TSTP Solution File: NUM517+3 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM517+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 02:49:41 EDT 2024
% Result : Theorem 20.53s 3.63s
% Output : CNFRefutation 20.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 89 ( 26 unt; 0 def)
% Number of atoms : 480 ( 155 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 562 ( 171 ~; 160 |; 207 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 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 : 142 ( 0 sgn 80 !; 52 ?)
% 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(f54,axiom,
( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& ? [X0] :
( sdtasdt0(xp,X0) = sdtasdt0(sdtsldt0(xn,xr),xm)
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2529) ).
fof(f55,axiom,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2686) ).
fof(f56,conjecture,
( doDivides0(xp,xm)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( doDivides0(xp,sdtsldt0(xn,xr))
| ? [X0] :
( sdtasdt0(xp,X0) = sdtsldt0(xn,xr)
& aNaturalNumber0(X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ( doDivides0(xp,xm)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( doDivides0(xp,sdtsldt0(xn,xr))
| ? [X0] :
( sdtasdt0(xp,X0) = sdtsldt0(xn,xr)
& aNaturalNumber0(X0) ) ) ) ),
inference(negated_conjecture,[],[f56]) ).
fof(f60,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(f61,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(f66,plain,
~ ( doDivides0(xp,xm)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( doDivides0(xp,sdtsldt0(xn,xr))
| ? [X1] :
( sdtsldt0(xn,xr) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ) ) ),
inference(rectify,[],[f57]) ).
fof(f67,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f68,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f67]) ).
fof(f111,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f112,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f111]) ).
fof(f131,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,[],[f60]) ).
fof(f132,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,[],[f131]) ).
fof(f133,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,[],[f61]) ).
fof(f134,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,[],[f133]) ).
fof(f142,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(ennf_transformation,[],[f55]) ).
fof(f143,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(flattening,[],[f142]) ).
fof(f144,plain,
( ~ doDivides0(xp,xm)
& ! [X0] :
( xm != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) )
& ~ doDivides0(xp,sdtsldt0(xn,xr))
& ! [X1] :
( sdtsldt0(xn,xr) != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(ennf_transformation,[],[f66]) ).
fof(f145,plain,
( ~ doDivides0(xp,xm)
& ! [X0] :
( xm != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) )
& ~ doDivides0(xp,sdtsldt0(xn,xr))
& ! [X1] :
( sdtsldt0(xn,xr) != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(flattening,[],[f144]) ).
fof(f146,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(f147,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(f148,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,[],[f132,f147,f146]) ).
fof(f170,plain,
! [X0,X2] :
( ( doDivides0(X2,X0)
& ? [X7] :
( sdtasdt0(X2,X7) = X0
& aNaturalNumber0(X7) ) )
| ~ sP1(X0,X2) ),
inference(nnf_transformation,[],[f147]) ).
fof(f171,plain,
! [X0,X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f170]) ).
fof(f172,plain,
! [X0,X1] :
( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,sK7(X0,X1)) = X0
& aNaturalNumber0(sK7(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f173,plain,
! [X0,X1] :
( ( doDivides0(X1,X0)
& sdtasdt0(X1,sK7(X0,X1)) = X0
& aNaturalNumber0(sK7(X0,X1)) )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f171,f172]) ).
fof(f174,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,[],[f146]) ).
fof(f175,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,[],[f174]) ).
fof(f176,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( sK8(X0) != X0
& sz10 != sK8(X0)
& doDivides0(sK8(X0),X0)
& ? [X2] :
( sdtasdt0(sK8(X0),X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f177,plain,
! [X0] :
( ? [X2] :
( sdtasdt0(sK8(X0),X2) = X0
& aNaturalNumber0(X2) )
=> ( sdtasdt0(sK8(X0),sK9(X0)) = X0
& aNaturalNumber0(sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f178,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ( sK8(X0) != X0
& sz10 != sK8(X0)
& doDivides0(sK8(X0),X0)
& sdtasdt0(sK8(X0),sK9(X0)) = X0
& aNaturalNumber0(sK9(X0))
& aNaturalNumber0(sK8(X0)) )
| sz10 = X0
| sz00 = X0 ) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f175,f177,f176]) ).
fof(f179,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,[],[f148]) ).
fof(f180,plain,
! [X1,X2] :
( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X2,sK10(X1,X2)) = X1
& aNaturalNumber0(sK10(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f181,plain,
! [X0,X1,X2] :
( ( doDivides0(X2,X1)
& sdtasdt0(X2,sK10(X1,X2)) = X1
& aNaturalNumber0(sK10(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,[sK10])],[f179,f180]) ).
fof(f182,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK11)
& aNaturalNumber0(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f183,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK11)
& aNaturalNumber0(sK11)
& 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,[sK11])],[f134,f182]) ).
fof(f204,plain,
( ? [X0] :
( sdtasdt0(xp,X0) = sdtasdt0(sdtsldt0(xn,xr),xm)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sK22)
& aNaturalNumber0(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f205,plain,
( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sK22)
& aNaturalNumber0(sK22)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f54,f204]) ).
fof(f206,plain,
( ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sK23)
& aNaturalNumber0(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f207,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sK23)
& aNaturalNumber0(sK23)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f143,f206]) ).
fof(f211,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f254,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f277,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f278,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f281,plain,
! [X0,X1] :
( doDivides0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
fof(f288,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f294,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,[],[f181]) ).
fof(f299,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f183]) ).
fof(f361,plain,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnf_transformation,[],[f205]) ).
