%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS251+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 : n005.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 12:59:59 PM UTC 2026
% Result : Theorem 4.91s 1.38s
% Output : CNFRefutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 88
% Syntax : Number of formulae : 403 ( 42 unt; 71 def)
% Number of atoms : 1074 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 1147 ( 476 ~; 463 |; 115 &)
% ( 86 <=>; 5 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 75 ( 74 usr; 72 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 27 con; 0-2 aty)
% Number of variables : 547 ( 460 !; 87 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Ax,C] :
( ( ~ ? [I1] : model(I1,Ax)
=> ~ ? [I2] : model(I2,C) )
<=> status(Ax,C,unp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Ax,C] :
( ( ? [I1] : model(I1,Ax)
=> ? [I2] : model(I2,C) )
<=> status(Ax,C,sap) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Ax,C] :
( ( ! [I2] :
( model(I2,Ax)
<=> model(I2,C) )
& ? [I1] : model(I1,Ax) )
<=> status(Ax,C,eqv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Ax,C] :
( ( ! [I2] : model(I2,C)
& ? [I1] : model(I1,Ax) )
<=> status(Ax,C,tac) ),
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(f13,axiom,
! [Ax,C] :
( ~ ? [I1] : model(I1,Ax)
<=> status(Ax,C,cax) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Ax,C] :
( ? [I1] :
( model(I1,not(C))
& model(I1,Ax) )
<=> status(Ax,C,csa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
<~> status(Ax,C,S2) )
<=> xora(S1,S2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [I,F] :
( model(I,F)
<~> model(I,not(F)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
? [F] :
! [I] : model(I,F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
? [F] :
( ? [I2] : ~ model(I2,F)
& ? [I1] : model(I1,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
? [F] :
! [I] : ~ model(I,F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
? [Ax,C] :
( ? [I2] :
( ~ model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] :
( model(I1,C)
& model(I1,Ax) ) ),
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(f32,axiom,
? [I1,Ax,C] :
( ? [I2] : model(I2,C)
& ~ model(I1,C)
& model(I1,Ax) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
xora(csa,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ xora(csa,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
! [Ax,C] :
( ( ! [I2] : ~ model(I2,C)
| ? [I1] : model(I1,Ax) )
<=> status(Ax,C,unp) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [Ax,C] :
( ( ~ status(Ax,C,unp)
| ! [I2] : ~ model(I2,C)
| ? [I1] : model(I1,Ax) )
& ( status(Ax,C,unp)
| ( ? [I2] : model(I2,C)
& ! [I1] : ~ model(I1,Ax) ) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
( ! [Ax,C] :
( ~ status(Ax,C,unp)
| ! [I2] : ~ model(I2,C)
| ? [I1] : model(I1,Ax) )
& ! [Ax,C] :
( status(Ax,C,unp)
| ( ? [I2] : model(I2,C)
& ! [I1] : ~ model(I1,Ax) ) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
( ! [Ax,C] :
( ~ status(Ax,C,unp)
| ! [I2] : ~ model(I2,C)
| model(sK1_skl(C,Ax),Ax) )
& ! [Ax,C] :
( status(Ax,C,unp)
| ( model(sK0_skl(C,Ax),C)
& ! [I1] : ~ model(I1,Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(I2,sK0_skl(C,Ax)),skolemize(I1,sK1_skl(C,Ax))],[f37]) ).
fof(f40,plain,
! [X0,X1] :
( status(X1,X0,unp)
| model(sK0_skl(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ status(X1,X0,unp)
| ~ model(X2,X0)
| model(sK1_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [Ax,C] :
( ( ? [I2] : model(I2,C)
| ! [I1] : ~ model(I1,Ax) )
<=> status(Ax,C,sap) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f43,plain,
! [Ax,C] :
( ( ~ status(Ax,C,sap)
| ? [I2] : model(I2,C)
| ! [I1] : ~ model(I1,Ax) )
& ( status(Ax,C,sap)
| ( ! [I2] : ~ model(I2,C)
& ? [I1] : model(I1,Ax) ) ) ),
inference(NNF_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
( ! [Ax,C] :
( ~ status(Ax,C,sap)
| ? [I2] : model(I2,C)
| ! [I1] : ~ model(I1,Ax) )
& ! [Ax,C] :
( status(Ax,C,sap)
| ( ! [I2] : ~ model(I2,C)
& ? [I1] : model(I1,Ax) ) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
( ! [Ax,C] :
( ~ status(Ax,C,sap)
| model(sK3_skl(C,Ax),C)
| ! [I1] : ~ model(I1,Ax) )
& ! [Ax,C] :
( status(Ax,C,sap)
| ( ! [I2] : ~ model(I2,C)
& model(sK2_skl(C,Ax),Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(I1,sK2_skl(C,Ax)),skolemize(I2,sK3_skl(C,Ax))],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( status(X1,X0,sap)
| model(sK2_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ status(X1,X2,sap)
| model(sK3_skl(X2,X1),X2)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
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(f69,plain,
! [Ax,C] :
( ( ~ status(Ax,C,eqv)
| ( ! [I2] :
( ( ~ model(I2,C)
| model(I2,Ax) )
& ( model(I2,C)
| ~ model(I2,Ax) ) )
& ? [I1] : model(I1,Ax) ) )
& ( status(Ax,C,eqv)
| ? [I2] :
( ( model(I2,C)
| model(I2,Ax) )
& ( ~ model(I2,C)
| ~ model(I2,Ax) ) )
| ! [I1] : ~ model(I1,Ax) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f70,plain,
( ! [Ax,C] :
( ~ status(Ax,C,eqv)
| ( ! [I2] :
( ~ model(I2,C)
| model(I2,Ax) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,eqv)
| ? [I2] :
( ( model(I2,C)
| model(I2,Ax) )
& ( ~ model(I2,C)
| ~ model(I2,Ax) ) )
| ! [I1] : ~ model(I1,Ax) ) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f71,plain,
( ! [Ax,C] :
( ~ status(Ax,C,eqv)
| ( ! [I2] :
( ~ model(I2,C)
| model(I2,Ax) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& model(sK11_skl(C,Ax),Ax) ) )
& ! [Ax,C] :
( status(Ax,C,eqv)
| ( ( model(sK10_skl(C,Ax),C)
| model(sK10_skl(C,Ax),Ax) )
& ( ~ model(sK10_skl(C,Ax),C)
| ~ model(sK10_skl(C,Ax),Ax) ) )
| ! [I1] : ~ model(I1,Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl]),skolemize(I2,sK10_skl(C,Ax)),skolemize(I1,sK11_skl(C,Ax))],[f70]) ).
