TSTP Solution File: NUM460+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM460+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:30:38 EDT 2023
% Result : Theorem 72.01s 10.81s
% Output : CNFRefutation 72.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 136 ( 40 unt; 0 def)
% Number of atoms : 434 ( 133 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 549 ( 251 ~; 245 |; 36 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 142 ( 0 sgn; 91 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f22,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__773) ).
fof(f23,conjecture,
( ( sdtlseqdt0(xn,xl)
& sdtlseqdt0(xm,xn) )
=> sdtlseqdt0(xm,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f24,negated_conjecture,
~ ( ( sdtlseqdt0(xn,xl)
& sdtlseqdt0(xm,xn) )
=> sdtlseqdt0(xm,xl) ),
inference(negated_conjecture,[],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f27,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f26]) ).
fof(f30,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f31,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f33,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f32]) ).
fof(f43,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f44,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f43]) ).
fof(f51,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f52,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f54,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f53]) ).
fof(f58,plain,
( ~ sdtlseqdt0(xm,xl)
& sdtlseqdt0(xn,xl)
& sdtlseqdt0(xm,xn) ),
inference(ennf_transformation,[],[f24]) ).
fof(f59,plain,
( ~ sdtlseqdt0(xm,xl)
& sdtlseqdt0(xn,xl)
& sdtlseqdt0(xm,xn) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f52]) ).
fof(f61,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f61,f62]) ).
fof(f64,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f54]) ).
fof(f65,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f64]) ).
fof(f69,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f71,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f72,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f83,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f90,plain,
! [X0,X1] :
( aNaturalNumber0(sK0(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f91,plain,
! [X0,X1] :
( sdtpldt0(X0,sK0(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f92,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f93,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f94,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X2) = X1
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f98,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f22]) ).
fof(f99,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f22]) ).
fof(f100,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f22]) ).
fof(f101,plain,
sdtlseqdt0(xm,xn),
inference(cnf_transformation,[],[f59]) ).
fof(f102,plain,
sdtlseqdt0(xn,xl),
inference(cnf_transformation,[],[f59]) ).
fof(f103,plain,
~ sdtlseqdt0(xm,xl),
inference(cnf_transformation,[],[f59]) ).
fof(f104,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f92]) ).
fof(f106,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f94]) ).
fof(f107,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f93]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f69]) ).
cnf(c_54,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f71]) ).
cnf(c_55,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f72]) ).
cnf(c_67,plain,
( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f104]) ).
cnf(c_74,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_75,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sK0(X0,X1)) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_77,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_78,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_81,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f100]) ).
cnf(c_82,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f99]) ).
cnf(c_83,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f98]) ).
cnf(c_84,negated_conjecture,
~ sdtlseqdt0(xm,xl),
inference(cnf_transformation,[],[f103]) ).
cnf(c_85,negated_conjecture,
sdtlseqdt0(xn,xl),
inference(cnf_transformation,[],[f102]) ).
cnf(c_86,negated_conjecture,
sdtlseqdt0(xm,xn),
inference(cnf_transformation,[],[f101]) ).
cnf(c_139,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_3729,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sK0(xn,xl)) = xl ),
inference(superposition,[status(thm)],[c_85,c_74]) ).
cnf(c_3730,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtpldt0(xm,sK0(xm,xn)) = xn ),
inference(superposition,[status(thm)],[c_86,c_74]) ).
cnf(c_3774,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sdtmndt0(xl,xn)) = xl ),
inference(superposition,[status(thm)],[c_85,c_77]) ).
cnf(c_3775,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtpldt0(xm,sdtmndt0(xn,xm)) = xn ),
inference(superposition,[status(thm)],[c_86,c_77]) ).
cnf(c_4877,plain,
sdtpldt0(xn,sK0(xn,xl)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3729,c_82,c_81,c_3729]) ).
cnf(c_4879,plain,
sdtpldt0(xm,sK0(xm,xn)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3730,c_83,c_82,c_3730]) ).
cnf(c_4881,plain,
sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3774,c_82,c_81,c_3774]) ).
cnf(c_4883,plain,
sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3775,c_83,c_82,c_3775]) ).
cnf(c_5868,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = X0 ),
inference(superposition,[status(thm)],[c_4877,c_67]) ).
cnf(c_5869,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = X0 ),
inference(superposition,[status(thm)],[c_4879,c_67]) ).
cnf(c_6079,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xl))
| sdtpldt0(xn,X0) != xl
| sK0(xn,xl) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_5868,c_82,c_5868]) ).
cnf(c_6080,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| sK0(xn,xl) = X0 ),
inference(renaming,[status(thm)],[c_6079]) ).
cnf(c_6086,plain,
( ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_4881,c_6080]) ).
cnf(c_6103,plain,
( ~ aNaturalNumber0(sdtmndt0(xl,xn))
| ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_75,c_6086]) ).
cnf(c_6115,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xn))
| sdtpldt0(xm,X0) != xn
| sK0(xm,xn) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_5869,c_83,c_5869]) ).
