TSTP Solution File: NUM462+2 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM462+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 53.34s 8.25s
% Output : CNFRefutation 53.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 21
% Syntax : Number of formulae : 174 ( 24 unt; 0 def)
% Number of atoms : 755 ( 203 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1037 ( 456 ~; 478 |; 78 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 272 ( 0 sgn 135 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 != X0
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtpldt0(X0,X1)
=> ( sz00 = X1
& sz00 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
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(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
fof(f25,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__897) ).
fof(f26,axiom,
( sdtlseqdt0(xl,xn)
& ? [X0] :
( xn = sdtpldt0(xl,X0)
& aNaturalNumber0(X0) )
& xl != xn
& sz00 != xm ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__897_03) ).
fof(f27,conjecture,
( ( sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ? [X0] :
( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xl,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ? [X0] :
( sdtasdt0(xm,xn) = sdtpldt0(sdtasdt0(xm,xl),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ( ( sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ? [X0] :
( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xl,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ? [X0] :
( sdtasdt0(xm,xn) = sdtpldt0(sdtasdt0(xm,xl),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ),
inference(negated_conjecture,[],[f27]) ).
fof(f30,plain,
~ ( ( sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ? [X0] :
( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xl,xm),X0)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ? [X1] :
( sdtasdt0(xm,xn) = sdtpldt0(sdtasdt0(xm,xl),X1)
& aNaturalNumber0(X1) ) )
& sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ),
inference(rectify,[],[f28]) ).
fof(f31,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f34,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f33]) ).
fof(f39,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f40,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f41,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f40]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f46]) ).
fof(f50,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f51,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f53,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f57,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f56]) ).
fof(f61,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f62,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f64,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f66,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
( ( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
& ! [X0] :
( sdtasdt0(xn,xm) != sdtpldt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(X0) ) )
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ( ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
& ! [X1] :
( sdtasdt0(xm,xn) != sdtpldt0(sdtasdt0(xm,xl),X1)
| ~ aNaturalNumber0(X1) ) )
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(ennf_transformation,[],[f30]) ).
fof(f70,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,[],[f57]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f73,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])],[f71,f72]) ).
fof(f76,plain,
( ? [X0] :
( xn = sdtpldt0(xl,X0)
& aNaturalNumber0(X0) )
=> ( xn = sdtpldt0(xl,sK1)
& aNaturalNumber0(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
( sdtlseqdt0(xl,xn)
& xn = sdtpldt0(xl,sK1)
& aNaturalNumber0(sK1)
& xl != xn
& sz00 != xm ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f26,f76]) ).
fof(f78,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f81,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f82,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f86,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f87,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f93,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f94,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f97,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f98,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f100,plain,
! [X0,X1] :
( sz00 = X1
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f104,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f109,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f110,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f112,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f114,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f118,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f25]) ).
fof(f119,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f25]) ).
fof(f120,plain,
sz00 != xm,
inference(cnf_transformation,[],[f77]) ).
fof(f121,plain,
xl != xn,
inference(cnf_transformation,[],[f77]) ).
fof(f122,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f77]) ).
fof(f123,plain,
xn = sdtpldt0(xl,sK1),
inference(cnf_transformation,[],[f77]) ).
fof(f125,plain,
! [X0,X1] :
( sdtasdt0(xn,xm) != sdtpldt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtpldt0(sdtasdt0(xm,xl),X1)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(cnf_transformation,[],[f69]) ).
fof(f127,plain,
! [X1] :
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtpldt0(sdtasdt0(xm,xl),X1)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(cnf_transformation,[],[f69]) ).
fof(f129,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f104]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f78]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f81]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f82]) ).
cnf(c_56,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f86]) ).
cnf(c_58,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_64,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) = sdtasdt0(sdtpldt0(X1,X2),X0) ),
inference(cnf_transformation,[],[f94]) ).
cnf(c_65,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) = sdtasdt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_68,plain,
( sdtasdt0(X0,X1) != sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X2
| X1 = sz00 ),
inference(cnf_transformation,[],[f98]) ).
cnf(c_69,plain,
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = sz00
| X1 = X2 ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_70,plain,
( sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X1 = sz00 ),
inference(cnf_transformation,[],[f100]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f129]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_81,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_82,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_84,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f116]) ).
cnf(c_86,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1)) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_88,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f119]) ).
cnf(c_89,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f118]) ).
