs(Z,W) )
& rinvR(Y,Z) )
& rr(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f66,definition,
! [Z,W] :
( sP0_prd(W,Z)
<=> ( cp(W)
| ~ rs(Z,W) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f67,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ cp(Y)
& ~ cq(Y)
& rs(X,Y) )
& ? [Y] :
( ! [Z0,Z1] :
( Z0 = Z1
| ~ rinvR(Y,Z1)
| ~ rinvR(Y,Z0) )
& ? [Z] :
( ! [W] : sP0_prd(W,Z)
& rinvR(Y,Z) )
& rr(X,Y) ) ) ),
inference(formula_renaming,[status(thm)],[f65,f66]) ).
fof(f68,plain,
! [X] :
( ( ! [Y] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ? [Z0,Z1] :
( Z0 != Z1
& rinvR(Y,Z1)
& rinvR(Y,Z0) )
| ! [Z] :
( ? [W] : ~ sP0_prd(W,Z)
| ~ rinvR(Y,Z) )
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( ? [Y] :
( ~ cp(Y)
& ~ cq(Y)
& rs(X,Y) )
& ? [Y] :
( ! [Z0,Z1] :
( Z0 = Z1
| ~ rinvR(Y,Z1)
| ~ rinvR(Y,Z0) )
& ? [Z] :
( ! [W] : sP0_prd(W,Z)
& rinvR(Y,Z) )
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
( ! [X] :
( ! [Y] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ? [Z0,Z1] :
( Z0 != Z1
& rinvR(Y,Z1)
& rinvR(Y,Z0) )
| ! [Z] :
( ? [W] : ~ sP0_prd(W,Z)
| ~ rinvR(Y,Z) )
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ? [Y] :
( ~ cp(Y)
& ~ cq(Y)
& rs(X,Y) )
& ? [Y] :
( ! [Z0,Z1] :
( Z0 = Z1
| ~ rinvR(Y,Z1)
| ~ rinvR(Y,Z0) )
& ? [Z] :
( ! [W] : sP0_prd(W,Z)
& rinvR(Y,Z) )
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f70,plain,
( ! [X] :
( ! [Y] :
( cp(Y)
| cq(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ( sK4_skl(Y,X) != sK5_skl(Y,X)
& rinvR(Y,sK5_skl(Y,X))
& rinvR(Y,sK4_skl(Y,X)) )
| ! [Z] :
( ~ sP0_prd(sK3_skl(Z,Y,X),Z)
| ~ rinvR(Y,Z) )
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ~ cp(sK2_skl(X))
& ~ cq(sK2_skl(X))
& rs(X,sK2_skl(X))
& ! [Z0,Z1] :
( Z0 = Z1
| ~ rinvR(sK0_skl(X),Z1)
| ~ rinvR(sK0_skl(X),Z0) )
& ! [W] : sP0_prd(W,sK1_skl(X))
& rinvR(sK0_skl(X),sK1_skl(X))
& rr(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(Y,sK0_skl(X)),skolemize(Z,sK1_skl(X)),skolemize(Y,sK2_skl(X)),skolemize(W,sK3_skl(Z,Y,X)),skolemize(Z0,sK4_skl(Y,X)),skolemize(Z1,sK5_skl(Y,X))],[f69]) ).
fof(f71,plain,
! [X0] :
( rr(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0] :
( rinvR(sK0_skl(X0),sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
! [X0,X1] :
( sP0_prd(X1,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f74,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rinvR(sK0_skl(X0),X2)
| ~ rinvR(sK0_skl(X0),X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f75,plain,
! [X0] :
( rs(X0,sK2_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f77,plain,
! [X0] :
( ~ cp(sK2_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f81,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f82,plain,
( ! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) )
& ! [X,Y] :
( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f84,plain,
! [X0,X1] :
( ~ rr(X1,X0)
| rinvR(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f85,plain,
cUnsatisfiable(i2003_11_14_17_19_13721),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f86,plain,
! [Z,W] :
( ( ( ~ cp(W)
& rs(Z,W) )
| sP0_prd(W,Z) )
& ( cp(W)
| ~ rs(Z,W)
| ~ sP0_prd(W,Z) ) ),
inference(NNF_transformation,[status(thm)],[f66]) ).