cnf(c_6116,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| sK0(xm,xn) = X0 ),
inference(renaming,[status(thm)],[c_6115]) ).
cnf(c_6124,plain,
( ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_4883,c_6116]) ).
cnf(c_6323,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_75,c_6124]) ).
cnf(c_7180,plain,
sdtpldt0(xn,sK0(xn,xl)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3729,c_82,c_81,c_3729]) ).
cnf(c_7182,plain,
sdtpldt0(xm,sK0(xm,xn)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3730,c_83,c_82,c_3730]) ).
cnf(c_7184,plain,
sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3774,c_82,c_81,c_3774]) ).
cnf(c_7186,plain,
sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3775,c_83,c_82,c_3775]) ).
cnf(c_8097,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = X0 ),
inference(superposition,[status(thm)],[c_7180,c_67]) ).
cnf(c_8098,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = X0 ),
inference(superposition,[status(thm)],[c_7182,c_67]) ).
cnf(c_8366,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xl))
| sdtpldt0(xn,X0) != xl
| sK0(xn,xl) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_8097,c_82,c_5868]) ).
cnf(c_8367,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| sK0(xn,xl) = X0 ),
inference(renaming,[status(thm)],[c_8366]) ).
cnf(c_8372,plain,
( ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_7184,c_8367]) ).
cnf(c_8373,plain,
( ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(global_subsumption_just,[status(thm)],[c_8372,c_82,c_81,c_85,c_6103]) ).
cnf(c_8375,plain,
( ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_78,c_8373]) ).
cnf(c_8376,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xn))
| sdtpldt0(xm,X0) != xn
| sK0(xm,xn) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_8098,c_83,c_5869]) ).
cnf(c_8377,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| sK0(xm,xn) = X0 ),
inference(renaming,[status(thm)],[c_8376]) ).
cnf(c_8384,plain,
( ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_7186,c_8377]) ).
cnf(c_8411,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(global_subsumption_just,[status(thm)],[c_8384,c_83,c_82,c_86,c_6323]) ).
cnf(c_8413,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_78,c_8411]) ).
cnf(c_8834,plain,
sK0(xn,xl) = sdtmndt0(xl,xn),
inference(global_subsumption_just,[status(thm)],[c_8375,c_82,c_81,c_85,c_8375]) ).
cnf(c_8836,plain,
( ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_8834,c_75]) ).
cnf(c_8840,plain,
sK0(xm,xn) = sdtmndt0(xn,xm),
inference(global_subsumption_just,[status(thm)],[c_8413,c_83,c_82,c_86,c_8413]) ).
cnf(c_8842,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_8840,c_75]) ).
cnf(c_9147,plain,
aNaturalNumber0(sdtmndt0(xl,xn)),
inference(global_subsumption_just,[status(thm)],[c_8836,c_82,c_81,c_85,c_8836]) ).
cnf(c_9155,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtmndt0(xl,xn),X0) = sdtpldt0(X0,sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_9147,c_54]) ).
cnf(c_9173,plain,
aNaturalNumber0(sdtmndt0(xn,xm)),
inference(global_subsumption_just,[status(thm)],[c_8842,c_83,c_82,c_86,c_8842]) ).
cnf(c_10462,plain,
sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)) = sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_9173,c_9155]) ).
cnf(c_11961,plain,
( ~ aNaturalNumber0(sdtmndt0(xl,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm))) ),
inference(superposition,[status(thm)],[c_10462,c_52]) ).
cnf(c_35902,plain,
sdtpldt0(xn,sK0(xn,xl)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3729,c_82,c_81,c_3729]) ).
cnf(c_35904,plain,
sdtpldt0(xm,sK0(xm,xn)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3730,c_83,c_82,c_3730]) ).
cnf(c_35906,plain,
sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3774,c_82,c_81,c_3774]) ).
cnf(c_35945,plain,
sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3775,c_83,c_82,c_3775]) ).
cnf(c_36778,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = X0 ),
inference(superposition,[status(thm)],[c_35902,c_67]) ).
cnf(c_36779,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = X0 ),
inference(superposition,[status(thm)],[c_35904,c_67]) ).
cnf(c_37005,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xl))
| sdtpldt0(xn,X0) != xl
| sK0(xn,xl) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_36778,c_82,c_5868]) ).
cnf(c_37006,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| sK0(xn,xl) = X0 ),
inference(renaming,[status(thm)],[c_37005]) ).
cnf(c_37011,plain,
( ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_35906,c_37006]) ).
cnf(c_37032,plain,
sK0(xn,xl) = sdtmndt0(xl,xn),
inference(global_subsumption_just,[status(thm)],[c_37011,c_82,c_81,c_85,c_8375]) ).
cnf(c_37034,plain,
( ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_37032,c_75]) ).
cnf(c_37037,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xn))
| sdtpldt0(xm,X0) != xn
| sK0(xm,xn) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_36779,c_83,c_5869]) ).