cnf(c_90,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f117]) ).
cnf(c_92,plain,
sdtpldt0(xl,sK1) = xn,
inference(cnf_transformation,[],[f123]) ).
cnf(c_93,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f122]) ).
cnf(c_94,plain,
xn != xl,
inference(cnf_transformation,[],[f121]) ).
cnf(c_95,plain,
sz00 != xm,
inference(cnf_transformation,[],[f120]) ).
cnf(c_97,negated_conjecture,
( sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xm,xn)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xn,xm) = sdtasdt0(xl,xm)
| sdtasdt0(xm,xn) = sdtasdt0(xm,xl) ),
inference(cnf_transformation,[],[f127]) ).
cnf(c_99,negated_conjecture,
( sdtpldt0(sdtasdt0(xl,xm),X0) != sdtasdt0(xn,xm)
| sdtpldt0(sdtasdt0(xm,xl),X1) != sdtasdt0(xm,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xn,xm) = sdtasdt0(xl,xm)
| sdtasdt0(xm,xn) = sdtasdt0(xm,xl) ),
inference(cnf_transformation,[],[f125]) ).
cnf(c_130,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_1364,negated_conjecture,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xm,xn)
| ~ sP0_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_def])],[c_99]) ).
cnf(c_1365,negated_conjecture,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtasdt0(xl,xm),X0) != sdtasdt0(xn,xm)
| ~ sP1_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[sP1_iProver_def])],[c_99]) ).
cnf(c_1366,negated_conjecture,
( sdtasdt0(xn,xm) = sdtasdt0(xl,xm)
| sdtasdt0(xm,xn) = sdtasdt0(xm,xl)
| sP0_iProver_def
| sP1_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_99]) ).
cnf(c_1368,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xl,xm)
| sdtasdt0(xm,xn) = sdtasdt0(xm,xl)
| sP0_iProver_def ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_97]) ).
cnf(c_1369,plain,
X0 = X0,
theory(equality) ).
cnf(c_1371,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_1374,plain,
( X0 != X1
| X2 != X3
| sdtasdt0(X0,X2) = sdtasdt0(X1,X3) ),
theory(equality) ).
cnf(c_2098,plain,
( sdtpldt0(sz00,sz00) != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_2099,plain,
( ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_2116,plain,
( sz00 != X0
| xm != X0
| sz00 = xm ),
inference(instantiation,[status(thm)],[c_1371]) ).
cnf(c_2209,plain,
( sdtasdt0(xn,X0) != sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| X0 = sz00
| xn = xl ),
inference(instantiation,[status(thm)],[c_68]) ).
cnf(c_2210,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xl,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| xn = xl
| xm = sz00 ),
inference(instantiation,[status(thm)],[c_2209]) ).
cnf(c_2227,plain,
( sdtasdt0(X0,xn) != sdtasdt0(X0,xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| X0 = sz00
| xn = xl ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_2228,plain,
( sdtasdt0(xm,xn) != sdtasdt0(xm,xl)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| xn = xl
| xm = sz00 ),
inference(instantiation,[status(thm)],[c_2227]) ).
cnf(c_2366,plain,
( sz00 != sz00
| xm != sz00
| sz00 = xm ),
inference(instantiation,[status(thm)],[c_2116]) ).
cnf(c_2451,negated_conjecture,
( sP0_iProver_def
| sP1_iProver_def ),
inference(global_subsumption_just,[status(thm)],[c_1366,c_90,c_89,c_88,c_49,c_95,c_94,c_1366,c_2098,c_2099,c_2210,c_2228,c_2366]) ).
cnf(c_2655,negated_conjecture,
( sP0_iProver_def
| sP1_iProver_def ),
inference(global_subsumption_just,[status(thm)],[c_1366,c_2451]) ).
cnf(c_2671,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| sP0_iProver_def ),
inference(global_subsumption_just,[status(thm)],[c_1368,c_90,c_89,c_88,c_49,c_95,c_94,c_1368,c_2098,c_2099,c_2210,c_2228,c_2366]) ).
cnf(c_2983,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xl,xm))
| sP0_iProver_def ),
inference(resolution,[status(thm)],[c_82,c_2671]) ).
cnf(c_3183,plain,
( X0 != xn
| sdtpldt0(xl,sK1) = X0 ),
inference(resolution,[status(thm)],[c_1371,c_92]) ).