fof(f87,plain,
( ! [Z,W] :
( ( ~ cp(W)
& rs(Z,W) )
| sP0_prd(W,Z) )
& ! [Z,W] :
( cp(W)
| ~ rs(Z,W)
| ~ sP0_prd(W,Z) ) ),
inference(miniscoping,[status(thm)],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( cp(X0)
| ~ rs(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f93,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| cp(sK2_skl(X0))
| ~ sP0_prd(sK2_skl(X0),X0) ),
inference(resolution,[status(thm)],[f88,f75]) ).
fof(f94,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ~ sP0_prd(sK2_skl(X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f77]) ).
fof(f95,plain,
~ sP0_prd(sK2_skl(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721),
inference(resolution,[status(thm)],[f94,f85]) ).
fof(f105,plain,
! [X0,X1] :
( X0 = X1
| ~ rinvR(sK0_skl(i2003_11_14_17_19_13721),X1)
| ~ rinvR(sK0_skl(i2003_11_14_17_19_13721),X0) ),
inference(resolution,[status(thm)],[f74,f85]) ).
fof(f106,plain,
! [X0] :
( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| X0 = sK1_skl(i2003_11_14_17_19_13721)
| ~ rinvR(sK0_skl(i2003_11_14_17_19_13721),X0) ),
inference(resolution,[status(thm)],[f105,f72]) ).
fof(f108,definition,
! [X0] :
( sQ2_spl
<=> ( X0 = sK1_skl(i2003_11_14_17_19_13721)
| ~ rinvR(sK0_skl(i2003_11_14_17_19_13721),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f109,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sK1_skl(i2003_11_14_17_19_13721)
| ~ rinvR(sK0_skl(i2003_11_14_17_19_13721),X0) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,definition,
( sQ3_spl
<=> cUnsatisfiable(i2003_11_14_17_19_13721) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( sQ3_spl
| ~ cUnsatisfiable(i2003_11_14_17_19_13721) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f106,f108,f111]) ).
fof(f116,plain,
! [X0] :
( ~ sQ2_spl
| ~ rr(X0,sK0_skl(i2003_11_14_17_19_13721))
| X0 = sK1_skl(i2003_11_14_17_19_13721) ),
inference(resolution,[status(thm)],[f109,f84]) ).
fof(f121,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f85]) ).
fof(f122,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f121]) ).
fof(f129,plain,
( ~ sQ2_spl
| ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| i2003_11_14_17_19_13721 = sK1_skl(i2003_11_14_17_19_13721) ),
inference(resolution,[status(thm)],[f116,f71]) ).
fof(f131,definition,
( sQ5_spl
<=> i2003_11_14_17_19_13721 = sK1_skl(i2003_11_14_17_19_13721) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ5_spl
| i2003_11_14_17_19_13721 = sK1_skl(i2003_11_14_17_19_13721) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f129,f131,f111,f108]) ).
fof(f139,plain,
! [X0] :
( ~ sQ5_spl
| sP0_prd(X0,i2003_11_14_17_19_13721)
| ~ cUnsatisfiable(i2003_11_14_17_19_13721) ),
inference(paramodulation,[status(thm)],[f132,f73]) ).
fof(f148,definition,
! [X0] :
( sQ8_spl
<=> sP0_prd(X0,i2003_11_14_17_19_13721) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f149,plain,
! [X0] :
( ~ sQ8_spl
| sP0_prd(X0,i2003_11_14_17_19_13721) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( ~ sQ5_spl
| sQ8_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f139,f111,f148,f131]) ).
fof(f152,plain,
( ~ sQ8_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f95,f149]) ).
fof(f153,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f152]) ).
fof(f154,plain,
$false,
inference(sat_refutation,[status(thm)],[f114,f122,f134,f151,f153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS078+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n010.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Sun Sep 20 22:52:55 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 % Drodi V4.1.1
% 0.15/0.58 % Refutation found
% 0.15/0.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.60 % Elapsed time: 0.028193 seconds
% 0.15/0.60 % CPU time: 0.077623 seconds
% 0.15/0.60 % Total memory used: 2.598 MB
% 0.15/0.60 % Net memory used: 2.525 MB
%------------------------------------------------------------------------------