TSTP Solution File: NUM495+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM495+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:30:55 EDT 2023
% Result : Theorem 120.32s 16.81s
% Output : CNFRefutation 120.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 85 ( 22 unt; 0 def)
% Number of atoms : 445 ( 135 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 530 ( 170 ~; 166 |; 174 &)
% ( 0 <=>; 20 =>; 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 : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn; 78 !; 50 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__1799) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( sdtasdt0(X0,X1) = xp
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xp = X0
| sz10 = X0 ) )
& sz10 != xp
& sz00 != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f43,axiom,
( xr = sdtmndt0(xn,xp)
& xn = sdtpldt0(xp,xr)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(f45,axiom,
( doDivides0(xp,sdtasdt0(xr,xm))
& ? [X0] :
( sdtasdt0(xp,X0) = sdtasdt0(xr,xm)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1913) ).
fof(f46,axiom,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0)
& aNaturalNumber0(X0) )
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xr,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2062) ).
fof(f47,conjecture,
( doDivides0(xp,xm)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| doDivides0(xp,xr)
| ? [X0] :
( sdtasdt0(xp,X0) = xr
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
~ ( doDivides0(xp,xm)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| doDivides0(xp,xr)
| ? [X0] :
( sdtasdt0(xp,X0) = xr
& aNaturalNumber0(X0) ) ),
inference(negated_conjecture,[],[f47]) ).
fof(f51,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(f52,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( sdtasdt0(X1,X2) = xp
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( xp = X1
| sz10 = X1 ) )
& sz10 != xp
& sz00 != xp ),
inference(rectify,[],[f41]) ).
fof(f53,plain,
~ ( doDivides0(xp,xm)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| doDivides0(xp,xr)
| ? [X1] :
( xr = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ),
inference(rectify,[],[f48]) ).
fof(f54,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f55,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f54]) ).
fof(f98,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f99,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f98]) ).
fof(f118,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,[],[f51]) ).
fof(f119,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,[],[f118]) ).
fof(f120,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(ennf_transformation,[],[f52]) ).
fof(f121,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
( ~ doDivides0(xp,xm)
& ! [X0] :
( xm != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) )
& ~ doDivides0(xp,xr)
& ! [X1] :
( xr != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f123,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(f124,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(f125,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,[],[f119,f124,f123]) ).
fof(f145,plain,
! [X0,X2] :
( ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) )
| ~ sP1(X0,X2) ),
inference(nnf_transformation,[],[f124]) ).
fof(f146,plain,
! [X0,X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f145]) ).
fof(f147,plain,
! [X0,X1] :
( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,sK6(X0,X1)) = X0
& aNaturalNumber0(sK6(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f148,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])],[f146,f147]) ).
fof(f149,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,[],[f123]) ).
fof(f150,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,[],[f149]) ).
fof(f151,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(f152,plain,
! [X0] :
( ? [X2] :
( sdtasdt0(sK7(X0),X2) = X0
& aNaturalNumber0(X2) )
=> ( sdtasdt0(sK7(X0),sK8(X0)) = X0
& aNaturalNumber0(sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f153,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])],[f150,f152,f151]) ).
fof(f154,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,[],[f125]) ).
fof(f155,plain,
! [X1,X2] :
( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X2,sK9(X1,X2)) = X1
& aNaturalNumber0(sK9(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f156,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])],[f154,f155]) ).
fof(f157,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK10)
& aNaturalNumber0(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK10)
& aNaturalNumber0(sK10)
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f121,f157]) ).
fof(f163,plain,
( ? [X0] :
( sdtasdt0(xp,X0) = sdtasdt0(xr,xm)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xr,xm) = sdtasdt0(xp,sK13)
& aNaturalNumber0(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f164,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
& sdtasdt0(xr,xm) = sdtasdt0(xp,sK13)
& aNaturalNumber0(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f45,f163]) ).
fof(f165,plain,
( ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),sK14)
& aNaturalNumber0(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f166,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),sK14)
& aNaturalNumber0(sK14)
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xr,xm),xp) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f46,f165]) ).
fof(f170,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f213,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f235,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f236,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f237,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f240,plain,
! [X0,X1] :
( doDivides0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f148]) ).
fof(f247,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f253,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,[],[f156]) ).
fof(f258,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f158]) ).
fof(f265,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f43]) ).
fof(f274,plain,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f164]) ).
fof(f275,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xr,xm),xp),
inference(cnf_transformation,[],[f166]) ).
fof(f278,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f166]) ).
fof(f280,plain,
~ doDivides0(xp,xr),
inference(cnf_transformation,[],[f122]) ).
fof(f282,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f122]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_94,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
cnf(c_116,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f237]) ).
cnf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f236]) ).
cnf(c_118,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f235]) ).
cnf(c_119,plain,
( ~ sP1(X0,X1)
| doDivides0(X1,X0) ),
inference(cnf_transformation,[],[f240]) ).
cnf(c_122,plain,
( ~ isPrime0(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f247]) ).