cnf(c_3185,plain,
( X0 != X1
| X1 = X0 ),
inference(resolution,[status(thm)],[c_1371,c_1369]) ).
cnf(c_3656,plain,
( X0 != xn
| X0 = sdtpldt0(xl,sK1) ),
inference(resolution,[status(thm)],[c_3183,c_3185]) ).
cnf(c_3697,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| sP0_iProver_def ),
inference(global_subsumption_just,[status(thm)],[c_1368,c_90,c_89,c_88,c_49,c_95,c_94,c_1368,c_2098,c_2099,c_2210,c_2228,c_2366]) ).
cnf(c_3897,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xl,xm))
| sP0_iProver_def ),
inference(superposition,[status(thm)],[c_82,c_3697]) ).
cnf(c_4495,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sdtasdt0(xn,xm),X0)
| sP0_iProver_def ),
inference(superposition,[status(thm)],[c_3897,c_81]) ).
cnf(c_4635,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xm),X0))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(sdtasdt0(xl,xm),X0))
| sP0_iProver_def ),
inference(superposition,[status(thm)],[c_130,c_4495]) ).
cnf(c_4922,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xl,xm),X0),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(sdtasdt0(xl,xm),X0))
| ~ aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xm),X0))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ sP1_iProver_def ),
inference(resolution,[status(thm)],[c_80,c_1365]) ).
cnf(c_5240,plain,
( ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,sdtasdt0(xl,xm))
| sP0_iProver_def ),
inference(resolution,[status(thm)],[c_81,c_2983]) ).
cnf(c_5433,plain,
( ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtasdt0(xl,xm))
| sP0_iProver_def ),
inference(resolution,[status(thm)],[c_5240,c_81]) ).
cnf(c_5595,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(xn,xm),X1)
| sdtlseqdt0(X0,sdtasdt0(xl,xm))
| sP0_iProver_def ),
inference(resolution,[status(thm)],[c_5433,c_82]) ).
cnf(c_7378,plain,
( X0 != sdtasdt0(sdtpldt0(X1,X2),X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) = X0 ),
inference(resolution,[status(thm)],[c_64,c_1371]) ).
cnf(c_8183,plain,
( X0 != sdtasdt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) = X0 ),
inference(resolution,[status(thm)],[c_65,c_1371]) ).
cnf(c_8308,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X2,X1))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sdtlseqdt0(sdtpldt0(X0,X1),sdtasdt0(xl,xm))
| sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(X2,X1))
| sP0_iProver_def ),
inference(resolution,[status(thm)],[c_84,c_5595]) ).
cnf(c_8325,plain,
( ~ sdtlseqdt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 = X3
| sdtlseqdt0(X0,sdtpldt0(X1,X3)) ),
inference(resolution,[status(thm)],[c_86,c_81]) ).
cnf(c_8817,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtpldt0(sdtasdt0(X0,X1),X2)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_15857,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl)
| aNaturalNumber0(sdtasdt0(xl,X0)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_15858,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xl,xm)) ),
inference(instantiation,[status(thm)],[c_15857]) ).
cnf(c_19402,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X2,X1))
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sdtlseqdt0(sdtpldt0(X0,X1),sdtasdt0(xl,xm))
| sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(X2,X1))
| sP0_iProver_def ),
inference(global_subsumption_just,[status(thm)],[c_8308,c_90,c_89,c_52,c_8308,c_15858]) ).
cnf(c_19403,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X2 = X0
| sdtlseqdt0(sdtpldt0(X2,X1),sdtasdt0(xl,xm))
| sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(X0,X1))
| sP0_iProver_def ),
inference(renaming,[status(thm)],[c_19402]) ).
cnf(c_19404,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X2 = X0
| sdtlseqdt0(sdtpldt0(X2,X1),sdtasdt0(xl,xm))
| sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(X0,X1))
| sP0_iProver_def ),
inference(global_subsumption_just,[status(thm)],[c_19403,c_52,c_19403]) ).
cnf(c_19405,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| sdtlseqdt0(sdtpldt0(X0,X2),sdtasdt0(xl,xm))
| sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(X1,X2))
| sP0_iProver_def ),
inference(renaming,[status(thm)],[c_19404]) ).
