TSTP Solution File: NUM460+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM460+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.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 : Fri May 3 02:49:23 EDT 2024
% Result : Theorem 69.42s 10.27s
% Output : CNFRefutation 69.42s
% 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/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f22,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__773) ).
fof(f23,conjecture,
( ( sdtlseqdt0(xn,xl)
& sdtlseqdt0(xm,xn) )
=> sdtlseqdt0(xm,xl) ),
file('/export/starexec/sandbox/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_3656,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sK0(xn,xl)) = xl ),
inference(superposition,[status(thm)],[c_85,c_74]) ).
cnf(c_3657,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtpldt0(xm,sK0(xm,xn)) = xn ),
inference(superposition,[status(thm)],[c_86,c_74]) ).
cnf(c_3687,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sdtmndt0(xl,xn)) = xl ),
inference(superposition,[status(thm)],[c_85,c_77]) ).
cnf(c_3688,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtpldt0(xm,sdtmndt0(xn,xm)) = xn ),
inference(superposition,[status(thm)],[c_86,c_77]) ).
cnf(c_4730,plain,
sdtpldt0(xn,sK0(xn,xl)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3656,c_82,c_81,c_3656]) ).
cnf(c_4732,plain,
sdtpldt0(xm,sK0(xm,xn)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3657,c_83,c_82,c_3657]) ).
cnf(c_4744,plain,
sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3687,c_82,c_81,c_3687]) ).
cnf(c_4746,plain,
sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3688,c_83,c_82,c_3688]) ).
cnf(c_5871,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = X0 ),
inference(superposition,[status(thm)],[c_4730,c_67]) ).
cnf(c_5872,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = X0 ),
inference(superposition,[status(thm)],[c_4732,c_67]) ).
cnf(c_6125,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xl))
| sdtpldt0(xn,X0) != xl
| sK0(xn,xl) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_5871,c_82,c_5871]) ).
cnf(c_6126,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| sK0(xn,xl) = X0 ),
inference(renaming,[status(thm)],[c_6125]) ).
cnf(c_6132,plain,
( ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_4744,c_6126]) ).
cnf(c_6317,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_6132]) ).
cnf(c_6318,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xn))
| sdtpldt0(xm,X0) != xn
| sK0(xm,xn) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_5872,c_83,c_5872]) ).
cnf(c_6319,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| sK0(xm,xn) = X0 ),
inference(renaming,[status(thm)],[c_6318]) ).
cnf(c_6327,plain,
( ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_4746,c_6319]) ).
cnf(c_6328,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_6327]) ).
cnf(c_7367,plain,
sdtpldt0(xn,sK0(xn,xl)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3656,c_82,c_81,c_3656]) ).
cnf(c_7369,plain,
sdtpldt0(xm,sK0(xm,xn)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3657,c_83,c_82,c_3657]) ).
cnf(c_7371,plain,
sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3687,c_82,c_81,c_3687]) ).
cnf(c_7373,plain,
sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3688,c_83,c_82,c_3688]) ).
cnf(c_8296,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = X0 ),
inference(superposition,[status(thm)],[c_7367,c_67]) ).
cnf(c_8297,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = X0 ),
inference(superposition,[status(thm)],[c_7369,c_67]) ).
cnf(c_8625,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xl))
| sdtpldt0(xn,X0) != xl
| sK0(xn,xl) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_8296,c_82,c_5871]) ).
cnf(c_8626,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| sK0(xn,xl) = X0 ),
inference(renaming,[status(thm)],[c_8625]) ).
cnf(c_8631,plain,
( ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_7371,c_8626]) ).
cnf(c_8632,plain,
( ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(global_subsumption_just,[status(thm)],[c_8631,c_82,c_81,c_85,c_6317]) ).
cnf(c_8634,plain,
( ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_78,c_8632]) ).
cnf(c_8635,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xn))
| sdtpldt0(xm,X0) != xn
| sK0(xm,xn) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_8297,c_83,c_5872]) ).
cnf(c_8636,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| sK0(xm,xn) = X0 ),
inference(renaming,[status(thm)],[c_8635]) ).
cnf(c_8643,plain,
( ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_7373,c_8636]) ).