fof(f73,plain,
! [X0,X1,X2] :
( status(X1,X2,eqv)
| model(sK10_skl(X2,X1),X2)
| model(sK10_skl(X2,X1),X1)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f74,plain,
! [X0,X1] :
( ~ status(X1,X0,eqv)
| model(sK11_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f77,plain,
! [Ax,C] :
( ( ~ status(Ax,C,tac)
| ( ! [I2] : model(I2,C)
& ? [I1] : model(I1,Ax) ) )
& ( status(Ax,C,tac)
| ? [I2] : ~ model(I2,C)
| ! [I1] : ~ model(I1,Ax) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f78,plain,
( ! [Ax,C] :
( ~ status(Ax,C,tac)
| ( ! [I2] : model(I2,C)
& ? [I1] : model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,tac)
| ? [I2] : ~ model(I2,C)
| ! [I1] : ~ model(I1,Ax) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
( ! [Ax,C] :
( ~ status(Ax,C,tac)
| ( ! [I2] : model(I2,C)
& model(sK13_skl(C,Ax),Ax) ) )
& ! [Ax,C] :
( status(Ax,C,tac)
| ~ model(sK12_skl(C,Ax),C)
| ! [I1] : ~ model(I1,Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(I2,sK12_skl(C,Ax)),skolemize(I1,sK13_skl(C,Ax))],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( status(X1,X2,tac)
| ~ model(sK12_skl(X2,X1),X2)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ status(X1,X0,tac)
| model(sK13_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ status(X2,X1,tac)
| model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
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(f124,plain,
! [X0,X1] :
( ~ status(X1,X0,wth)
| ~ model(sK27_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f126,plain,
! [Ax,C] :
( ! [I1] : ~ model(I1,Ax)
<=> status(Ax,C,cax) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f127,plain,
! [Ax,C] :
( ( ~ status(Ax,C,cax)
| ! [I1] : ~ model(I1,Ax) )
& ( status(Ax,C,cax)
| ? [I1] : model(I1,Ax) ) ),
inference(NNF_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
( ! [Ax] :
( ! [C] : ~ status(Ax,C,cax)
| ! [I1] : ~ model(I1,Ax) )
& ! [Ax] :
( ! [C] : status(Ax,C,cax)
| ? [I1] : model(I1,Ax) ) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ! [Ax] :
( ! [C] : ~ status(Ax,C,cax)
| ! [I1] : ~ model(I1,Ax) )
& ! [Ax] :
( ! [C] : status(Ax,C,cax)
| model(sK29_skl(Ax),Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl]),skolemize(I1,sK29_skl(Ax))],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( status(X0,X1,cax)
| model(sK29_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ status(X1,X2,cax)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f154,plain,
! [Ax,C] :
( ( ~ status(Ax,C,csa)
| ? [I1] :
( model(I1,not(C))
& model(I1,Ax) ) )
& ( status(Ax,C,csa)
| ! [I1] :
( ~ model(I1,not(C))
| ~ model(I1,Ax) ) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f155,plain,
( ! [Ax,C] :
( ~ status(Ax,C,csa)
| ? [I1] :
( model(I1,not(C))
& model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,csa)
| ! [I1] :
( ~ model(I1,not(C))
| ~ model(I1,Ax) ) ) ),
inference(miniscoping,[status(thm)],[f154]) ).
fof(f156,plain,
( ! [Ax,C] :
( ~ status(Ax,C,csa)
| ( model(sK37_skl(C,Ax),not(C))
& model(sK37_skl(C,Ax),Ax) ) )
& ! [Ax,C] :
( status(Ax,C,csa)
| ! [I1] :
( ~ model(I1,not(C))
| ~ model(I1,Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37_skl]),skolemize(I1,sK37_skl(C,Ax))],[f155]) ).
fof(f157,plain,
! [X0,X1,X2] :
( status(X1,X2,csa)
| ~ model(X0,not(X2))
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f158,plain,
! [X0,X1] :
( ~ status(X1,X0,csa)
| model(sK37_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f159,plain,
! [X0,X1] :
( ~ status(X1,X0,csa)
| model(sK37_skl(X0,X1),not(X0)) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f200,plain,
! [S1,S2] :
( ( ~ xora(S1,S2)
| ! [Ax,C] :
( ( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) )
& ( status(Ax,C,S2)
| status(Ax,C,S1) ) ) )
& ( xora(S1,S2)
| ? [Ax,C] :
( ( ~ status(Ax,C,S2)
| status(Ax,C,S1) )
& ( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f201,plain,
( ! [S1,S2] :
( ~ xora(S1,S2)
| ( ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) )
& ! [Ax,C] :
( status(Ax,C,S2)
| status(Ax,C,S1) ) ) )
& ! [S1,S2] :
( xora(S1,S2)
| ? [Ax,C] :
( ( ~ status(Ax,C,S2)
| status(Ax,C,S1) )
& ( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ) ),
inference(miniscoping,[status(thm)],[f200]) ).
fof(f202,plain,
( ! [S1,S2] :
( ~ xora(S1,S2)
| ( ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) )
& ! [Ax,C] :
( status(Ax,C,S2)
| status(Ax,C,S1) ) ) )
& ! [S1,S2] :
( xora(S1,S2)
| ( ( ~ status(sK50_skl(S2,S1),sK51_skl(S2,S1),S2)
| status(sK50_skl(S2,S1),sK51_skl(S2,S1),S1) )
& ( status(sK50_skl(S2,S1),sK51_skl(S2,S1),S2)
| ~ status(sK50_skl(S2,S1),sK51_skl(S2,S1),S1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50_skl,sK51_skl]),skolemize(Ax,sK50_skl(S2,S1)),skolemize(C,sK51_skl(S2,S1))],[f201]) ).
fof(f203,plain,
! [X0,X1] :
( xora(X1,X0)
| status(sK50_skl(X0,X1),sK51_skl(X0,X1),X0)
| ~ status(sK50_skl(X0,X1),sK51_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0,X1] :
( xora(X1,X0)
| ~ status(sK50_skl(X0,X1),sK51_skl(X0,X1),X0)
| status(sK50_skl(X0,X1),sK51_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f207,plain,
! [I,F] :
( ( ~ model(I,not(F))
| ~ model(I,F) )
& ( model(I,not(F))
| model(I,F) ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f208,plain,
( ! [I,F] :
( ~ model(I,not(F))
| ~ model(I,F) )
& ! [I,F] :
( model(I,not(F))
| model(I,F) ) ),
inference(miniscoping,[status(thm)],[f207]) ).
fof(f209,plain,
! [X0,X1] :
( model(X0,not(X1))
| model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f210,plain,
! [X0,X1] :
( ~ model(X0,not(X1))
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f215,plain,
! [I] : model(I,sK52_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl]),skolemize(F,sK52_skl)],[f27]) ).
fof(f216,plain,
! [X0] : model(X0,sK52_skl),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f217,plain,
( ~ model(sK55_skl,sK53_skl)
& model(sK54_skl,sK53_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl,sK54_skl,sK55_skl]),skolemize(F,sK53_skl),skolemize(I1,sK54_skl),skolemize(I2,sK55_skl)],[f28]) ).
fof(f218,plain,
model(sK54_skl,sK53_skl),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
~ model(sK55_skl,sK53_skl),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [I] : ~ model(I,sK56_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56_skl]),skolemize(F,sK56_skl)],[f29]) ).
fof(f221,plain,
! [X0] : ~ model(X0,sK56_skl),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f222,plain,
? [Ax,C] :
( ( ? [I2] : ~ model(I2,C)
| ? [I2] : ~ model(I2,Ax) )
& ? [I1] :
( model(I1,C)
& model(I1,Ax) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f223,plain,
( ( ~ model(sK61_skl,sK58_skl)
| ~ model(sK60_skl,sK57_skl) )
& model(sK59_skl,sK58_skl)
& model(sK59_skl,sK57_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57_skl,sK58_skl,sK59_skl,sK60_skl,sK61_skl]),skolemize(Ax,sK57_skl),skolemize(C,sK58_skl),skolemize(I1,sK59_skl),skolemize(I2,sK60_skl),skolemize(I2,sK61_skl)],[f222]) ).
fof(f224,plain,
model(sK59_skl,sK57_skl),
inference(cnf_transformation,[status(thm)],[f223]) ).
fof(f225,plain,
model(sK59_skl,sK58_skl),
inference(cnf_transformation,[status(thm)],[f223]) ).
fof(f226,plain,
( ~ model(sK61_skl,sK58_skl)
| ~ model(sK60_skl,sK57_skl) ),
inference(cnf_transformation,[status(thm)],[f223]) ).