cnf(c_19465,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xl,xm),X0),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xm),X0))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sP1_iProver_def
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xl,xm),X0),X1),sdtasdt0(xl,xm))
| sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(sdtasdt0(xn,xm),X1))
| sP0_iProver_def ),
inference(resolution,[status(thm)],[c_19405,c_1365]) ).
cnf(c_20596,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xl,xm),X0),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xm),X0))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| sP0_iProver_def ),
inference(global_subsumption_just,[status(thm)],[c_19465,c_90,c_89,c_88,c_49,c_95,c_94,c_1366,c_2098,c_2099,c_2210,c_2228,c_2366,c_4635,c_4922,c_15858]) ).
cnf(c_20619,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xm),X0))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(sdtasdt0(xl,xm),X0))
| sP0_iProver_def ),
inference(resolution,[status(thm)],[c_20596,c_82]) ).
cnf(c_30608,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xn,X0)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_30609,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_30608]) ).
cnf(c_49693,plain,
( sdtasdt0(xn,xm) != sdtasdt0(sdtpldt0(xl,X0),xm)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ sP1_iProver_def ),
inference(resolution,[status(thm)],[c_7378,c_1365]) ).
cnf(c_50037,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xm) = sdtasdt0(xm,X0) ),
inference(superposition,[status(thm)],[c_90,c_58]) ).
cnf(c_50577,plain,
sdtasdt0(xm,sK1) = sdtasdt0(sK1,xm),
inference(superposition,[status(thm)],[c_93,c_50037]) ).
cnf(c_57796,plain,
( sdtasdt0(xm,xn) != sdtasdt0(xm,sdtpldt0(xl,X0))
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ sP0_iProver_def ),
inference(resolution,[status(thm)],[c_8183,c_1364]) ).
cnf(c_59146,plain,
( sdtasdt0(xn,xm) != sdtasdt0(sdtpldt0(xl,X0),xm)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ sP1_iProver_def ),
inference(global_subsumption_just,[status(thm)],[c_49693,c_90,c_89,c_49693]) ).
cnf(c_59169,plain,
( xn != sdtpldt0(xl,X0)
| xm != xm
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ sP1_iProver_def ),
inference(resolution,[status(thm)],[c_59146,c_1374]) ).
cnf(c_59170,plain,
( xn != sdtpldt0(xl,X0)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ sP1_iProver_def ),
inference(equality_resolution_simp,[status(thm)],[c_59169]) ).
cnf(c_59172,plain,
( sdtasdt0(xm,xn) != sdtasdt0(xm,sdtpldt0(xl,X0))
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ sP0_iProver_def ),
inference(global_subsumption_just,[status(thm)],[c_57796,c_90,c_89,c_57796]) ).
cnf(c_59194,plain,
( xn != sdtpldt0(xl,X0)
| xm != xm
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ sP0_iProver_def ),
inference(resolution,[status(thm)],[c_59172,c_1374]) ).
cnf(c_59195,plain,
( xn != sdtpldt0(xl,X0)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| ~ sP0_iProver_def ),
inference(equality_resolution_simp,[status(thm)],[c_59194]) ).
cnf(c_61207,plain,
( xn != xn
| ~ aNaturalNumber0(sdtasdt0(sK1,xm))
| ~ aNaturalNumber0(sK1)
| ~ sP1_iProver_def ),
inference(resolution,[status(thm)],[c_59170,c_3656]) ).
cnf(c_61208,plain,
( ~ aNaturalNumber0(sdtasdt0(sK1,xm))
| ~ aNaturalNumber0(sK1)
| ~ sP1_iProver_def ),
inference(equality_resolution_simp,[status(thm)],[c_61207]) ).
cnf(c_61220,plain,
( xn != xn
| ~ aNaturalNumber0(sdtasdt0(xm,sK1))
| ~ aNaturalNumber0(sK1)
| ~ sP0_iProver_def ),
inference(resolution,[status(thm)],[c_59195,c_3656]) ).
cnf(c_61221,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK1))
| ~ aNaturalNumber0(sK1)
| ~ sP0_iProver_def ),
inference(equality_resolution_simp,[status(thm)],[c_61220]) ).
cnf(c_61584,plain,
( ~ sdtlseqdt0(X0,sdtpldt0(X1,X2))
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 = X3
| sdtlseqdt0(X0,sdtpldt0(X1,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8325,c_52,c_52]) ).