fof(f364,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),
inference(cnf_transformation,[],[f207]) ).
fof(f367,plain,
aNaturalNumber0(sK23),
inference(cnf_transformation,[],[f207]) ).
fof(f368,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sK23),
inference(cnf_transformation,[],[f207]) ).
fof(f369,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f207]) ).
fof(f370,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f145]) ).
fof(f373,plain,
~ doDivides0(xp,sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f145]) ).
fof(f375,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f145]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_94,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f254]) ).
cnf(c_116,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f278]) ).
cnf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f277]) ).
cnf(c_119,plain,
( ~ sP1(X0,X1)
| doDivides0(X1,X0) ),
inference(cnf_transformation,[],[f281]) ).
cnf(c_122,negated_conjecture,
( ~ isPrime0(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f288]) ).
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,[],[f294]) ).
cnf(c_138,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f299]) ).
cnf(c_197,plain,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnf_transformation,[],[f361]) ).
cnf(c_202,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f369]) ).
cnf(c_203,plain,
sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sK23) = sdtpldt0(sdtpldt0(xn,xm),xp),
inference(cnf_transformation,[],[f368]) ).
cnf(c_204,plain,
aNaturalNumber0(sK23),
inference(cnf_transformation,[],[f367]) ).
cnf(c_207,negated_conjecture,
sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(cnf_transformation,[],[f364]) ).
cnf(c_210,negated_conjecture,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f375]) ).
cnf(c_212,negated_conjecture,
~ doDivides0(xp,sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f373]) ).
cnf(c_215,negated_conjecture,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f370]) ).
cnf(c_503,plain,
~ sP0(xp),
inference(superposition,[status(thm)],[c_138,c_122]) ).
cnf(c_4994,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolution,[status(thm)],[c_94,c_207]) ).
cnf(c_5138,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sK23)
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(superposition,[status(thm)],[c_203,c_52]) ).
cnf(c_5632,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(superposition,[status(thm)],[c_202,c_94]) ).
cnf(c_6037,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(global_subsumption_just,[status(thm)],[c_4994,c_204,c_207,c_5138,c_5632]) ).
cnf(c_12730,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_16236,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| sP1(sdtsldt0(xn,xr),xp)
| doDivides0(xp,xm)
| sP0(xp) ),
inference(resolution,[status(thm)],[c_129,c_6037]) ).
cnf(c_16271,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| sP1(sdtsldt0(xn,xr),xp) ),
inference(global_subsumption_just,[status(thm)],[c_16236,c_117,c_116,c_215,c_210,c_197,c_503,c_16236]) ).
cnf(c_16281,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| sP1(sdtsldt0(xn,xr),xp) ),
inference(resolution,[status(thm)],[c_16271,c_52]) ).
cnf(c_16282,plain,
sP1(sdtsldt0(xn,xr),xp),
inference(global_subsumption_just,[status(thm)],[c_16281,c_117,c_116,c_215,c_12730,c_16281]) ).
cnf(c_16357,plain,
doDivides0(xp,sdtsldt0(xn,xr)),
inference(resolution,[status(thm)],[c_119,c_16282]) ).
cnf(c_16358,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16357,c_212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : NUM517+3 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11 % Command : run_iprover %s %d THM
% 0.11/0.31 % Computer : n027.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 20:06:50 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 20.53/3.63 % SZS status Started for theBenchmark.p
% 20.53/3.63 % SZS status Theorem for theBenchmark.p
% 20.53/3.63
% 20.53/3.63 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 20.53/3.63
% 20.53/3.63 ------ iProver source info
% 20.53/3.63
% 20.53/3.63 git: date: 2024-05-02 19:28:25 +0000
% 20.53/3.63 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 20.53/3.63 git: non_committed_changes: false
% 20.53/3.63
% 20.53/3.63 ------ Parsing...
% 20.53/3.63 ------ Clausification by vclausify_rel & Parsing by iProver...
% 20.53/3.63
% 20.53/3.63 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e
% 20.53/3.63
% 20.53/3.63 ------ Preprocessing...
% 20.53/3.63
% 20.53/3.63 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 20.53/3.63 ------ Proving...
% 20.53/3.63 ------ Problem Properties
% 20.53/3.63
% 20.53/3.63
% 20.53/3.63 clauses 149
% 20.53/3.63 conjectures 24
% 20.53/3.63 EPR 56
% 20.53/3.63 Horn 106
% 20.53/3.63 unary 63
% 20.53/3.63 binary 20
% 20.53/3.63 lits 427
% 20.53/3.63 lits eq 133
% 20.53/3.63 fd_pure 0
% 20.53/3.63 fd_pseudo 0
% 20.53/3.63 fd_cond 24
% 20.53/3.63 fd_pseudo_cond 11
% 20.53/3.63 AC symbols 0
% 20.53/3.63
% 20.53/3.63 ------ Input Options Time Limit: Unbounded
% 20.53/3.63
% 20.53/3.63
% 20.53/3.63 ------
% 20.53/3.63 Current options:
% 20.53/3.63 ------
% 20.53/3.63
% 20.53/3.63
% 20.53/3.63
% 20.53/3.63
% 20.53/3.63 ------ Proving...
% 20.53/3.63
% 20.53/3.63
% 20.53/3.63 % SZS status Theorem for theBenchmark.p
% 20.53/3.63
% 20.53/3.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.53/3.63
% 20.53/3.64
%------------------------------------------------------------------------------