%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM506+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:40:47 PM UTC 2026
% Result : Theorem 107.85s 14.10s
% Output : CNFRefutation 107.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 19
% Syntax : Number of formulae : 130 ( 20 unt; 3 def)
% Number of atoms : 699 ( 177 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 924 ( 355 ~; 388 |; 156 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 183 ( 152 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W2,W0) != sdtpldt0(W2,W1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( W1 != sz00
& doDivides0(W0,W1) )
=> sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( ( doDivides0(W2,sdtasdt0(W0,W1))
| ? [W3] :
( sdtasdt0(W0,W1) = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
& ( isPrime0(W2)
| ( ! [W3] :
( ( doDivides0(W3,W2)
& ? [W4] :
( W2 = sdtasdt0(W3,W4)
& aNaturalNumber0(W4) )
& aNaturalNumber0(W3) )
=> ( W3 = W2
| W3 = sz10 ) )
& W2 != sz10
& W2 != sz00 ) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( doDivides0(W2,W1)
& ? [W3] :
( W1 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| ( doDivides0(W2,W0)
& ? [W3] :
( W0 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
( isPrime0(xr)
& ! [W0] :
( ( ( doDivides0(W0,xr)
| ? [W1] :
( xr = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xr
| W0 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [W0] :
( xk = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
& ? [W0] :
( sdtpldt0(xr,W0) = xk
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
( sdtlseqdt0(xk,xp)
& ? [W0] :
( sdtpldt0(xk,W0) = xp
& aNaturalNumber0(W0) )
& xk != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,conjecture,
( doDivides0(xr,xm)
| ? [W0] :
( xm = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
| doDivides0(xr,xn)
| ? [W0] :
( xn = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
~ ( doDivides0(xr,xm)
| ? [W0] :
( xm = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
| doDivides0(xr,xn)
| ? [W0] :
( xn = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f59,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f60,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f83,plain,
! [W0,W1,W2] :
( W1 = W2
| ( sdtpldt0(W1,W0) != sdtpldt0(W2,W0)
& sdtpldt0(W0,W1) != sdtpldt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| X2 = X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f94,plain,
! [W0,W1] :
( ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f95,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ( sdtpldt0(W0,sK0_skl(W1,W0)) = W1
& aNaturalNumber0(sK0_skl(W1,W0)) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f95]) ).
fof(f99,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f108,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f109,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f111,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [W0,W1] :
( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f114,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,plain,
! [W0,W1] :
( ! [W2] :
( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
| ~ aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1)
| W0 = W1
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| X1 = X0
| ~ sdtlseqdt0(X1,X0)
| sdtlseqdt0(sdtpldt0(X2,X1),sdtpldt0(X2,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f132,plain,
! [W0,W1] :
( iLess0(W0,W1)
| ~ sdtlseqdt0(W0,W1)
| W0 = W1
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f133,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f152,plain,
! [W0,W1] :
( sdtlseqdt0(W0,W1)
| W1 = sz00
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f153,plain,
! [X0,X1] :
( X1 = sz00
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f171,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f172,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f173,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f174,plain,
! [W0,W1,W2] :
( ( doDivides0(W2,W1)
& ? [W3] :
( W1 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| ( doDivides0(W2,W0)
& ? [W3] :
( W0 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3] :
( sdtasdt0(W0,W1) != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) ) )
| ( ~ isPrime0(W2)
& ( ? [W3] :
( W3 != W2
& W3 != sz10
& doDivides0(W3,W2)
& ? [W4] :
( W2 = sdtasdt0(W3,W4)
& aNaturalNumber0(W4) )
& aNaturalNumber0(W3) )
| W2 = sz10
| W2 = sz00 ) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f175,definition,
! [W2] :
( sP0_prd(W2)
<=> ( ~ isPrime0(W2)
& ( ? [W3] :
( W3 != W2
& W3 != sz10
& doDivides0(W3,W2)
& ? [W4] :
( W2 = sdtasdt0(W3,W4)
& aNaturalNumber0(W4) )
& aNaturalNumber0(W3) )
| W2 = sz10
| W2 = sz00 ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f176,definition,
! [W0,W2] :
( sP1_prd(W2,W0)
<=> ( doDivides0(W2,W0)
& ? [W3] :
( W0 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f177,plain,
! [W0,W1,W2] :
( ( doDivides0(W2,W1)
& ? [W3] :
( W1 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| sP1_prd(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3] :
( sdtasdt0(W0,W1) != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) ) )
| sP0_prd(W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(formula_renaming,[status(thm)],[f174,f176,f175]) ).