cnf(c_61622,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xm),X0))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(sdtasdt0(xl,xm),X1))
| sP0_iProver_def ),
inference(resolution,[status(thm)],[c_61584,c_20619]) ).
cnf(c_64346,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sK1)
| aNaturalNumber0(sdtasdt0(xm,sK1)) ),
inference(superposition,[status(thm)],[c_50577,c_53]) ).
cnf(c_64349,plain,
aNaturalNumber0(sdtasdt0(xm,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_64346,c_93,c_90]) ).
cnf(c_64989,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xm),X0)) ),
inference(instantiation,[status(thm)],[c_8817]) ).
cnf(c_73980,plain,
( sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(sdtasdt0(xl,xm),X1))
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_61622,c_93,c_90,c_89,c_88,c_15858,c_30609,c_61221,c_61622,c_64349,c_64989]) ).
cnf(c_73981,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(sdtasdt0(xl,xm),X1)) ),
inference(renaming,[status(thm)],[c_73980]) ).
cnf(c_74060,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xm,xl),X0),sdtasdt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(sdtasdt0(xm,xl),X0))
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(X0)
| ~ sP0_iProver_def
| sdtlseqdt0(sdtasdt0(xn,xm),sdtpldt0(sdtasdt0(xl,xm),sdtasdt0(xm,xn))) ),
inference(resolution,[status(thm)],[c_73981,c_1364]) ).
cnf(c_74971,plain,
~ sP0_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_74060,c_93,c_61221,c_64349]) ).
cnf(c_77366,plain,
sP1_iProver_def,
inference(backward_subsumption_resolution,[status(thm)],[c_2655,c_74971]) ).
cnf(c_78427,plain,
( ~ aNaturalNumber0(sdtasdt0(sK1,xm))
| ~ aNaturalNumber0(sK1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_61208,c_77366]) ).
cnf(c_78516,plain,
~ aNaturalNumber0(sdtasdt0(sK1,xm)),
inference(global_subsumption_just,[status(thm)],[c_78427,c_93,c_2451,c_61208,c_61221,c_64349]) ).
cnf(c_78522,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sK1) ),
inference(resolution,[status(thm)],[c_78516,c_53]) ).
cnf(c_78523,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_78522,c_90,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM462+2 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n025.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 20:01:43 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 53.34/8.25 % SZS status Started for theBenchmark.p
% 53.34/8.25 % SZS status Theorem for theBenchmark.p
% 53.34/8.25
% 53.34/8.25 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 53.34/8.25
% 53.34/8.25 ------ iProver source info
% 53.34/8.25
% 53.34/8.25 git: date: 2024-05-02 19:28:25 +0000
% 53.34/8.25 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 53.34/8.25 git: non_committed_changes: false
% 53.34/8.25
% 53.34/8.25 ------ Parsing...
% 53.34/8.25 ------ Clausification by vclausify_rel & Parsing by iProver...
% 53.34/8.25
% 53.34/8.25 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 53.34/8.25
% 53.34/8.25 ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e
% 53.34/8.25
% 53.34/8.25 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 53.34/8.25 ------ Proving...
% 53.34/8.25 ------ Problem Properties
% 53.34/8.25
% 53.34/8.25
% 53.34/8.25 clauses 50
% 53.34/8.25 conjectures 6
% 53.34/8.25 EPR 14
% 53.34/8.25 Horn 40
% 53.34/8.25 unary 11
% 53.34/8.25 binary 7
% 53.34/8.25 lits 159
% 53.34/8.25 lits eq 49
% 53.34/8.25 fd_pure 0
% 53.34/8.25 fd_pseudo 0
% 53.34/8.25 fd_cond 3
% 53.34/8.25 fd_pseudo_cond 7
% 53.34/8.25 AC symbols 0
% 53.34/8.25
% 53.34/8.25 ------ Input Options Time Limit: Unbounded
% 53.34/8.25
% 53.34/8.25
% 53.34/8.25 ------
% 53.34/8.25 Current options:
% 53.34/8.25 ------
% 53.34/8.25
% 53.34/8.25
% 53.34/8.25
% 53.34/8.25
% 53.34/8.25 ------ Proving...
% 53.34/8.25
% 53.34/8.25
% 53.34/8.25 % SZS status Theorem for theBenchmark.p
% 53.34/8.25
% 53.34/8.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 53.34/8.26
% 53.34/8.26
%------------------------------------------------------------------------------