cnf(c_37038,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| sK0(xm,xn) = X0 ),
inference(renaming,[status(thm)],[c_37037]) ).
cnf(c_37045,plain,
( ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_35945,c_37038]) ).
cnf(c_37046,plain,
sK0(xm,xn) = sdtmndt0(xn,xm),
inference(global_subsumption_just,[status(thm)],[c_37045,c_83,c_82,c_86,c_8413]) ).
cnf(c_37048,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_37046,c_75]) ).
cnf(c_37386,plain,
aNaturalNumber0(sdtmndt0(xl,xn)),
inference(global_subsumption_just,[status(thm)],[c_37034,c_82,c_81,c_85,c_8836]) ).
cnf(c_37394,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtmndt0(xl,xn),X0) = sdtpldt0(X0,sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_37386,c_54]) ).
cnf(c_37401,plain,
aNaturalNumber0(sdtmndt0(xn,xm)),
inference(global_subsumption_just,[status(thm)],[c_37048,c_83,c_82,c_86,c_8842]) ).
cnf(c_37406,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X0,sdtmndt0(xn,xm)),X1) = sdtpldt0(X0,sdtpldt0(sdtmndt0(xn,xm),X1)) ),
inference(superposition,[status(thm)],[c_37401,c_55]) ).
cnf(c_38447,plain,
sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)) = sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_37401,c_37394]) ).
cnf(c_40112,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,sdtmndt0(xn,xm)),sdtmndt0(xl,xn)) = sdtpldt0(X0,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn))) ),
inference(superposition,[status(thm)],[c_37386,c_37406]) ).
cnf(c_40787,plain,
sdtpldt0(sdtpldt0(xm,sdtmndt0(xn,xm)),sdtmndt0(xl,xn)) = sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn))),
inference(superposition,[status(thm)],[c_83,c_40112]) ).
cnf(c_59816,plain,
sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn))) = sdtpldt0(xn,sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_35945,c_40787]) ).
cnf(c_59828,plain,
sdtpldt0(xm,sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm))) = sdtpldt0(xn,sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_38447,c_59816]) ).
cnf(c_59833,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)))
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))) ),
inference(superposition,[status(thm)],[c_59816,c_139]) ).
cnf(c_59853,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)))
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))) ),
inference(superposition,[status(thm)],[c_59828,c_139]) ).
cnf(c_59893,plain,
sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))),
inference(global_subsumption_just,[status(thm)],[c_59833,c_83,c_82,c_81,c_86,c_85,c_8836,c_8842,c_11961,c_59853]) ).
cnf(c_59895,plain,
sdtlseqdt0(xm,xl),
inference(superposition,[status(thm)],[c_35906,c_59893]) ).
cnf(c_59899,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_59895,c_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM460+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 14:27:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.46 Running first-order theorem proving
% 0.21/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 72.01/10.81 % SZS status Started for theBenchmark.p
% 72.01/10.81 % SZS status Theorem for theBenchmark.p
% 72.01/10.81
% 72.01/10.81 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 72.01/10.81
% 72.01/10.81 ------ iProver source info
% 72.01/10.81
% 72.01/10.81 git: date: 2023-05-31 18:12:56 +0000
% 72.01/10.81 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 72.01/10.81 git: non_committed_changes: false
% 72.01/10.81 git: last_make_outside_of_git: false
% 72.01/10.81
% 72.01/10.81 ------ Parsing...
% 72.01/10.81 ------ Clausification by vclausify_rel & Parsing by iProver...
% 72.01/10.81
% 72.01/10.81 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 72.01/10.81
% 72.01/10.81 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 72.01/10.81
% 72.01/10.81 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 72.01/10.81 ------ Proving...
% 72.01/10.81 ------ Problem Properties
% 72.01/10.81
% 72.01/10.81
% 72.01/10.81 clauses 38
% 72.01/10.81 conjectures 3
% 72.01/10.81 EPR 11
% 72.01/10.81 Horn 35
% 72.01/10.81 unary 9
% 72.01/10.81 binary 7
% 72.01/10.81 lits 113
% 72.01/10.81 lits eq 34
% 72.01/10.81 fd_pure 0
% 72.01/10.81 fd_pseudo 0
% 72.01/10.81 fd_cond 3
% 72.01/10.81 fd_pseudo_cond 5
% 72.01/10.81 AC symbols 0
% 72.01/10.81
% 72.01/10.81 ------ Input Options Time Limit: Unbounded
% 72.01/10.81
% 72.01/10.81
% 72.01/10.81 ------
% 72.01/10.81 Current options:
% 72.01/10.81 ------
% 72.01/10.81
% 72.01/10.81
% 72.01/10.81
% 72.01/10.81
% 72.01/10.81 ------ Proving...
% 72.01/10.81
% 72.01/10.81
% 72.01/10.81 % SZS status Theorem for theBenchmark.p
% 72.01/10.81
% 72.01/10.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 72.01/10.81
% 72.01/10.81
%------------------------------------------------------------------------------