TSTP Solution File: NUM508+3 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM508+3 : TPTP v8.1.2. 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 : Fri May 3 02:49:39 EDT 2024
% Result : Theorem 123.81s 17.21s
% Output : CNFRefutation 123.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 86 ( 22 unt; 0 def)
% Number of atoms : 460 ( 139 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 544 ( 170 ~; 166 |; 187 &)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn 78 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( ( doDivides0(X2,sdtasdt0(X0,X1))
| ? [X3] :
( sdtasdt0(X0,X1) = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) ) )
& ( isPrime0(X2)
| ( ! [X3] :
( ( doDivides0(X3,X2)
& ? [X4] :
( sdtasdt0(X3,X4) = X2
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) )
=> ( X2 = X3
| sz10 = X3 ) )
& sz10 != X2
& sz00 != X2 ) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( doDivides0(X2,X1)
& ? [X3] :
( sdtasdt0(X2,X3) = X1
& aNaturalNumber0(X3) ) )
| ( doDivides0(X2,X0)
& ? [X3] :
( sdtasdt0(X2,X3) = X0
& aNaturalNumber0(X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1799) ).
fof(f48,axiom,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( sdtasdt0(X0,X1) = xr
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xr = X0
| sz10 = X0 ) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& ? [X0] :
( xk = sdtpldt0(xr,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(f51,axiom,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0)
& aNaturalNumber0(X0) )
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2478) ).
fof(f52,conjecture,
( doDivides0(xr,xm)
| ? [X0] :
( xm = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
| doDivides0(xr,xn)
| ? [X0] :
( xn = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f53,negated_conjecture,
~ ( doDivides0(xr,xm)
| ? [X0] :
( xm = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
| doDivides0(xr,xn)
| ? [X0] :
( xn = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) ) ),
inference(negated_conjecture,[],[f52]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( ( doDivides0(X2,sdtasdt0(X0,X1))
| ? [X3] :
( sdtasdt0(X0,X1) = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) ) )
& ( isPrime0(X2)
| ( ! [X4] :
( ( doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) )
=> ( X2 = X4
| sz10 = X4 ) )
& sz10 != X2
& sz00 != X2 ) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( doDivides0(X2,X1)
& ? [X6] :
( sdtasdt0(X2,X6) = X1
& aNaturalNumber0(X6) ) )
| ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
fof(f59,plain,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( sdtasdt0(X0,X1) = xr
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xr = X0
| sz10 = X0 ) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(rectify,[],[f48]) ).
fof(f60,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& ? [X1] :
( xk = sdtpldt0(xr,X1)
& aNaturalNumber0(X1) ) ),
inference(rectify,[],[f49]) ).
fof(f61,plain,
~ ( doDivides0(xr,xm)
| ? [X0] :
( xm = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
| doDivides0(xr,xn)
| ? [X1] :
( xn = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) ) ),
inference(rectify,[],[f53]) ).
fof(f62,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f63,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f62]) ).
fof(f106,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f107,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f106]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ( doDivides0(X2,X1)
& ? [X6] :
( sdtasdt0(X2,X6) = X1
& aNaturalNumber0(X6) ) )
| ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) )
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X3] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ) )
| ( ~ isPrime0(X2)
& ( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) )
| sz10 = X2
| sz00 = X2 ) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ( doDivides0(X2,X1)
& ? [X6] :
( sdtasdt0(X2,X6) = X1
& aNaturalNumber0(X6) ) )
| ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) )
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X3] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ) )
| ( ~ isPrime0(X2)
& ( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) )
| sz10 = X2
| sz00 = X2 ) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f126]) ).
fof(f133,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(ennf_transformation,[],[f59]) ).
fof(f134,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
( ~ doDivides0(xr,xm)
& ! [X0] :
( xm != sdtasdt0(xr,X0)
| ~ aNaturalNumber0(X0) )
& ~ doDivides0(xr,xn)
& ! [X1] :
( xn != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1) ) ),
inference(ennf_transformation,[],[f61]) ).
fof(f136,plain,
! [X2] :
( ( ~ isPrime0(X2)
& ( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) )
| sz10 = X2
| sz00 = X2 ) )
| ~ sP0(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f137,plain,
! [X0,X2] :
( ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) )
| ~ sP1(X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ( doDivides0(X2,X1)
& ? [X6] :
( sdtasdt0(X2,X6) = X1
& aNaturalNumber0(X6) ) )
| sP1(X0,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X3] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ) )
| sP0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f127,f137,f136]) ).
fof(f158,plain,
! [X0,X2] :
( ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) )
| ~ sP1(X0,X2) ),
inference(nnf_transformation,[],[f137]) ).