cnf(c_8644,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(global_subsumption_just,[status(thm)],[c_8643,c_83,c_82,c_86,c_6328]) ).
cnf(c_8646,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_78,c_8644]) ).
cnf(c_8975,plain,
sK0(xn,xl) = sdtmndt0(xl,xn),
inference(global_subsumption_just,[status(thm)],[c_8634,c_82,c_81,c_85,c_8634]) ).
cnf(c_8977,plain,
( ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_8975,c_75]) ).
cnf(c_8981,plain,
sK0(xm,xn) = sdtmndt0(xn,xm),
inference(global_subsumption_just,[status(thm)],[c_8646,c_83,c_82,c_86,c_8646]) ).
cnf(c_8983,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_8981,c_75]) ).
cnf(c_9334,plain,
aNaturalNumber0(sdtmndt0(xl,xn)),
inference(global_subsumption_just,[status(thm)],[c_8977,c_82,c_81,c_85,c_8977]) ).
cnf(c_9342,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtmndt0(xl,xn),X0) = sdtpldt0(X0,sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_9334,c_54]) ).
cnf(c_9360,plain,
aNaturalNumber0(sdtmndt0(xn,xm)),
inference(global_subsumption_just,[status(thm)],[c_8983,c_83,c_82,c_86,c_8983]) ).
cnf(c_10466,plain,
sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)) = sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_9360,c_9342]) ).
cnf(c_10799,plain,
( ~ aNaturalNumber0(sdtmndt0(xl,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm))) ),
inference(superposition,[status(thm)],[c_10466,c_52]) ).
cnf(c_35012,plain,
sdtpldt0(xn,sK0(xn,xl)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3656,c_82,c_81,c_3656]) ).
cnf(c_35014,plain,
sdtpldt0(xm,sK0(xm,xn)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3657,c_83,c_82,c_3657]) ).
cnf(c_35016,plain,
sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
inference(global_subsumption_just,[status(thm)],[c_3687,c_82,c_81,c_3687]) ).
cnf(c_35018,plain,
sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
inference(global_subsumption_just,[status(thm)],[c_3688,c_83,c_82,c_3688]) ).
cnf(c_35929,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sK0(xn,xl) = X0 ),
inference(superposition,[status(thm)],[c_35012,c_67]) ).
cnf(c_35930,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sK0(xm,xn) = X0 ),
inference(superposition,[status(thm)],[c_35014,c_67]) ).
cnf(c_36120,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xn,xl))
| sdtpldt0(xn,X0) != xl
| sK0(xn,xl) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_35929,c_82,c_5871]) ).
cnf(c_36121,plain,
( sdtpldt0(xn,X0) != xl
| ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(X0)
| sK0(xn,xl) = X0 ),
inference(renaming,[status(thm)],[c_36120]) ).
cnf(c_36126,plain,
( ~ aNaturalNumber0(sK0(xn,xl))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| sK0(xn,xl) = sdtmndt0(xl,xn) ),
inference(superposition,[status(thm)],[c_35016,c_36121]) ).
cnf(c_36127,plain,
sK0(xn,xl) = sdtmndt0(xl,xn),
inference(global_subsumption_just,[status(thm)],[c_36126,c_82,c_81,c_85,c_8634]) ).
cnf(c_36129,plain,
( ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_36127,c_75]) ).
cnf(c_36132,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK0(xm,xn))
| sdtpldt0(xm,X0) != xn
| sK0(xm,xn) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_35930,c_83,c_5872]) ).
cnf(c_36133,plain,
( sdtpldt0(xm,X0) != xn
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(X0)
| sK0(xm,xn) = X0 ),
inference(renaming,[status(thm)],[c_36132]) ).
cnf(c_36140,plain,
( ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| sK0(xm,xn) = sdtmndt0(xn,xm) ),
inference(superposition,[status(thm)],[c_35018,c_36133]) ).
cnf(c_36141,plain,
sK0(xm,xn) = sdtmndt0(xn,xm),
inference(global_subsumption_just,[status(thm)],[c_36140,c_83,c_82,c_86,c_8646]) ).
cnf(c_36143,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_36141,c_75]) ).