fof(f178,plain,
! [W0,W1,W2] :
( ( doDivides0(W2,W1)
& W1 = sdtasdt0(W2,sK4_skl(W2,W1,W0))
& aNaturalNumber0(sK4_skl(W2,W1,W0)) )
| sP1_prd(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3] :
( sdtasdt0(W0,W1) != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) ) )
| sP0_prd(W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(W3,sK4_skl(W2,W1,W0))],[f177]) ).
fof(f179,plain,
! [X0,X1,X2,X3] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sP0_prd(X0)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X2,X1) != sdtasdt0(X0,X3)
| sP1_prd(X0,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X2,X1),X0),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sK4_skl(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f180,plain,
! [X0,X1,X2,X3] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X3)
| sP1_prd(X2,X0)
| sdtasdt0(X2,sK4_skl(X2,X1,X0)) = X1
| sP0_prd(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X3)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f210,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f213,plain,
( xk != sz10
& xk != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f214,plain,
xk != sz00,
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f218,plain,
( isPrime0(xr)
& ! [W0] :
( W0 = xr
| W0 = sz10
| ( ~ doDivides0(W0,xr)
& ! [W1] :
( xr != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [W0] :
( xk = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
& aNaturalNumber0(xr) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f219,plain,
( isPrime0(xr)
& ! [W0] :
( W0 = xr
| W0 = sz10
| ( ~ doDivides0(W0,xr)
& ! [W1] :
( xr != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK8_skl)
& aNaturalNumber0(sK8_skl)
& aNaturalNumber0(xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(W0,sK8_skl)],[f218]) ).
fof(f220,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f223,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f228,plain,
isPrime0(xr),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f229,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK10_skl)
& aNaturalNumber0(sK10_skl)
& sdtpldt0(xr,sK9_skl) = xk
& aNaturalNumber0(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(W0,sK9_skl),skolemize(W0,sK10_skl)],[f49]) ).
fof(f230,plain,
aNaturalNumber0(sK9_skl),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f231,plain,
sdtpldt0(xr,sK9_skl) = xk,
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f232,plain,
aNaturalNumber0(sK10_skl),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f233,plain,
sdtasdt0(xr,sK10_skl) = sdtasdt0(xn,xm),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f235,plain,
( sdtlseqdt0(xk,xp)
& sdtpldt0(xk,sK11_skl) = xp
& aNaturalNumber0(sK11_skl)
& xk != xp ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(W0,sK11_skl)],[f50]) ).
fof(f236,plain,
xp != xk,
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f239,plain,
sdtlseqdt0(xk,xp),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f240,plain,
( ~ doDivides0(xr,xm)
& ! [W0] :
( xm != sdtasdt0(xr,W0)
| ~ aNaturalNumber0(W0) )
& ~ doDivides0(xr,xn)
& ! [W0] :
( xn != sdtasdt0(xr,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f241,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xr,X0) ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f243,plain,
! [X0] :
( xm != sdtasdt0(xr,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f245,plain,
! [W2] :
( ( isPrime0(W2)
| ( ! [W3] :
( W3 = W2
| W3 = sz10
| ~ doDivides0(W3,W2)
| ! [W4] :
( W2 != sdtasdt0(W3,W4)
| ~ aNaturalNumber0(W4) )
| ~ aNaturalNumber0(W3) )
& W2 != sz10
& W2 != sz00 )
| sP0_prd(W2) )
& ( ( ~ isPrime0(W2)
& ( ? [W3] :
( W3 != W2
& W3 != sz10
& doDivides0(W3,W2)
& ? [W4] :
( W2 = sdtasdt0(W3,W4)
& aNaturalNumber0(W4) )
& aNaturalNumber0(W3) )
| W2 = sz10
| W2 = sz00 ) )
| ~ sP0_prd(W2) ) ),
inference(NNF_transformation,[status(thm)],[f175]) ).
