TSTP Solution File: NUM460+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM460+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 : Mon Jun 24 12:52:31 EDT 2024
% Result : Theorem 68.72s 10.22s
% Output : CNFRefutation 68.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 138 ( 42 unt; 0 def)
% Number of atoms : 436 ( 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_379,negated_conjecture,
sdtlseqdt0(xm,xn),
inference(demodulation,[status(thm)],[c_86]) ).
cnf(c_380,negated_conjecture,
sdtlseqdt0(xn,xl),
inference(demodulation,[status(thm)],[c_85]) ).
cnf(c_3912,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sK0(xn,xl)) = xl ),
inference(superposition,[status(thm)],[c_380,c_74]) ).
cnf(c_3913,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtpldt0(xm,sK0(xm,xn)) = xn ),
inference(superposition,[status(thm)],[c_379,c_74]) ).
cnf(c_3949,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sdtmndt0(xl,xn)) = xl ),
inference(superposition,[status(thm)],[c_380,c_77]) ).
cnf(c_3950,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtpldt0(xm,sdtmndt0(xn,xm)) = xn ),
inference(superposition,[status(thm)],[c_379,c_77]) ).
cnf(c_5092,plain,
sdtpldt0(xn,sK0(xn,xl)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3912,c_82,c_81,c_3912]) ).
cnf(c_5094,plain,
sdtpldt0(xm,sK0(xm,xn)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3913,c_83,c_82,c_3913]) ).
cnf(c_5096,plain,
sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3949,c_82,c_81,c_3949]) ).
cnf(c_5098,plain,
sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3950,c_83,c_82,c_3950]) ).
cnf(c_6151,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = X0 ),
inference(superposition,[status(thm)],[c_5092,c_67]) ).
cnf(c_6152,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = X0 ),
inference(superposition,[status(thm)],[c_5094,c_67]) ).
cnf(c_6312,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xl))
| sdtpldt0(xn,X0) != xl
| sK0(xn,xl) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_6151,c_82,c_6151]) ).
cnf(c_6313,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| sK0(xn,xl) = X0 ),
inference(renaming,[status(thm)],[c_6312]) ).
cnf(c_6319,plain,
( ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_5096,c_6313]) ).
cnf(c_6320,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_6319]) ).
cnf(c_6321,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xn))
| sdtpldt0(xm,X0) != xn
| sK0(xm,xn) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_6152,c_83,c_6152]) ).
cnf(c_6322,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| sK0(xm,xn) = X0 ),
inference(renaming,[status(thm)],[c_6321]) ).
cnf(c_6330,plain,
( ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_5098,c_6322]) ).
cnf(c_6402,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_6330]) ).
cnf(c_7512,plain,
sdtpldt0(xn,sK0(xn,xl)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3912,c_82,c_81,c_3912]) ).
cnf(c_7514,plain,
sdtpldt0(xm,sK0(xm,xn)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3913,c_83,c_82,c_3913]) ).
cnf(c_7516,plain,
sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3949,c_82,c_81,c_3949]) ).
cnf(c_7518,plain,
sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3950,c_83,c_82,c_3950]) ).
cnf(c_8529,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = X0 ),
inference(superposition,[status(thm)],[c_7512,c_67]) ).
cnf(c_8530,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = X0 ),
inference(superposition,[status(thm)],[c_7514,c_67]) ).
cnf(c_8958,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xl))
| sdtpldt0(xn,X0) != xl
| sK0(xn,xl) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_8529,c_82,c_6151]) ).
cnf(c_8959,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| sK0(xn,xl) = X0 ),
inference(renaming,[status(thm)],[c_8958]) ).
cnf(c_8964,plain,
( ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_7516,c_8959]) ).
cnf(c_8965,plain,
( ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(global_subsumption_just,[status(thm)],[c_8964,c_82,c_81,c_85,c_6320]) ).
cnf(c_8967,plain,
( ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_78,c_8965]) ).
cnf(c_8968,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xn))
| sdtpldt0(xm,X0) != xn
| sK0(xm,xn) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_8530,c_83,c_6152]) ).