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(f235,plain,
? [C] :
( ? [I2] : model(I2,C)
& ? [I1] :
( ~ model(I1,C)
& ? [Ax] : model(I1,Ax) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f236,plain,
( model(sK70_skl,sK67_skl)
& ~ model(sK68_skl,sK67_skl)
& model(sK68_skl,sK69_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67_skl,sK68_skl,sK69_skl,sK70_skl]),skolemize(C,sK67_skl),skolemize(I1,sK68_skl),skolemize(Ax,sK69_skl),skolemize(I2,sK70_skl)],[f235]) ).
fof(f237,plain,
model(sK68_skl,sK69_skl),
inference(cnf_transformation,[status(thm)],[f236]) ).
fof(f238,plain,
~ model(sK68_skl,sK67_skl),
inference(cnf_transformation,[status(thm)],[f236]) ).
fof(f239,plain,
model(sK70_skl,sK67_skl),
inference(cnf_transformation,[status(thm)],[f236]) ).
fof(f240,plain,
~ xora(csa,thm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f241,definition,
( sQ0_spl
<=> model(sK60_skl,sK57_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( sQ0_spl
| ~ model(sK60_skl,sK57_skl) ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
( sQ1_spl
<=> model(sK61_skl,sK58_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( sQ1_spl
| ~ model(sK61_skl,sK58_skl) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f226,f241,f244]) ).
fof(f248,plain,
! [X0,X1,X2] :
( model(X2,X0)
| ~ model(X2,X1)
| ~ model(sK9_skl(X0,X1),X0) ),
inference(resolution,[status(thm)],[f67,f68]) ).
fof(f252,plain,
! [X0,X1] :
( ~ status(X1,sK56_skl,thm)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f221,f68]) ).
fof(f254,plain,
! [X0] :
( ~ status(X0,sK53_skl,thm)
| ~ model(sK55_skl,X0) ),
inference(resolution,[status(thm)],[f219,f68]) ).
fof(f255,plain,
! [X0,X1] :
( ~ status(sK56_skl,X1,unp)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f41,f221]) ).
fof(f289,plain,
! [X0] :
( ~ status(X0,sK62_skl,thm)
| ~ model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f234,f68]) ).
fof(f290,plain,
! [X0,X1] :
( ~ status(X1,sK56_skl,sap)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f48,f221]) ).
fof(f329,plain,
! [X0] :
( ~ status(X0,sK67_skl,thm)
| ~ model(sK68_skl,X0) ),
inference(resolution,[status(thm)],[f238,f68]) ).
fof(f330,plain,
! [X0] :
( sQ0_spl
| ~ model(sK60_skl,X0)
| ~ model(sK9_skl(sK57_skl,X0),sK57_skl) ),
inference(resolution,[status(thm)],[f243,f248]) ).
fof(f331,plain,
! [X0] :
( sQ0_spl
| ~ status(X0,sK57_skl,thm)
| ~ model(sK60_skl,X0) ),
inference(resolution,[status(thm)],[f243,f68]) ).
fof(f362,plain,
! [X0,X1] :
( sQ0_spl
| ~ model(sK9_skl(sK57_skl,X0),X1)
| ~ model(sK9_skl(sK57_skl,X1),sK57_skl)
| ~ model(sK60_skl,X0) ),
inference(resolution,[status(thm)],[f330,f248]) ).
fof(f364,definition,
( sQ14_spl
<=> status(sK57_skl,sK57_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f387,plain,
! [X0] :
( sQ0_spl
| status(sK57_skl,sK57_skl,thm)
| ~ model(sK9_skl(sK57_skl,X0),sK57_skl)
| ~ model(sK60_skl,X0) ),
inference(resolution,[status(thm)],[f362,f66]) ).
fof(f390,definition,
! [X0] :
( sQ16_spl
<=> ( ~ model(sK9_skl(sK57_skl,X0),sK57_skl)
| ~ model(sK60_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( sQ0_spl
| sQ14_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f387,f390,f364,f241]) ).
fof(f405,plain,
! [X0] :
( sQ1_spl
| ~ model(sK61_skl,X0)
| ~ model(sK9_skl(sK58_skl,X0),sK58_skl) ),
inference(resolution,[status(thm)],[f246,f248]) ).
fof(f406,plain,
! [X0] :
( sQ1_spl
| ~ status(X0,sK58_skl,thm)
| ~ model(sK61_skl,X0) ),
inference(resolution,[status(thm)],[f246,f68]) ).
fof(f409,plain,
! [X0] : ~ status(sK56_skl,X0,eqv),
inference(resolution,[status(thm)],[f74,f221]) ).
fof(f413,plain,
! [X0,X1] :
( sQ1_spl
| ~ model(sK9_skl(sK58_skl,X0),X1)
| ~ model(sK9_skl(sK58_skl,X1),sK58_skl)
| ~ model(sK61_skl,X0) ),
inference(resolution,[status(thm)],[f405,f248]) ).
fof(f415,definition,
( sQ18_spl
<=> status(sK58_skl,sK58_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f421,plain,
! [X0] :
( sQ1_spl
| status(sK58_skl,sK58_skl,thm)
| ~ model(sK9_skl(sK58_skl,X0),sK58_skl)
| ~ model(sK61_skl,X0) ),
inference(resolution,[status(thm)],[f413,f66]) ).
fof(f424,definition,
! [X0] :
( sQ19_spl
<=> ( ~ model(sK9_skl(sK58_skl,X0),sK58_skl)
| ~ model(sK61_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( sQ1_spl
| sQ18_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f421,f424,f415,f244]) ).
fof(f437,plain,
! [X0,X1] :
( model(sK10_skl(X1,sK56_skl),X1)
| model(sK10_skl(X1,sK56_skl),sK56_skl)
| ~ model(X0,sK56_skl) ),
inference(resolution,[status(thm)],[f409,f73]) ).
fof(f439,definition,
! [X0] :
( sQ20_spl
<=> ~ model(X0,sK56_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f442,definition,
! [X1] :
( sQ21_spl
<=> ( model(sK10_skl(X1,sK56_skl),X1)
| model(sK10_skl(X1,sK56_skl),sK56_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f443,plain,
! [X0] :
( ~ sQ21_spl
| model(sK10_skl(X0,sK56_skl),X0)
| model(sK10_skl(X0,sK56_skl),sK56_skl) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f437,f439,f442]) ).
fof(f450,plain,
! [X0] :
( ~ sQ21_spl
| model(sK10_skl(X0,sK56_skl),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f443,f221]) ).
fof(f451,plain,
( ~ sQ21_spl
| $false ),
inference(resolution,[status(thm)],[f450,f221]) ).
fof(f452,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f451]) ).
fof(f460,plain,
! [X0,X1] :
( ~ status(X1,X0,csa)
| ~ model(sK37_skl(X0,X1),X0) ),
inference(resolution,[status(thm)],[f210,f159]) ).
fof(f485,plain,
! [X0,X1,X2] :
( ~ model(X2,not(X0))
| ~ model(X2,X1)
| ~ model(sK37_skl(X0,X1),X0) ),
inference(resolution,[status(thm)],[f460,f157]) ).
fof(f486,plain,
~ model(sK66_skl,sK63_skl),
inference(resolution,[status(thm)],[f231,f234]) ).
fof(f490,plain,
! [X0] :
( ~ status(X0,sK63_skl,thm)
| ~ model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f486,f68]) ).
fof(f491,plain,
! [X0,X1] :
( model(sK0_skl(X1,sK56_skl),X1)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f255,f40]) ).
fof(f493,definition,
! [X0,X1] :
( sQ23_spl
<=> ~ model(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f494,plain,
! [X0,X1] :
( ~ sQ23_spl
| ~ model(X0,X1) ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f514,plain,
! [X0,X1] :
( ~ model(X0,not(sK52_skl))
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f485,f216]) ).
fof(f546,plain,
! [X0,X1] :
( ~ sQ23_spl
| model(X0,not(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f209,f494]) ).
fof(f568,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f494]) ).
fof(f569,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f591,plain,
! [X0] :
( ~ status(sK67_skl,X0,thm)
| model(sK70_skl,X0) ),
inference(resolution,[status(thm)],[f239,f68]) ).
