%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS264+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 01:00:00 PM UTC 2026
% Result : Theorem 6.05s 1.19s
% Output : CNFRefutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 68 ( 15 unt; 4 def)
% Number of atoms : 249 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 300 ( 119 ~; 114 |; 55 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 180 ( 143 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Ax,C] :
( ( ? [I4] : ~ model(I4,C)
& ? [I3] :
( ~ model(I3,Ax)
& model(I3,C) )
& ! [I2] :
( model(I2,Ax)
=> model(I2,C) )
& ? [I1] : model(I1,Ax) )
<=> status(Ax,C,wth) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [S1,S2] :
( ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) )
<=> mighta(S1,S2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
? [Ax,C] :
( ? [I4] : ~ model(I4,C)
& ? [I3] :
( model(I3,C)
& ~ model(I3,Ax) )
& ! [I2] :
( model(I2,Ax)
=> model(I2,C) )
& ? [I1] : model(I1,Ax) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
mighta(wth,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ mighta(wth,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f62,plain,
! [Ax,C] :
( ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) )
<=> status(Ax,C,thm) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f63,plain,
! [Ax,C] :
( ( ~ status(Ax,C,thm)
| ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) ) )
& ( status(Ax,C,thm)
| ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ) ),
inference(NNF_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
( ! [Ax,C] :
( ~ status(Ax,C,thm)
| ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,thm)
| ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
( ! [Ax,C] :
( ~ status(Ax,C,thm)
| ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,thm)
| ( ~ model(sK9_skl(C,Ax),C)
& model(sK9_skl(C,Ax),Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(I1,sK9_skl(C,Ax))],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( status(X1,X0,thm)
| model(sK9_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( status(X1,X0,thm)
| ~ model(sK9_skl(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ status(X1,X2,thm)
| model(X0,X2)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f115,plain,
! [Ax,C] :
( ( ? [I4] : ~ model(I4,C)
& ? [I3] :
( ~ model(I3,Ax)
& model(I3,C) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) )
<=> status(Ax,C,wth) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f116,plain,
! [Ax,C] :
( ( ~ status(Ax,C,wth)
| ( ? [I4] : ~ model(I4,C)
& ? [I3] :
( ~ model(I3,Ax)
& model(I3,C) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) ) )
& ( status(Ax,C,wth)
| ! [I4] : model(I4,C)
| ! [I3] :
( model(I3,Ax)
| ~ model(I3,C) )
| ? [I2] :
( ~ model(I2,C)
& model(I2,Ax) )
| ! [I1] : ~ model(I1,Ax) ) ),
inference(NNF_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
( ! [Ax,C] :
( ~ status(Ax,C,wth)
| ( ? [I4] : ~ model(I4,C)
& ? [I3] :
( ~ model(I3,Ax)
& model(I3,C) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,wth)
| ! [I4] : model(I4,C)
| ! [I3] :
( model(I3,Ax)
| ~ model(I3,C) )
| ? [I2] :
( ~ model(I2,C)
& model(I2,Ax) )
| ! [I1] : ~ model(I1,Ax) ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f118,plain,
( ! [Ax,C] :
( ~ status(Ax,C,wth)
| ( ~ model(sK28_skl(C,Ax),C)
& ~ model(sK27_skl(C,Ax),Ax)
& model(sK27_skl(C,Ax),C)
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& model(sK26_skl(C,Ax),Ax) ) )
& ! [Ax,C] :
( status(Ax,C,wth)
| ! [I4] : model(I4,C)
| ! [I3] :
( model(I3,Ax)
| ~ model(I3,C) )
| ( ~ model(sK25_skl(C,Ax),C)
& model(sK25_skl(C,Ax),Ax) )
| ! [I1] : ~ model(I1,Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl,sK26_skl,sK27_skl,sK28_skl]),skolemize(I2,sK25_skl(C,Ax)),skolemize(I1,sK26_skl(C,Ax)),skolemize(I3,sK27_skl(C,Ax)),skolemize(I4,sK28_skl(C,Ax))],[f117]) ).
fof(f119,plain,
! [X0,X1,X2,X3,X4] :
( status(X1,X2,wth)
| model(X4,X2)
| model(X3,X1)
| ~ model(X3,X2)
| model(sK25_skl(X2,X1),X1)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4] :
( status(X1,X2,wth)
| model(X4,X2)
| model(X3,X1)
| ~ model(X3,X2)
| ~ model(sK25_skl(X2,X1),X2)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ~ status(X1,X2,wth)
| model(X0,X2)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f174,plain,
! [S1,S2] :
( ( ~ mighta(S1,S2)
| ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ( mighta(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f175,plain,
( ! [S1,S2] :
( ~ mighta(S1,S2)
| ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ! [S1,S2] :
( mighta(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(miniscoping,[status(thm)],[f174]) ).