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,[],[f253]) ).
cnf(c_138,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f258]) ).
cnf(c_148,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f265]) ).
cnf(c_153,plain,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f274]) ).
cnf(c_156,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f278]) ).
cnf(c_159,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xr,xm),xp),
inference(cnf_transformation,[],[f275]) ).
cnf(c_160,negated_conjecture,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f282]) ).
cnf(c_162,negated_conjecture,
~ doDivides0(xp,xr),
inference(cnf_transformation,[],[f280]) ).
cnf(c_1447,plain,
( X0 != xp
| ~ sP0(X0) ),
inference(resolution_lifted,[status(thm)],[c_122,c_138]) ).
cnf(c_1448,plain,
~ sP0(xp),
inference(unflattening,[status(thm)],[c_1447]) ).
cnf(c_9145,plain,
( ~ iLess0(sdtpldt0(sdtpldt0(X0,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| sP1(X0,xp)
| doDivides0(xp,xm)
| sP0(xp) ),
inference(instantiation,[status(thm)],[c_129]) ).
cnf(c_9154,plain,
( ~ sP1(xr,xp)
| doDivides0(xp,xr) ),
inference(instantiation,[status(thm)],[c_119]) ).
cnf(c_9351,plain,
( ~ iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(xp,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| doDivides0(xp,xm)
| sP1(xr,xp)
| sP0(xp) ),
inference(instantiation,[status(thm)],[c_9145]) ).
cnf(c_15356,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xr,xm),xp)
| iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(superposition,[status(thm)],[c_156,c_94]) ).
cnf(c_66178,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,xm))
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(sdtpldt0(X0,xm),xp)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_79920,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_120016,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_120134,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_66178]) ).
cnf(c_134504,plain,
( ~ aNaturalNumber0(sdtpldt0(xr,xm))
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
inference(instantiation,[status(thm)],[c_66178]) ).
cnf(c_134505,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_134504,c_120134,c_120016,c_79920,c_15356,c_9351,c_9154,c_1448,c_159,c_153,c_160,c_162,c_116,c_117,c_118,c_148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM495+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 11:10:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 120.32/16.81 % SZS status Started for theBenchmark.p
% 120.32/16.81 % SZS status Theorem for theBenchmark.p
% 120.32/16.81
% 120.32/16.81 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 120.32/16.81
% 120.32/16.81 ------ iProver source info
% 120.32/16.81
% 120.32/16.81 git: date: 2023-05-31 18:12:56 +0000
% 120.32/16.81 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 120.32/16.81 git: non_committed_changes: false
% 120.32/16.81 git: last_make_outside_of_git: false
% 120.32/16.81
% 120.32/16.81 ------ Parsing...
% 120.32/16.81 ------ Clausification by vclausify_rel & Parsing by iProver...
% 120.32/16.81
% 120.32/16.81 ------ 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
% 120.32/16.81
% 120.32/16.81 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 120.32/16.81
% 120.32/16.81 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 120.32/16.81 ------ Proving...
% 120.32/16.81 ------ Problem Properties
% 120.32/16.81
% 120.32/16.81
% 120.32/16.81 clauses 110
% 120.32/16.81 conjectures 4
% 120.32/16.81 EPR 34
% 120.32/16.81 Horn 72
% 120.32/16.81 unary 33
% 120.32/16.81 binary 13
% 120.32/16.81 lits 374
% 120.32/16.81 lits eq 110
% 120.32/16.81 fd_pure 0
% 120.32/16.81 fd_pseudo 0
% 120.32/16.81 fd_cond 22
% 120.32/16.81 fd_pseudo_cond 11
% 120.32/16.81 AC symbols 0
% 120.32/16.81
% 120.32/16.81 ------ Input Options Time Limit: Unbounded
% 120.32/16.81
% 120.32/16.81
% 120.32/16.81 ------
% 120.32/16.81 Current options:
% 120.32/16.81 ------
% 120.32/16.81
% 120.32/16.81
% 120.32/16.81
% 120.32/16.81
% 120.32/16.81 ------ Proving...
% 120.32/16.81
% 120.32/16.81
% 120.32/16.81 % SZS status Theorem for theBenchmark.p
% 120.32/16.81
% 120.32/16.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 120.32/16.81
% 120.32/16.82
%------------------------------------------------------------------------------