cnf(c_8969,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| sK0(xm,xn) = X0 ),
inference(renaming,[status(thm)],[c_8968]) ).
cnf(c_8976,plain,
( ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_7518,c_8969]) ).
cnf(c_8977,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(global_subsumption_just,[status(thm)],[c_8976,c_83,c_82,c_86,c_6402]) ).
cnf(c_8979,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_78,c_8977]) ).
cnf(c_9798,plain,
sK0(xn,xl) = sdtmndt0(xl,xn),
inference(global_subsumption_just,[status(thm)],[c_8967,c_82,c_81,c_85,c_8967]) ).
cnf(c_9800,plain,
( ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_9798,c_75]) ).
cnf(c_9804,plain,
sK0(xm,xn) = sdtmndt0(xn,xm),
inference(global_subsumption_just,[status(thm)],[c_8979,c_83,c_82,c_86,c_8979]) ).
cnf(c_9806,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_9804,c_75]) ).
cnf(c_9999,plain,
aNaturalNumber0(sdtmndt0(xl,xn)),
inference(global_subsumption_just,[status(thm)],[c_9800,c_82,c_81,c_85,c_9800]) ).
cnf(c_10007,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtmndt0(xl,xn),X0) = sdtpldt0(X0,sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_9999,c_54]) ).
cnf(c_10030,plain,
aNaturalNumber0(sdtmndt0(xn,xm)),
inference(global_subsumption_just,[status(thm)],[c_9806,c_83,c_82,c_86,c_9806]) ).
cnf(c_11046,plain,
sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)) = sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_10030,c_10007]) ).
cnf(c_11609,plain,
( ~ aNaturalNumber0(sdtmndt0(xl,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm))) ),
inference(superposition,[status(thm)],[c_11046,c_52]) ).
cnf(c_35562,plain,
sdtpldt0(xn,sK0(xn,xl)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3912,c_82,c_81,c_3912]) ).
cnf(c_35564,plain,
sdtpldt0(xm,sK0(xm,xn)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3913,c_83,c_82,c_3913]) ).
cnf(c_35566,plain,
sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3949,c_82,c_81,c_3949]) ).
cnf(c_35568,plain,
sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3950,c_83,c_82,c_3950]) ).
cnf(c_36457,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = X0 ),
inference(superposition,[status(thm)],[c_35562,c_67]) ).
cnf(c_36458,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = X0 ),
inference(superposition,[status(thm)],[c_35564,c_67]) ).
cnf(c_36720,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xl))
| sdtpldt0(xn,X0) != xl
| sK0(xn,xl) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_36457,c_82,c_6151]) ).
cnf(c_36721,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| sK0(xn,xl) = X0 ),
inference(renaming,[status(thm)],[c_36720]) ).
cnf(c_36726,plain,
( ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_35566,c_36721]) ).
cnf(c_36727,plain,
sK0(xn,xl) = sdtmndt0(xl,xn),
inference(global_subsumption_just,[status(thm)],[c_36726,c_82,c_81,c_85,c_8967]) ).
cnf(c_36729,plain,
( ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_36727,c_75]) ).
cnf(c_36732,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xn))
| sdtpldt0(xm,X0) != xn
| sK0(xm,xn) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_36458,c_83,c_6152]) ).
cnf(c_36733,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| sK0(xm,xn) = X0 ),
inference(renaming,[status(thm)],[c_36732]) ).
cnf(c_36740,plain,
( ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_35568,c_36733]) ).
cnf(c_36781,plain,
sK0(xm,xn) = sdtmndt0(xn,xm),
inference(global_subsumption_just,[status(thm)],[c_36740,c_83,c_82,c_86,c_8979]) ).
cnf(c_36783,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_36781,c_75]) ).
cnf(c_37145,plain,
aNaturalNumber0(sdtmndt0(xl,xn)),
inference(global_subsumption_just,[status(thm)],[c_36729,c_82,c_81,c_85,c_9800]) ).