fof(f176,plain,
( ! [S1,S2] :
( ~ mighta(S1,S2)
| ( status(sK42_skl(S2,S1),sK43_skl(S2,S1),S2)
& status(sK42_skl(S2,S1),sK43_skl(S2,S1),S1) ) )
& ! [S1,S2] :
( mighta(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42_skl,sK43_skl]),skolemize(Ax,sK42_skl(S2,S1)),skolemize(C,sK43_skl(S2,S1))],[f175]) ).
fof(f177,plain,
! [X0,X1,X2,X3] :
( mighta(X2,X3)
| ~ status(X0,X1,X3)
| ~ status(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f227,plain,
? [Ax,C] :
( ? [I4] : ~ model(I4,C)
& ? [I3] :
( model(I3,C)
& ~ model(I3,Ax) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f228,plain,
? [C] :
( ? [I4] : ~ model(I4,C)
& ? [Ax] :
( ? [I3] :
( model(I3,C)
& ~ model(I3,Ax) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) ) ),
inference(miniscoping,[status(thm)],[f227]) ).
fof(f229,plain,
( ~ model(sK66_skl,sK62_skl)
& model(sK65_skl,sK62_skl)
& ~ model(sK65_skl,sK63_skl)
& ! [I2] :
( model(I2,sK62_skl)
| ~ model(I2,sK63_skl) )
& model(sK64_skl,sK63_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62_skl,sK63_skl,sK64_skl,sK65_skl,sK66_skl]),skolemize(C,sK62_skl),skolemize(Ax,sK63_skl),skolemize(I1,sK64_skl),skolemize(I3,sK65_skl),skolemize(I4,sK66_skl)],[f228]) ).
fof(f230,plain,
model(sK64_skl,sK63_skl),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f231,plain,
! [X0] :
( model(X0,sK62_skl)
| ~ model(X0,sK63_skl) ),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f232,plain,
~ model(sK65_skl,sK63_skl),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f233,plain,
model(sK65_skl,sK62_skl),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f234,plain,
~ model(sK66_skl,sK62_skl),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f240,plain,
~ mighta(wth,thm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f248,plain,
! [X0,X1] :
( ~ status(X0,X1,thm)
| ~ status(X0,X1,wth) ),
inference(resolution,[status(thm)],[f177,f240]) ).
fof(f249,plain,
! [X0] :
( status(X0,X0,thm)
| status(X0,X0,thm) ),
inference(resolution,[status(thm)],[f67,f66]) ).
fof(f250,plain,
! [X0,X1,X2] :
( ~ status(X2,X1,wth)
| ~ model(sK9_skl(X1,X0),X2)
| status(X0,X1,thm) ),
inference(resolution,[status(thm)],[f67,f122]) ).
fof(f252,plain,
! [X0] : status(X0,X0,thm),
inference(duplicate_literals_removal,[status(thm)],[f249]) ).
fof(f253,plain,
! [X0,X1] :
( status(X0,X1,thm)
| ~ status(X0,X1,wth)
| status(X0,X1,thm) ),
inference(resolution,[status(thm)],[f250,f66]) ).
fof(f256,plain,
! [X0,X1] :
( ~ status(X0,X1,wth)
| status(X0,X1,thm) ),
inference(duplicate_literals_removal,[status(thm)],[f253]) ).
fof(f257,plain,
! [X0,X1] : ~ status(X0,X1,wth),
inference(forward_subsumption_resolution,[status(thm)],[f256,f248]) ).
fof(f411,plain,
! [X0] :
( ~ status(X0,sK63_skl,thm)
| ~ model(sK65_skl,X0) ),
inference(resolution,[status(thm)],[f232,f68]) ).
fof(f412,plain,
! [X0] :
( ~ status(X0,sK62_skl,thm)
| ~ model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f234,f68]) ).
fof(f559,plain,
! [X0,X1] :
( ~ status(X1,sK63_skl,thm)
| ~ model(X0,X1)
| model(X0,sK62_skl) ),
inference(resolution,[status(thm)],[f231,f68]) ).