fof(f601,plain,
! [X0] :
( model(sK9_skl(X0,sK67_skl),sK67_skl)
| model(sK70_skl,X0) ),
inference(resolution,[status(thm)],[f591,f66]) ).
fof(f609,plain,
! [X0] :
( ~ status(sK69_skl,X0,thm)
| model(sK68_skl,X0) ),
inference(resolution,[status(thm)],[f237,f68]) ).
fof(f613,plain,
! [X0] :
( ~ status(sK62_skl,X0,thm)
| model(sK65_skl,X0) ),
inference(resolution,[status(thm)],[f233,f68]) ).
fof(f616,plain,
! [X0] :
( ~ status(sK63_skl,X0,thm)
| model(sK64_skl,X0) ),
inference(resolution,[status(thm)],[f230,f68]) ).
fof(f619,plain,
! [X0] :
( ~ status(sK58_skl,X0,thm)
| model(sK59_skl,X0) ),
inference(resolution,[status(thm)],[f225,f68]) ).
fof(f622,plain,
! [X0] :
( ~ status(sK57_skl,X0,thm)
| model(sK59_skl,X0) ),
inference(resolution,[status(thm)],[f224,f68]) ).
fof(f625,plain,
! [X0] :
( ~ status(sK53_skl,X0,thm)
| model(sK54_skl,X0) ),
inference(resolution,[status(thm)],[f218,f68]) ).
fof(f631,plain,
! [X0] :
( model(sK9_skl(X0,sK69_skl),sK69_skl)
| model(sK68_skl,X0) ),
inference(resolution,[status(thm)],[f609,f66]) ).
fof(f638,plain,
! [X0] :
( model(sK9_skl(X0,sK62_skl),sK62_skl)
| model(sK65_skl,X0) ),
inference(resolution,[status(thm)],[f613,f66]) ).
fof(f642,plain,
! [X0] :
( model(sK9_skl(X0,sK63_skl),sK63_skl)
| model(sK64_skl,X0) ),
inference(resolution,[status(thm)],[f616,f66]) ).
fof(f648,definition,
! [X0] :
( sQ26_spl
<=> ~ model(X0,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f649,plain,
! [X0] :
( ~ sQ26_spl
| ~ model(X0,sK52_skl) ),
inference(component_clause,[status(thm)],[f648]) ).
fof(f651,definition,
! [X1] :
( sQ27_spl
<=> model(X1,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f658,definition,
! [X2] :
( sQ29_spl
<=> ( ~ model(sK17_skl(X2,sK52_skl),X2)
| ~ model(sK17_skl(X2,sK52_skl),sK52_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f659,plain,
! [X0] :
( ~ sQ29_spl
| ~ model(sK17_skl(X0,sK52_skl),X0)
| ~ model(sK17_skl(X0,sK52_skl),sK52_skl) ),
inference(component_clause,[status(thm)],[f658]) ).
fof(f662,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f649,f216]) ).
fof(f663,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f662]) ).
fof(f664,plain,
! [X0] :
( ~ sQ29_spl
| ~ model(sK17_skl(X0,sK52_skl),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f659,f216]) ).
fof(f667,plain,
( ~ sQ29_spl
| $false ),
inference(resolution,[status(thm)],[f664,f216]) ).
fof(f668,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f667]) ).
fof(f680,plain,
! [X0] :
( model(sK9_skl(X0,sK58_skl),sK58_skl)
| model(sK59_skl,X0) ),
inference(resolution,[status(thm)],[f619,f66]) ).
fof(f695,plain,
! [X0] :
( model(sK9_skl(X0,sK57_skl),sK57_skl)
| model(sK59_skl,X0) ),
inference(resolution,[status(thm)],[f622,f66]) ).
fof(f698,plain,
! [X0] :
( model(sK9_skl(X0,sK53_skl),sK53_skl)
| model(sK54_skl,X0) ),
inference(resolution,[status(thm)],[f625,f66]) ).
fof(f700,definition,
! [X2] :
( sQ30_spl
<=> ~ model(sK22_skl(X2,sK52_skl),X2) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f701,plain,
! [X0] :
( ~ sQ30_spl
| ~ model(sK22_skl(X0,sK52_skl),X0) ),
inference(component_clause,[status(thm)],[f700]) ).
fof(f704,plain,
( ~ sQ30_spl
| $false ),
inference(resolution,[status(thm)],[f701,f216]) ).
fof(f705,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f704]) ).
fof(f731,plain,
! [X0,X1,X2] :
( model(X2,not(X0))
| ~ model(X2,X1)
| model(sK9_skl(not(X0),X1),X0) ),
inference(resolution,[status(thm)],[f209,f248]) ).
fof(f737,plain,
! [X0,X1,X2] :
( status(X2,X1,csa)
| ~ model(X0,X2)
| model(X0,X1) ),
inference(resolution,[status(thm)],[f209,f157]) ).
fof(f748,plain,
! [X0] : ~ status(sK52_skl,X0,wth),
inference(resolution,[status(thm)],[f124,f216]) ).
fof(f759,plain,
! [X0] :
( ~ status(sK67_skl,sK56_skl,thm)
| model(sK70_skl,X0) ),
inference(resolution,[status(thm)],[f601,f252]) ).
fof(f770,definition,
! [X0] :
( sQ33_spl
<=> model(sK70_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f771,plain,
! [X0] :
( ~ sQ33_spl
| model(sK70_skl,X0) ),
inference(component_clause,[status(thm)],[f770]) ).
fof(f773,definition,
( sQ34_spl
<=> status(sK67_skl,sK56_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f776,plain,
( ~ sQ34_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f759,f770,f773]) ).
fof(f779,plain,
( ~ sQ33_spl
| $false ),
inference(resolution,[status(thm)],[f771,f221]) ).
fof(f787,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f779]) ).
fof(f796,plain,
! [X0,X1,X2,X3] :
( model(X3,X1)
| model(X2,sK52_skl)
| ~ model(X2,X1)
| ~ model(sK25_skl(X1,sK52_skl),X1)
| ~ model(X0,sK52_skl) ),
inference(resolution,[status(thm)],[f748,f120]) ).
fof(f797,plain,
! [X0,X1,X2,X3] :
( model(X3,X1)
| model(X2,sK52_skl)
| ~ model(X2,X1)
| model(sK25_skl(X1,sK52_skl),sK52_skl)
| ~ model(X0,sK52_skl) ),
inference(resolution,[status(thm)],[f748,f119]) ).
fof(f798,definition,
! [X1,X2,X3] :
( sQ35_spl
<=> ( model(X3,X1)
| model(X2,sK52_skl)
| ~ model(X2,X1)
| ~ model(sK25_skl(X1,sK52_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f801,plain,
( sQ35_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f796,f648,f798]) ).
fof(f802,definition,
! [X1,X2,X3] :
( sQ36_spl
<=> ( model(X3,X1)
| model(X2,sK52_skl)
| ~ model(X2,X1)
| model(sK25_skl(X1,sK52_skl),sK52_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f805,plain,
( sQ36_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f797,f648,f802]) ).
fof(f820,plain,
! [X0,X1] :
( ~ model(X1,X0)
| model(sK29_skl(X0),X0) ),
inference(resolution,[status(thm)],[f130,f131]) ).
fof(f830,plain,
! [X0] :
( ~ status(sK69_skl,sK56_skl,thm)
| model(sK68_skl,X0) ),
inference(resolution,[status(thm)],[f631,f252]) ).
fof(f843,definition,
! [X0] :
( sQ42_spl
<=> model(sK68_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f844,plain,
! [X0] :
( ~ sQ42_spl
| model(sK68_skl,X0) ),
inference(component_clause,[status(thm)],[f843]) ).
fof(f846,definition,
( sQ43_spl
<=> status(sK69_skl,sK56_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f849,plain,
( ~ sQ43_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f830,f843,f846]) ).