cnf(c_36536,plain,
aNaturalNumber0(sdtmndt0(xl,xn)),
inference(global_subsumption_just,[status(thm)],[c_36129,c_82,c_81,c_85,c_8977]) ).
cnf(c_36544,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtmndt0(xl,xn),X0) = sdtpldt0(X0,sdtmndt0(xl,xn)) ),
inference(superposition,[status(thm)],[c_36536,c_54]) ).
cnf(c_36606,plain,
aNaturalNumber0(sdtmndt0(xn,xm)),
inference(global_subsumption_just,[status(thm)],[c_36143,c_83,c_82,c_86,c_8983]) ).
cnf(c_36611,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X0,sdtmndt0(xn,xm)),X1) = sdtpldt0(X0,sdtpldt0(sdtmndt0(xn,xm),X1)) ),
inference(superposition,[status(thm)],[c_36606,c_55]) ).
cnf(c_37527,plain,
sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)) = sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_36606,c_36544]) ).
cnf(c_39489,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_36536,c_36611]) ).
cnf(c_39996,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_39489]) ).
cnf(c_59045,plain,
sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn))) = sdtpldt0(xn,sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_35018,c_39996]) ).
cnf(c_59057,plain,
sdtpldt0(xm,sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm))) = sdtpldt0(xn,sdtmndt0(xl,xn)),
inference(superposition,[status(thm)],[c_37527,c_59045]) ).
cnf(c_59062,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)))
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))) ),
inference(superposition,[status(thm)],[c_59045,c_139]) ).
cnf(c_59074,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)))
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))) ),
inference(superposition,[status(thm)],[c_59057,c_139]) ).
cnf(c_59086,plain,
sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))),
inference(global_subsumption_just,[status(thm)],[c_59062,c_83,c_82,c_81,c_86,c_85,c_8977,c_8983,c_10799,c_59074]) ).
cnf(c_59088,plain,
sdtlseqdt0(xm,xl),
inference(superposition,[status(thm)],[c_35016,c_59086]) ).
cnf(c_59092,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_59088,c_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM460+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 19:43:27 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 69.42/10.27 % SZS status Started for theBenchmark.p
% 69.42/10.27 % SZS status Theorem for theBenchmark.p
% 69.42/10.27
% 69.42/10.27 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 69.42/10.27
% 69.42/10.27 ------ iProver source info
% 69.42/10.27
% 69.42/10.27 git: date: 2024-05-02 19:28:25 +0000
% 69.42/10.27 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 69.42/10.27 git: non_committed_changes: false
% 69.42/10.27
% 69.42/10.27 ------ Parsing...
% 69.42/10.27 ------ Clausification by vclausify_rel & Parsing by iProver...
% 69.42/10.27
% 69.42/10.27 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 69.42/10.27
% 69.42/10.27 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 69.42/10.27
% 69.42/10.27 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 69.42/10.27 ------ Proving...
% 69.42/10.27 ------ Problem Properties
% 69.42/10.27
% 69.42/10.27
% 69.42/10.27 clauses 38
% 69.42/10.27 conjectures 3
% 69.42/10.27 EPR 11
% 69.42/10.27 Horn 35
% 69.42/10.27 unary 9
% 69.42/10.27 binary 7
% 69.42/10.27 lits 113
% 69.42/10.27 lits eq 34
% 69.42/10.27 fd_pure 0
% 69.42/10.27 fd_pseudo 0
% 69.42/10.27 fd_cond 3
% 69.42/10.27 fd_pseudo_cond 5
% 69.42/10.27 AC symbols 0
% 69.42/10.27
% 69.42/10.27 ------ Input Options Time Limit: Unbounded
% 69.42/10.27
% 69.42/10.27
% 69.42/10.27 ------
% 69.42/10.27 Current options:
% 69.42/10.27 ------
% 69.42/10.27
% 69.42/10.27
% 69.42/10.27
% 69.42/10.27
% 69.42/10.27 ------ Proving...
% 69.42/10.27
% 69.42/10.27
% 69.42/10.27 % SZS status Theorem for theBenchmark.p
% 69.42/10.27
% 69.42/10.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 69.42/10.27
% 69.42/10.28
%------------------------------------------------------------------------------