fof(f622,plain,
~ model(sK66_skl,sK62_skl),
inference(resolution,[status(thm)],[f412,f252]) ).
fof(f625,plain,
~ model(sK65_skl,sK63_skl),
inference(resolution,[status(thm)],[f411,f252]) ).
fof(f631,plain,
! [X0] :
( ~ model(X0,sK63_skl)
| model(X0,sK62_skl) ),
inference(resolution,[status(thm)],[f559,f252]) ).
fof(f870,definition,
! [X2] :
( sQ13_spl
<=> ~ model(X2,sK63_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f871,plain,
! [X0] :
( ~ sQ13_spl
| ~ model(X0,sK63_skl) ),
inference(component_clause,[status(thm)],[f870]) ).
fof(f981,plain,
( ~ sQ13_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f230,f871]) ).
fof(f991,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f981]) ).
fof(f2110,plain,
! [X0,X1,X2,X3,X4] :
( model(X4,X2)
| model(X3,X1)
| ~ model(X3,X2)
| model(sK25_skl(X2,X1),X1)
| ~ model(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f257]) ).
fof(f2111,plain,
! [X0,X1,X2,X3] :
( model(sK25_skl(X2,sK63_skl),sK62_skl)
| model(X3,X2)
| model(X1,sK63_skl)
| ~ model(X1,X2)
| ~ model(X0,sK63_skl) ),
inference(resolution,[status(thm)],[f2110,f631]) ).
fof(f2116,definition,
! [X1,X2,X3] :
( sQ53_spl
<=> ( model(sK25_skl(X2,sK63_skl),sK62_skl)
| model(X3,X2)
| model(X1,sK63_skl)
| ~ model(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f2117,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| model(sK25_skl(X1,sK63_skl),sK62_skl)
| model(X2,X1)
| model(X0,sK63_skl)
| ~ model(X0,X1) ),
inference(component_clause,[status(thm)],[f2116]) ).
fof(f2119,plain,
( sQ53_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f2111,f870,f2116]) ).
fof(f2125,plain,
! [X0,X1,X2,X3,X4] :
( model(X4,X2)
| model(X3,X1)
| ~ model(X3,X2)
| ~ model(sK25_skl(X2,X1),X2)
| ~ model(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f257]) ).
fof(f2160,definition,
! [X1] :
( sQ56_spl
<=> model(X1,sK62_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f2161,plain,
! [X0] :
( ~ sQ56_spl
| model(X0,sK62_skl) ),
inference(component_clause,[status(thm)],[f2160]) ).
fof(f2189,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ53_spl
| model(X4,sK62_skl)
| model(X3,sK63_skl)
| ~ model(X3,sK62_skl)
| model(X2,sK62_skl)
| model(X1,sK63_skl)
| ~ model(X1,sK62_skl)
| ~ model(X0,sK63_skl) ),
inference(resolution,[status(thm)],[f2125,f2117]) ).
fof(f2194,definition,
! [X1] :
( sQ57_spl
<=> ( model(X1,sK63_skl)
| ~ model(X1,sK62_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f2195,plain,
! [X0] :
( ~ sQ57_spl
| model(X0,sK63_skl)
| ~ model(X0,sK62_skl) ),
inference(component_clause,[status(thm)],[f2194]) ).
fof(f2197,plain,
( ~ sQ53_spl
| sQ56_spl
| sQ57_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f2189,f870,f2194,f2160,f2116]) ).
fof(f2199,plain,
( ~ sQ56_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f622,f2161]) ).
fof(f2208,plain,
~ sQ56_spl,
inference(contradiction_clause,[status(thm)],[f2199]) ).
fof(f2212,plain,
( ~ sQ57_spl
| ~ model(sK65_skl,sK62_skl) ),
inference(resolution,[status(thm)],[f2195,f625]) ).
fof(f2317,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f2212]) ).
fof(f2318,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f2317]) ).
fof(f2319,plain,
$false,
inference(sat_refutation,[status(thm)],[f991,f2119,f2197,f2208,f2318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS264+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 23:01:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 6.05/1.19 % Refutation found
% 6.05/1.19 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.05/1.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.37/1.20 % Elapsed time: 0.837053 seconds
% 0.37/1.20 % CPU time: 6.341335 seconds
% 0.37/1.20 % Total memory used: 71.341 MB
% 0.37/1.20 % Net memory used: 61.172 MB
%------------------------------------------------------------------------------