fof(f852,plain,
( ~ sQ42_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f238,f844]) ).
fof(f863,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f852]) ).
fof(f874,plain,
! [X0] :
( model(sK29_skl(sK63_skl),sK62_skl)
| ~ model(X0,sK63_skl) ),
inference(resolution,[status(thm)],[f820,f231]) ).
fof(f876,plain,
! [X0,X1] :
( ~ model(sK29_skl(not(sK52_skl)),X1)
| ~ model(X0,not(sK52_skl)) ),
inference(resolution,[status(thm)],[f820,f514]) ).
fof(f883,definition,
! [X0] :
( sQ44_spl
<=> ~ model(X0,sK63_skl) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f884,plain,
! [X0] :
( ~ sQ44_spl
| ~ model(X0,sK63_skl) ),
inference(component_clause,[status(thm)],[f883]) ).
fof(f886,definition,
( sQ45_spl
<=> model(sK29_skl(sK63_skl),sK62_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f889,plain,
( sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f874,f883,f886]) ).
fof(f890,definition,
! [X0] :
( sQ46_spl
<=> ~ model(X0,not(sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f891,plain,
! [X0] :
( ~ sQ46_spl
| ~ model(X0,not(sK52_skl)) ),
inference(component_clause,[status(thm)],[f890]) ).
fof(f893,definition,
! [X1] :
( sQ47_spl
<=> ~ model(sK29_skl(not(sK52_skl)),X1) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f894,plain,
! [X0] :
( ~ sQ47_spl
| ~ model(sK29_skl(not(sK52_skl)),X0) ),
inference(component_clause,[status(thm)],[f893]) ).
fof(f896,plain,
( sQ47_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f876,f890,f893]) ).
fof(f904,plain,
! [X0] :
( ~ sQ47_spl
| model(sK29_skl(not(sK52_skl)),X0) ),
inference(resolution,[status(thm)],[f894,f209]) ).
fof(f906,plain,
( ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f904,f894]) ).
fof(f907,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f906]) ).
fof(f912,plain,
! [X0] :
( ~ status(sK62_skl,sK56_skl,thm)
| model(sK65_skl,X0) ),
inference(resolution,[status(thm)],[f638,f252]) ).
fof(f923,definition,
! [X0] :
( sQ50_spl
<=> model(sK65_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f924,plain,
! [X0] :
( ~ sQ50_spl
| model(sK65_skl,X0) ),
inference(component_clause,[status(thm)],[f923]) ).
fof(f926,definition,
( sQ51_spl
<=> status(sK62_skl,sK56_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f929,plain,
( ~ sQ51_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f912,f923,f926]) ).
fof(f932,plain,
( ~ sQ50_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f232,f924]) ).
fof(f943,plain,
~ sQ50_spl,
inference(contradiction_clause,[status(thm)],[f932]) ).
fof(f959,plain,
! [X0] :
( ~ status(sK63_skl,sK56_skl,thm)
| model(sK64_skl,X0) ),
inference(resolution,[status(thm)],[f642,f252]) ).
fof(f974,definition,
! [X0] :
( sQ55_spl
<=> model(sK64_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f975,plain,
! [X0] :
( ~ sQ55_spl
| model(sK64_skl,X0) ),
inference(component_clause,[status(thm)],[f974]) ).
fof(f977,definition,
( sQ56_spl
<=> status(sK63_skl,sK56_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f980,plain,
( ~ sQ56_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f959,f974,f977]) ).
fof(f981,plain,
! [X0] :
( model(X0,sK58_skl)
| ~ model(X0,sK58_skl)
| model(sK59_skl,sK58_skl) ),
inference(resolution,[status(thm)],[f680,f248]) ).
fof(f982,plain,
( status(sK58_skl,sK58_skl,thm)
| model(sK59_skl,sK58_skl) ),
inference(resolution,[status(thm)],[f680,f67]) ).
fof(f984,plain,
! [X0] :
( ~ status(sK58_skl,sK56_skl,thm)
| model(sK59_skl,X0) ),
inference(resolution,[status(thm)],[f680,f252]) ).
fof(f986,definition,
( sQ57_spl
<=> model(sK59_skl,sK58_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f989,definition,
! [X0] :
( sQ58_spl
<=> ( model(X0,sK58_skl)
| ~ model(X0,sK58_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f992,plain,
( sQ58_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f981,f986,f989]) ).
fof(f993,plain,
( sQ18_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f982,f986,f415]) ).
fof(f994,definition,
! [X0] :
( sQ59_spl
<=> model(sK59_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f995,plain,
! [X0] :
( ~ sQ59_spl
| model(sK59_skl,X0) ),
inference(component_clause,[status(thm)],[f994]) ).
fof(f997,definition,
( sQ60_spl
<=> status(sK58_skl,sK56_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1000,plain,
( ~ sQ60_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f984,f994,f997]) ).
fof(f1001,plain,
( ~ sQ44_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f230,f884]) ).
fof(f1005,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f1001]) ).
fof(f1007,plain,
( ~ sQ55_spl
| $false ),
inference(resolution,[status(thm)],[f975,f221]) ).
fof(f1015,plain,
~ sQ55_spl,
inference(contradiction_clause,[status(thm)],[f1007]) ).
fof(f1018,plain,
( ~ sQ59_spl
| $false ),
inference(resolution,[status(thm)],[f995,f221]) ).
fof(f1026,plain,
~ sQ59_spl,
inference(contradiction_clause,[status(thm)],[f1018]) ).
fof(f1051,plain,
( status(sK57_skl,sK57_skl,thm)
| model(sK59_skl,sK57_skl) ),
inference(resolution,[status(thm)],[f695,f67]) ).
fof(f1053,plain,
! [X0] :
( ~ status(sK57_skl,sK56_skl,thm)
| model(sK59_skl,X0) ),
inference(resolution,[status(thm)],[f695,f252]) ).
fof(f1055,definition,
( sQ61_spl
<=> model(sK59_skl,sK57_skl) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1063,plain,
( sQ14_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f1051,f1055,f364]) ).
fof(f1064,definition,
( sQ63_spl
<=> status(sK57_skl,sK56_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1067,plain,
( ~ sQ63_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f1053,f994,f1064]) ).
fof(f1072,plain,
! [X0] :
( ~ status(sK53_skl,sK56_skl,thm)
| model(sK54_skl,X0) ),
inference(resolution,[status(thm)],[f698,f252]) ).
fof(f1083,definition,
! [X0] :
( sQ66_spl
<=> model(sK54_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1084,plain,
! [X0] :
( ~ sQ66_spl
| model(sK54_skl,X0) ),
inference(component_clause,[status(thm)],[f1083]) ).
fof(f1086,definition,
( sQ67_spl
<=> status(sK53_skl,sK56_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1089,plain,
( ~ sQ67_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1072,f1083,f1086]) ).
fof(f1091,plain,
( ~ sQ66_spl
| $false ),
inference(resolution,[status(thm)],[f1084,f221]) ).
fof(f1099,plain,
~ sQ66_spl,
inference(contradiction_clause,[status(thm)],[f1091]) ).
fof(f1136,plain,
! [X0,X1] :
( model(X0,not(sK56_skl))
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f731,f221]) ).
fof(f1137,plain,
! [X0,X1] :
( ~ sQ46_spl
| model(X0,not(not(sK52_skl)))
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f731,f891]) ).
fof(f1147,plain,
! [X0] :
( ~ status(not(sK56_skl),sK67_skl,thm)
| ~ model(sK68_skl,X0) ),
inference(resolution,[status(thm)],[f1136,f329]) ).
fof(f1152,plain,
! [X0] :
( ~ status(not(sK56_skl),sK53_skl,thm)
| ~ model(sK55_skl,X0) ),
inference(resolution,[status(thm)],[f1136,f254]) ).