fof(f159,plain,
! [X0,X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f158]) ).
fof(f160,plain,
! [X0,X1] :
( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,sK6(X0,X1)) = X0
& aNaturalNumber0(sK6(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
! [X0,X1] :
( ( doDivides0(X1,X0)
& sdtasdt0(X1,sK6(X0,X1)) = X0
& aNaturalNumber0(sK6(X0,X1)) )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f159,f160]) ).
fof(f162,plain,
! [X2] :
( ( ~ isPrime0(X2)
& ( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) )
| sz10 = X2
| sz00 = X2 ) )
| ~ sP0(X2) ),
inference(nnf_transformation,[],[f136]) ).
fof(f163,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 ) )
| ~ sP0(X0) ),
inference(rectify,[],[f162]) ).
fof(f164,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( sK7(X0) != X0
& sz10 != sK7(X0)
& doDivides0(sK7(X0),X0)
& ? [X2] :
( sdtasdt0(sK7(X0),X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f165,plain,
! [X0] :
( ? [X2] :
( sdtasdt0(sK7(X0),X2) = X0
& aNaturalNumber0(X2) )
=> ( sdtasdt0(sK7(X0),sK8(X0)) = X0
& aNaturalNumber0(sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f166,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ( sK7(X0) != X0
& sz10 != sK7(X0)
& doDivides0(sK7(X0),X0)
& sdtasdt0(sK7(X0),sK8(X0)) = X0
& aNaturalNumber0(sK8(X0))
& aNaturalNumber0(sK7(X0)) )
| sz10 = X0
| sz00 = X0 ) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f163,f165,f164]) ).
fof(f167,plain,
! [X0,X1,X2] :
( ( doDivides0(X2,X1)
& ? [X3] :
( sdtasdt0(X2,X3) = X1
& aNaturalNumber0(X3) ) )
| sP1(X0,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X4] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X4)
| ~ aNaturalNumber0(X4) ) )
| sP0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f138]) ).
fof(f168,plain,
! [X1,X2] :
( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X2,sK9(X1,X2)) = X1
& aNaturalNumber0(sK9(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f169,plain,
! [X0,X1,X2] :
( ( doDivides0(X2,X1)
& sdtasdt0(X2,sK9(X1,X2)) = X1
& aNaturalNumber0(sK9(X1,X2)) )
| sP1(X0,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X4] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X4)
| ~ aNaturalNumber0(X4) ) )
| sP0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f167,f168]) ).
fof(f175,plain,
( ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
=> ( xk = sdtasdt0(xr,sK13)
& aNaturalNumber0(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f176,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK13)
& aNaturalNumber0(sK13)
& aNaturalNumber0(xr) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f134,f175]) ).
fof(f177,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xr,sK14)
& aNaturalNumber0(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f178,plain,
( ? [X1] :
( xk = sdtpldt0(xr,X1)
& aNaturalNumber0(X1) )
=> ( xk = sdtpldt0(xr,sK15)
& aNaturalNumber0(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f179,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK14)
& aNaturalNumber0(sK14)
& xk = sdtpldt0(xr,sK15)
& aNaturalNumber0(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f60,f178,f177]) ).
fof(f182,plain,
( ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),sK17)
& aNaturalNumber0(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f183,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),sK17)
& aNaturalNumber0(sK17)
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xr) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f51,f182]) ).
fof(f187,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f230,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f252,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f253,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f254,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f257,plain,
! [X0,X1] :
( doDivides0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f161]) ).
fof(f264,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f166]) ).
fof(f270,plain,
! [X2,X0,X1] :
( doDivides0(X2,X1)
| sP1(X0,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| sP0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f298,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f176]) ).
fof(f306,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f176]) ).
fof(f311,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f179]) ).
fof(f316,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xr),
inference(cnf_transformation,[],[f183]) ).
fof(f319,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f183]) ).
fof(f321,plain,
~ doDivides0(xr,xn),
inference(cnf_transformation,[],[f135]) ).
fof(f323,plain,
~ doDivides0(xr,xm),
inference(cnf_transformation,[],[f135]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f187]) ).
cnf(c_94,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f230]) ).
cnf(c_116,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f254]) ).
cnf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f253]) ).
cnf(c_118,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f252]) ).
cnf(c_119,plain,
( ~ sP1(X0,X1)
| doDivides0(X1,X0) ),
inference(cnf_transformation,[],[f257]) ).
cnf(c_122,plain,
( ~ isPrime0(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f264]) ).