cnf(c_37153,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtmndt0(xl,xn),X0) = sdtpldt0(X0,sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_37145,c_54]) ).
cnf(c_37160,plain,
aNaturalNumber0(sdtmndt0(xn,xm)),
inference(global_subsumption_just,[status(thm)],[c_36783,c_83,c_82,c_86,c_9806]) ).
cnf(c_37165,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X0,sdtmndt0(xn,xm)),X1) = sdtpldt0(X0,sdtpldt0(sdtmndt0(xn,xm),X1)) ),
inference(superposition,[status(thm)],[c_37160,c_55]) ).
cnf(c_38572,plain,
sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)) = sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_37160,c_37153]) ).
cnf(c_40016,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_37145,c_37165]) ).
cnf(c_40761,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_40016]) ).
cnf(c_59483,plain,
sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn))) = sdtpldt0(xn,sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_35568,c_40761]) ).
cnf(c_59495,plain,
sdtpldt0(xm,sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm))) = sdtpldt0(xn,sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_38572,c_59483]) ).
cnf(c_59500,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)))
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))) ),
inference(superposition,[status(thm)],[c_59483,c_139]) ).
cnf(c_59555,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)))
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))) ),
inference(superposition,[status(thm)],[c_59495,c_139]) ).
cnf(c_59565,plain,
sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))),
inference(global_subsumption_just,[status(thm)],[c_59500,c_83,c_82,c_81,c_86,c_85,c_9800,c_9806,c_11609,c_59555]) ).
cnf(c_59567,plain,
sdtlseqdt0(xm,xl),
inference(superposition,[status(thm)],[c_35566,c_59565]) ).
cnf(c_59571,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_59567,c_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM460+1 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.12 % Command : run_iprover %s %d THM
% 0.12/0.32 % Computer : n020.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun Jun 23 01:01:39 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.17/0.45 Running first-order theorem proving
% 0.17/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 68.72/10.22 % SZS status Started for theBenchmark.p
% 68.72/10.22 % SZS status Theorem for theBenchmark.p
% 68.72/10.22
% 68.72/10.22 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 68.72/10.22
% 68.72/10.22 ------ iProver source info
% 68.72/10.22
% 68.72/10.22 git: date: 2024-06-12 09:56:46 +0000
% 68.72/10.22 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 68.72/10.22 git: non_committed_changes: false
% 68.72/10.22
% 68.72/10.22 ------ Parsing...
% 68.72/10.22 ------ Clausification by vclausify_rel & Parsing by iProver...
% 68.72/10.22
% 68.72/10.22 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 68.72/10.22
% 68.72/10.22 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 68.72/10.22
% 68.72/10.22 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 68.72/10.22 ------ Proving...
% 68.72/10.22 ------ Problem Properties
% 68.72/10.22
% 68.72/10.22
% 68.72/10.22 clauses 38
% 68.72/10.22 conjectures 3
% 68.72/10.22 EPR 11
% 68.72/10.22 Horn 35
% 68.72/10.22 unary 9
% 68.72/10.22 binary 7
% 68.72/10.22 lits 113
% 68.72/10.22 lits eq 34
% 68.72/10.22 fd_pure 0
% 68.72/10.22 fd_pseudo 0
% 68.72/10.22 fd_cond 3
% 68.72/10.22 fd_pseudo_cond 5
% 68.72/10.22 AC symbols 0
% 68.72/10.22
% 68.72/10.22 ------ Input Options Time Limit: Unbounded
% 68.72/10.22
% 68.72/10.22
% 68.72/10.22 ------
% 68.72/10.22 Current options:
% 68.72/10.22 ------
% 68.72/10.22
% 68.72/10.22
% 68.72/10.22
% 68.72/10.22
% 68.72/10.22 ------ Proving...
% 68.72/10.22
% 68.72/10.22
% 68.72/10.22 % SZS status Theorem for theBenchmark.p
% 68.72/10.22
% 68.72/10.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 68.72/10.22
% 68.72/10.23
%------------------------------------------------------------------------------