fof(f1153,plain,
! [X0] :
( ~ status(not(sK56_skl),sK62_skl,thm)
| ~ model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f1136,f289]) ).
fof(f1154,plain,
! [X0] :
( ~ status(not(sK56_skl),sK63_skl,thm)
| ~ model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f1136,f490]) ).
fof(f1155,plain,
! [X0] :
( sQ0_spl
| ~ status(not(sK56_skl),sK57_skl,thm)
| ~ model(sK60_skl,X0) ),
inference(resolution,[status(thm)],[f1136,f331]) ).
fof(f1164,plain,
! [X0,X1] :
( ~ status(not(sK56_skl),sK56_skl,thm)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f1136,f252]) ).
fof(f1169,definition,
( sQ69_spl
<=> model(sK9_skl(sK63_skl,not(sK56_skl)),not(sK56_skl)) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1173,definition,
! [X0] :
( sQ70_spl
<=> ~ model(sK68_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1174,plain,
! [X0] :
( ~ sQ70_spl
| ~ model(sK68_skl,X0) ),
inference(component_clause,[status(thm)],[f1173]) ).
fof(f1176,definition,
( sQ71_spl
<=> status(not(sK56_skl),sK67_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1179,plain,
( ~ sQ71_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f1147,f1173,f1176]) ).
fof(f1180,definition,
! [X0] :
( sQ72_spl
<=> ~ model(sK55_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1181,plain,
! [X0] :
( ~ sQ72_spl
| ~ model(sK55_skl,X0) ),
inference(component_clause,[status(thm)],[f1180]) ).
fof(f1183,definition,
( sQ73_spl
<=> status(not(sK56_skl),sK53_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1186,plain,
( ~ sQ73_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f1152,f1180,f1183]) ).
fof(f1187,definition,
! [X0] :
( sQ74_spl
<=> ~ model(sK66_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1188,plain,
! [X0] :
( ~ sQ74_spl
| ~ model(sK66_skl,X0) ),
inference(component_clause,[status(thm)],[f1187]) ).
fof(f1190,definition,
( sQ75_spl
<=> status(not(sK56_skl),sK62_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1193,plain,
( ~ sQ75_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f1153,f1187,f1190]) ).
fof(f1194,definition,
( sQ76_spl
<=> status(not(sK56_skl),sK63_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1197,plain,
( ~ sQ76_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f1154,f1187,f1194]) ).
fof(f1198,definition,
! [X0] :
( sQ77_spl
<=> ~ model(sK60_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1199,plain,
! [X0] :
( ~ sQ77_spl
| ~ model(sK60_skl,X0) ),
inference(component_clause,[status(thm)],[f1198]) ).
fof(f1201,definition,
( sQ78_spl
<=> status(not(sK56_skl),sK57_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1204,plain,
( sQ0_spl
| ~ sQ78_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f1155,f1198,f1201,f241]) ).
fof(f1205,definition,
( sQ79_spl
<=> status(not(sK56_skl),sK56_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1208,plain,
( ~ sQ79_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1164,f493,f1205]) ).
fof(f1212,plain,
! [X0] :
( ~ sQ74_spl
| model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f1188,f209]) ).
fof(f1214,plain,
( ~ sQ74_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1212,f1188]) ).
fof(f1215,plain,
~ sQ74_spl,
inference(contradiction_clause,[status(thm)],[f1214]) ).
fof(f1218,plain,
! [X0] :
( ~ sQ72_spl
| model(sK55_skl,X0) ),
inference(resolution,[status(thm)],[f1181,f209]) ).
fof(f1220,plain,
( ~ sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1218,f1181]) ).
fof(f1221,plain,
~ sQ72_spl,
inference(contradiction_clause,[status(thm)],[f1220]) ).
fof(f1224,plain,
( ~ sQ70_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f237,f1174]) ).
fof(f1228,plain,
~ sQ70_spl,
inference(contradiction_clause,[status(thm)],[f1224]) ).
fof(f1231,plain,
! [X0] :
( model(sK9_skl(sK62_skl,X0),X0)
| ~ model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f289,f66]) ).
fof(f1234,plain,
! [X0] :
( model(sK9_skl(sK53_skl,X0),X0)
| ~ model(sK55_skl,X0) ),
inference(resolution,[status(thm)],[f254,f66]) ).
fof(f1244,plain,
! [X0] :
( ~ sQ77_spl
| model(sK60_skl,X0) ),
inference(resolution,[status(thm)],[f1199,f209]) ).
fof(f1246,plain,
( ~ sQ77_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1244,f1199]) ).
fof(f1247,plain,
~ sQ77_spl,
inference(contradiction_clause,[status(thm)],[f1246]) ).
fof(f1252,plain,
! [X0] :
( model(sK9_skl(sK67_skl,X0),X0)
| ~ model(sK68_skl,X0) ),
inference(resolution,[status(thm)],[f329,f66]) ).
fof(f1279,plain,
! [X0] :
( model(sK9_skl(sK63_skl,X0),X0)
| ~ model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f490,f66]) ).
fof(f1282,plain,
! [X0] :
( sQ0_spl
| model(sK9_skl(sK57_skl,X0),X0)
| ~ model(sK60_skl,X0) ),
inference(resolution,[status(thm)],[f331,f66]) ).
fof(f1293,plain,
! [X0] :
( model(sK0_skl(sK63_skl,sK56_skl),sK62_skl)
| ~ model(X0,sK63_skl) ),
inference(resolution,[status(thm)],[f491,f231]) ).
fof(f1302,definition,
( sQ80_spl
<=> model(sK0_skl(sK63_skl,sK56_skl),sK62_skl) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1305,plain,
( sQ80_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f1293,f883,f1302]) ).
fof(f1309,plain,
! [X0,X1] :
( ~ model(X1,X0)
| model(sK2_skl(sK56_skl,X0),X0) ),
inference(resolution,[status(thm)],[f46,f290]) ).
fof(f1310,plain,
! [X0] :
( model(sK2_skl(sK56_skl,sK63_skl),sK62_skl)
| ~ model(X0,sK63_skl) ),
inference(resolution,[status(thm)],[f1309,f231]) ).
fof(f1319,definition,
( sQ81_spl
<=> model(sK2_skl(sK56_skl,sK63_skl),sK62_skl) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1322,plain,
( sQ81_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f1310,f883,f1319]) ).
fof(f1339,plain,
! [X0,X1] :
( ~ sQ46_spl
| ~ status(not(not(sK52_skl)),sK56_skl,thm)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f1137,f252]) ).
fof(f1341,definition,
( sQ82_spl
<=> status(not(not(sK52_skl)),sK56_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1344,plain,
( ~ sQ46_spl
| ~ sQ82_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1339,f493,f1341,f890]) ).
fof(f1356,plain,
! [X0] :
( ~ sQ46_spl
| ~ model(sK66_skl,X0)
| model(sK9_skl(sK62_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
inference(resolution,[status(thm)],[f1231,f1137]) ).
fof(f1357,plain,
! [X0] :
( ~ model(sK66_skl,X0)
| model(sK9_skl(sK62_skl,not(sK56_skl)),not(sK56_skl)) ),
inference(resolution,[status(thm)],[f1231,f1136]) ).
fof(f1360,definition,
( sQ83_spl
<=> model(sK9_skl(sK62_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1363,plain,
( ~ sQ46_spl
| sQ74_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f1356,f1360,f1187,f890]) ).
fof(f1364,definition,
( sQ84_spl
<=> model(sK9_skl(sK62_skl,not(sK56_skl)),not(sK56_skl)) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1367,plain,
( sQ74_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f1357,f1364,f1187]) ).
fof(f1368,plain,
! [X0] :
( ~ sQ46_spl
| ~ model(sK55_skl,X0)
| model(sK9_skl(sK53_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
inference(resolution,[status(thm)],[f1234,f1137]) ).