cnf(c_129,plain,
( ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| doDivides0(X2,X1)
| sP1(X0,X2)
| sP0(X2) ),
inference(cnf_transformation,[],[f270]) ).
cnf(c_162,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f306]) ).
cnf(c_170,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f298]) ).
cnf(c_171,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f311]) ).
cnf(c_180,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f319]) ).
cnf(c_183,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xr),
inference(cnf_transformation,[],[f316]) ).
cnf(c_184,negated_conjecture,
~ doDivides0(xr,xm),
inference(cnf_transformation,[],[f323]) ).
cnf(c_186,negated_conjecture,
~ doDivides0(xr,xn),
inference(cnf_transformation,[],[f321]) ).
cnf(c_1544,plain,
( X0 != xr
| ~ sP0(X0) ),
inference(resolution_lifted,[status(thm)],[c_122,c_162]) ).
cnf(c_1545,plain,
~ sP0(xr),
inference(unflattening,[status(thm)],[c_1544]) ).
cnf(c_9481,plain,
( ~ iLess0(sdtpldt0(sdtpldt0(X0,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(xr,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| sP1(X0,xr)
| doDivides0(xr,xm)
| sP0(xr) ),
inference(instantiation,[status(thm)],[c_129]) ).
cnf(c_9490,plain,
( ~ sP1(xn,xr)
| doDivides0(xr,xn) ),
inference(instantiation,[status(thm)],[c_119]) ).
cnf(c_9688,plain,
( ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| doDivides0(xr,xm)
| sP1(xn,xr)
| sP0(xr) ),
inference(instantiation,[status(thm)],[c_9481]) ).
cnf(c_17316,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(superposition,[status(thm)],[c_180,c_94]) ).
cnf(c_73739,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,xm))
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(sdtpldt0(X0,xm),X1)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_73773,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,X0),X1)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_103640,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_115745,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_73739]) ).
cnf(c_149892,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xr)
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(instantiation,[status(thm)],[c_73773]) ).
cnf(c_149893,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_149892,c_115745,c_103640,c_17316,c_9688,c_9490,c_1545,c_183,c_171,c_184,c_186,c_116,c_117,c_118,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : NUM508+3 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.11 % Command : run_iprover %s %d THM
% 0.11/0.31 % Computer : n020.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu May 2 19:28:46 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.17/0.41 Running first-order theorem proving
% 0.17/0.41 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
% 123.81/17.21 % SZS status Started for theBenchmark.p
% 123.81/17.21 % SZS status Theorem for theBenchmark.p
% 123.81/17.21
% 123.81/17.21 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 123.81/17.21
% 123.81/17.21 ------ iProver source info
% 123.81/17.21
% 123.81/17.21 git: date: 2024-05-02 19:28:25 +0000
% 123.81/17.21 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 123.81/17.21 git: non_committed_changes: false
% 123.81/17.21
% 123.81/17.21 ------ Parsing...
% 123.81/17.21 ------ Clausification by vclausify_rel & Parsing by iProver...
% 123.81/17.21
% 123.81/17.21 ------ Preprocessing... sup_sim: 2 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
% 123.81/17.21
% 123.81/17.21 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 123.81/17.21
% 123.81/17.21 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 123.81/17.21 ------ Proving...
% 123.81/17.21 ------ Problem Properties
% 123.81/17.21
% 123.81/17.21
% 123.81/17.21 clauses 132
% 123.81/17.21 conjectures 4
% 123.81/17.21 EPR 50
% 123.81/17.21 Horn 92
% 123.81/17.21 unary 51
% 123.81/17.21 binary 15
% 123.81/17.21 lits 405
% 123.81/17.21 lits eq 126
% 123.81/17.21 fd_pure 0
% 123.81/17.21 fd_pseudo 0
% 123.81/17.21 fd_cond 24
% 123.81/17.21 fd_pseudo_cond 11
% 123.81/17.21 AC symbols 0
% 123.81/17.21
% 123.81/17.21 ------ Input Options Time Limit: Unbounded
% 123.81/17.21
% 123.81/17.21
% 123.81/17.21 ------
% 123.81/17.21 Current options:
% 123.81/17.21 ------
% 123.81/17.21
% 123.81/17.21
% 123.81/17.21
% 123.81/17.21
% 123.81/17.21 ------ Proving...
% 123.81/17.21
% 123.81/17.21
% 123.81/17.21 % SZS status Theorem for theBenchmark.p
% 123.81/17.21
% 123.81/17.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 123.81/17.21
% 123.81/17.21
%------------------------------------------------------------------------------