fof(f1369,plain,
! [X0] :
( ~ model(sK55_skl,X0)
| model(sK9_skl(sK53_skl,not(sK56_skl)),not(sK56_skl)) ),
inference(resolution,[status(thm)],[f1234,f1136]) ).
fof(f1372,definition,
( sQ85_spl
<=> model(sK9_skl(sK53_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1375,plain,
( ~ sQ46_spl
| sQ72_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1368,f1372,f1180,f890]) ).
fof(f1376,definition,
( sQ86_spl
<=> model(sK9_skl(sK53_skl,not(sK56_skl)),not(sK56_skl)) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1379,plain,
( sQ72_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f1369,f1376,f1180]) ).
fof(f1385,definition,
( sQ87_spl
<=> model(sK9_skl(sK63_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1391,plain,
! [X0] :
( ~ sQ46_spl
| ~ model(sK68_skl,X0)
| model(sK9_skl(sK67_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
inference(resolution,[status(thm)],[f1252,f1137]) ).
fof(f1392,plain,
! [X0] :
( ~ model(sK68_skl,X0)
| model(sK9_skl(sK67_skl,not(sK56_skl)),not(sK56_skl)) ),
inference(resolution,[status(thm)],[f1252,f1136]) ).
fof(f1395,definition,
( sQ88_spl
<=> model(sK9_skl(sK67_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1398,plain,
( ~ sQ46_spl
| sQ70_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f1391,f1395,f1173,f890]) ).
fof(f1399,definition,
( sQ89_spl
<=> model(sK9_skl(sK67_skl,not(sK56_skl)),not(sK56_skl)) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1402,plain,
( sQ70_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f1392,f1399,f1173]) ).
fof(f1427,plain,
( status(sK50_skl(thm,csa),sK51_skl(thm,csa),thm)
| ~ status(sK50_skl(thm,csa),sK51_skl(thm,csa),csa) ),
inference(resolution,[status(thm)],[f203,f240]) ).
fof(f1430,definition,
( sQ90_spl
<=> status(sK50_skl(thm,csa),sK51_skl(thm,csa),csa) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1431,plain,
( ~ sQ90_spl
| status(sK50_skl(thm,csa),sK51_skl(thm,csa),csa) ),
inference(component_clause,[status(thm)],[f1430]) ).
fof(f1432,plain,
( sQ90_spl
| ~ status(sK50_skl(thm,csa),sK51_skl(thm,csa),csa) ),
inference(component_clause,[status(thm)],[f1430]) ).
fof(f1433,definition,
( sQ91_spl
<=> status(sK50_skl(thm,csa),sK51_skl(thm,csa),thm) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1434,plain,
( ~ sQ91_spl
| status(sK50_skl(thm,csa),sK51_skl(thm,csa),thm) ),
inference(component_clause,[status(thm)],[f1433]) ).
fof(f1435,plain,
( sQ91_spl
| ~ status(sK50_skl(thm,csa),sK51_skl(thm,csa),thm) ),
inference(component_clause,[status(thm)],[f1433]) ).
fof(f1436,plain,
( sQ91_spl
| ~ sQ90_spl ),
inference(split_clause,[status(thm)],[f1427,f1430,f1433]) ).
fof(f1437,plain,
! [X0] :
( sQ90_spl
| ~ model(X0,sK50_skl(thm,csa))
| model(X0,sK51_skl(thm,csa)) ),
inference(resolution,[status(thm)],[f1432,f737]) ).
fof(f1446,definition,
! [X0] :
( sQ93_spl
<=> ~ model(X0,sK50_skl(thm,csa)) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1447,plain,
! [X0] :
( ~ sQ93_spl
| ~ model(X0,sK50_skl(thm,csa)) ),
inference(component_clause,[status(thm)],[f1446]) ).
fof(f1477,plain,
! [X0,X1] :
( ~ sQ93_spl
| model(X0,not(sK50_skl(thm,csa)))
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f1447,f731]) ).
fof(f1478,plain,
! [X0] :
( ~ sQ46_spl
| ~ model(sK66_skl,X0)
| model(sK9_skl(sK63_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
inference(resolution,[status(thm)],[f1279,f1137]) ).
fof(f1479,plain,
! [X0] :
( ~ model(sK66_skl,X0)
| model(sK9_skl(sK63_skl,not(sK56_skl)),not(sK56_skl)) ),
inference(resolution,[status(thm)],[f1279,f1136]) ).
fof(f1482,plain,
( ~ sQ46_spl
| sQ74_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1478,f1385,f1187,f890]) ).
fof(f1483,plain,
( sQ74_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1479,f1169,f1187]) ).
fof(f1484,plain,
! [X0] :
( ~ sQ46_spl
| sQ0_spl
| ~ model(sK60_skl,X0)
| model(sK9_skl(sK57_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
inference(resolution,[status(thm)],[f1282,f1137]) ).
fof(f1485,plain,
! [X0] :
( sQ0_spl
| ~ model(sK60_skl,X0)
| model(sK9_skl(sK57_skl,not(sK56_skl)),not(sK56_skl)) ),
inference(resolution,[status(thm)],[f1282,f1136]) ).
fof(f1488,definition,
( sQ99_spl
<=> model(sK9_skl(sK57_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1491,plain,
( ~ sQ46_spl
| sQ0_spl
| sQ77_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f1484,f1488,f1198,f241,f890]) ).
fof(f1492,definition,
( sQ100_spl
<=> model(sK9_skl(sK57_skl,not(sK56_skl)),not(sK56_skl)) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1495,plain,
( sQ0_spl
| sQ77_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1485,f1492,f1198,f241]) ).
fof(f1498,plain,
! [X0] :
( sQ1_spl
| model(sK9_skl(sK58_skl,X0),X0)
| ~ model(sK61_skl,X0) ),
inference(resolution,[status(thm)],[f406,f66]) ).
fof(f1536,plain,
! [X0] :
( ~ sQ46_spl
| sQ1_spl
| ~ model(sK61_skl,X0)
| model(sK9_skl(sK58_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
inference(resolution,[status(thm)],[f1498,f1137]) ).
fof(f1537,plain,
! [X0] :
( sQ1_spl
| ~ model(sK61_skl,X0)
| model(sK9_skl(sK58_skl,not(sK56_skl)),not(sK56_skl)) ),
inference(resolution,[status(thm)],[f1498,f1136]) ).
fof(f1540,definition,
( sQ101_spl
<=> model(sK9_skl(sK58_skl,not(not(sK52_skl))),not(not(sK52_skl))) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1543,definition,
! [X0] :
( sQ102_spl
<=> ~ model(sK61_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1544,plain,
! [X0] :
( ~ sQ102_spl
| ~ model(sK61_skl,X0) ),
inference(component_clause,[status(thm)],[f1543]) ).
fof(f1546,plain,
( ~ sQ46_spl
| sQ1_spl
| sQ102_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f1536,f1540,f1543,f244,f890]) ).
fof(f1547,definition,
( sQ103_spl
<=> model(sK9_skl(sK58_skl,not(sK56_skl)),not(sK56_skl)) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1550,plain,
( sQ1_spl
| sQ102_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1537,f1547,f1543,f244]) ).
fof(f1551,plain,
( ~ status(sK50_skl(thm,csa),sK51_skl(thm,csa),thm)
| status(sK50_skl(thm,csa),sK51_skl(thm,csa),csa) ),
inference(resolution,[status(thm)],[f204,f240]) ).
fof(f1554,plain,
( ~ sQ91_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f1551,f1430,f1433]) ).
fof(f1563,plain,
! [X0,X1] :
( status(X1,sK52_skl,tac)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f80,f216]) ).
fof(f1566,plain,
( ~ sQ90_spl
| model(sK37_skl(sK51_skl(thm,csa),sK50_skl(thm,csa)),not(sK51_skl(thm,csa))) ),
inference(resolution,[status(thm)],[f1431,f159]) ).
fof(f1567,plain,
( ~ sQ90_spl
| model(sK37_skl(sK51_skl(thm,csa),sK50_skl(thm,csa)),sK50_skl(thm,csa)) ),
inference(resolution,[status(thm)],[f1431,f158]) ).
fof(f1584,plain,
! [X0] :
( ~ sQ102_spl
| model(sK61_skl,X0) ),
inference(resolution,[status(thm)],[f1544,f209]) ).
fof(f1586,plain,
( ~ sQ102_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1584,f1544]) ).
fof(f1587,plain,
~ sQ102_spl,
inference(contradiction_clause,[status(thm)],[f1586]) ).
fof(f1623,plain,
! [X0,X1] :
( model(sK13_skl(sK52_skl,X1),X1)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f1563,f81]) ).
fof(f1624,plain,
! [X0,X1,X2] :
( model(X2,sK52_skl)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f1563,f82]) ).
fof(f1625,plain,
( sQ27_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1624,f493,f651]) ).
fof(f1627,plain,
! [X0] :
( model(sK13_skl(sK52_skl,sK63_skl),sK62_skl)
| ~ model(X0,sK63_skl) ),
inference(resolution,[status(thm)],[f1623,f231]) ).
fof(f1636,definition,
( sQ106_spl
<=> model(sK13_skl(sK52_skl,sK63_skl),sK62_skl) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1639,plain,
( sQ106_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f1627,f883,f1636]) ).
fof(f1662,plain,
! [X0] :
( sQ1_spl
| ~ sQ93_spl
| model(sK9_skl(sK58_skl,not(sK50_skl(thm,csa))),not(sK50_skl(thm,csa)))
| ~ model(sK61_skl,X0) ),
inference(resolution,[status(thm)],[f1477,f1498]) ).
fof(f1666,plain,
! [X0] :
( ~ sQ93_spl
| model(sK9_skl(sK67_skl,not(sK50_skl(thm,csa))),not(sK50_skl(thm,csa)))
| ~ model(sK68_skl,X0) ),
inference(resolution,[status(thm)],[f1477,f1252]) ).
fof(f1667,plain,
! [X0] :
( ~ sQ93_spl
| model(sK9_skl(sK53_skl,not(sK50_skl(thm,csa))),not(sK50_skl(thm,csa)))
| ~ model(sK55_skl,X0) ),
inference(resolution,[status(thm)],[f1477,f1234]) ).
fof(f1668,plain,
! [X0] :
( ~ sQ93_spl
| model(sK9_skl(sK63_skl,not(sK50_skl(thm,csa))),not(sK50_skl(thm,csa)))
| ~ model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f1477,f1279]) ).
fof(f1669,plain,
! [X0] :
( ~ sQ93_spl
| model(sK9_skl(sK62_skl,not(sK50_skl(thm,csa))),not(sK50_skl(thm,csa)))
| ~ model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f1477,f1231]) ).
fof(f1684,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ status(not(sK50_skl(thm,csa)),sK56_skl,thm)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f1477,f252]) ).
fof(f1686,definition,
( sQ107_spl
<=> model(sK9_skl(sK58_skl,not(sK50_skl(thm,csa))),not(sK50_skl(thm,csa))) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1689,plain,
( sQ1_spl
| ~ sQ93_spl
| sQ107_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f1662,f1543,f1686,f1446,f244]) ).
fof(f1690,definition,
( sQ108_spl
<=> model(sK9_skl(sK63_skl,not(sK50_skl(thm,csa))),not(sK50_skl(thm,csa))) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1694,definition,
( sQ109_spl
<=> model(sK9_skl(sK67_skl,not(sK50_skl(thm,csa))),not(sK50_skl(thm,csa))) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1697,plain,
( ~ sQ93_spl
| sQ109_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f1666,f1173,f1694,f1446]) ).
fof(f1698,definition,
( sQ110_spl
<=> model(sK9_skl(sK53_skl,not(sK50_skl(thm,csa))),not(sK50_skl(thm,csa))) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1701,plain,
( ~ sQ93_spl
| sQ110_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f1667,f1180,f1698,f1446]) ).
fof(f1702,plain,
( ~ sQ93_spl
| sQ108_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f1668,f1187,f1690,f1446]) ).
fof(f1703,definition,
( sQ111_spl
<=> model(sK9_skl(sK62_skl,not(sK50_skl(thm,csa))),not(sK50_skl(thm,csa))) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1706,plain,
( ~ sQ93_spl
| sQ111_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f1669,f1187,f1703,f1446]) ).
fof(f1707,definition,
( sQ112_spl
<=> status(not(sK50_skl(thm,csa)),sK56_skl,thm) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1710,plain,
( ~ sQ93_spl
| ~ sQ112_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1684,f493,f1707,f1446]) ).
fof(f1723,plain,
! [X0] :
( ~ sQ90_spl
| ~ status(sK50_skl(thm,csa),X0,thm)
| model(sK37_skl(sK51_skl(thm,csa),sK50_skl(thm,csa)),X0) ),
inference(resolution,[status(thm)],[f1567,f68]) ).
fof(f1725,plain,
( ~ sQ90_spl
| ~ model(sK37_skl(sK51_skl(thm,csa),sK50_skl(thm,csa)),sK51_skl(thm,csa)) ),
inference(resolution,[status(thm)],[f1566,f210]) ).
fof(f1874,plain,
( ~ sQ91_spl
| ~ sQ90_spl
| model(sK37_skl(sK51_skl(thm,csa),sK50_skl(thm,csa)),sK51_skl(thm,csa)) ),
inference(resolution,[status(thm)],[f1723,f1434]) ).
fof(f1878,plain,
( ~ sQ91_spl
| ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1874,f1725]) ).
fof(f1879,plain,
( ~ sQ91_spl
| ~ sQ90_spl ),
inference(contradiction_clause,[status(thm)],[f1878]) ).
fof(f1890,plain,
( sQ91_spl
| model(sK9_skl(sK51_skl(thm,csa),sK50_skl(thm,csa)),sK50_skl(thm,csa)) ),
inference(resolution,[status(thm)],[f1435,f66]) ).
fof(f1995,plain,
( sQ91_spl
| sQ90_spl
| model(sK9_skl(sK51_skl(thm,csa),sK50_skl(thm,csa)),sK51_skl(thm,csa)) ),
inference(resolution,[status(thm)],[f1437,f1890]) ).
fof(f2023,plain,
( sQ91_spl
| sQ90_spl
| status(sK50_skl(thm,csa),sK51_skl(thm,csa),thm) ),
inference(resolution,[status(thm)],[f1995,f67]) ).
fof(f2027,plain,
( sQ90_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f2023,f1433,f1430]) ).
fof(f2028,plain,
$false,
inference(sat_refutation,[status(thm)],[f247,f393,f427,f445,f452,f569,f663,f668,f705,f776,f787,f801,f805,f849,f863,f889,f896,f907,f929,f943,f980,f992,f993,f1000,f1005,f1015,f1026,f1063,f1067,f1089,f1099,f1179,f1186,f1193,f1197,f1204,f1208,f1215,f1221,f1228,f1247,f1305,f1322,f1344,f1363,f1367,f1375,f1379,f1398,f1402,f1436,f1482,f1483,f1491,f1495,f1546,f1550,f1554,f1587,f1625,f1639,f1689,f1697,f1701,f1702,f1706,f1710,f1879,f2027]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS251+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 20 22:59:19 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 4.91/1.38 % Refutation found
% 4.91/1.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.91/1.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.91/1.40 % Elapsed time: 0.957842 seconds
% 4.91/1.40 % CPU time: 7.128603 seconds
% 4.91/1.40 % Total memory used: 59.193 MB
% 4.91/1.40 % Net memory used: 51.074 MB
%------------------------------------------------------------------------------