fof(f246,plain,
( ! [W2] :
( isPrime0(W2)
| ( ! [W3] :
( W3 = W2
| W3 = sz10
| ~ doDivides0(W3,W2)
| ! [W4] :
( W2 != sdtasdt0(W3,W4)
| ~ aNaturalNumber0(W4) )
| ~ aNaturalNumber0(W3) )
& W2 != sz10
& W2 != sz00 )
| sP0_prd(W2) )
& ! [W2] :
( ( ~ isPrime0(W2)
& ( ? [W3] :
( W3 != W2
& W3 != sz10
& doDivides0(W3,W2)
& ? [W4] :
( W2 = sdtasdt0(W3,W4)
& aNaturalNumber0(W4) )
& aNaturalNumber0(W3) )
| W2 = sz10
| W2 = sz00 ) )
| ~ sP0_prd(W2) ) ),
inference(miniscoping,[status(thm)],[f245]) ).
fof(f247,plain,
( ! [W2] :
( isPrime0(W2)
| ( ! [W3] :
( W3 = W2
| W3 = sz10
| ~ doDivides0(W3,W2)
| ! [W4] :
( W2 != sdtasdt0(W3,W4)
| ~ aNaturalNumber0(W4) )
| ~ aNaturalNumber0(W3) )
& W2 != sz10
& W2 != sz00 )
| sP0_prd(W2) )
& ! [W2] :
( ( ~ isPrime0(W2)
& ( ( sK12_skl(W2) != W2
& sK12_skl(W2) != sz10
& doDivides0(sK12_skl(W2),W2)
& W2 = sdtasdt0(sK12_skl(W2),sK13_skl(W2))
& aNaturalNumber0(sK13_skl(W2))
& aNaturalNumber0(sK12_skl(W2)) )
| W2 = sz10
| W2 = sz00 ) )
| ~ sP0_prd(W2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(W3,sK12_skl(W2)),skolemize(W4,sK13_skl(W2))],[f246]) ).
fof(f254,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f247]) ).
fof(f258,plain,
! [W0,W2] :
( ( ~ doDivides0(W2,W0)
| ! [W3] :
( W0 != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) )
| sP1_prd(W2,W0) )
& ( ( doDivides0(W2,W0)
& ? [W3] :
( W0 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| ~ sP1_prd(W2,W0) ) ),
inference(NNF_transformation,[status(thm)],[f176]) ).
fof(f259,plain,
( ! [W0,W2] :
( ~ doDivides0(W2,W0)
| ! [W3] :
( W0 != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) )
| sP1_prd(W2,W0) )
& ! [W0,W2] :
( ( doDivides0(W2,W0)
& ? [W3] :
( W0 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| ~ sP1_prd(W2,W0) ) ),
inference(miniscoping,[status(thm)],[f258]) ).
fof(f260,plain,
( ! [W0,W2] :
( ~ doDivides0(W2,W0)
| ! [W3] :
( W0 != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) )
| sP1_prd(W2,W0) )
& ! [W0,W2] :
( ( doDivides0(W2,W0)
& W0 = sdtasdt0(W2,sK14_skl(W2,W0))
& aNaturalNumber0(sK14_skl(W2,W0)) )
| ~ sP1_prd(W2,W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(W3,sK14_skl(W2,W0))],[f259]) ).
fof(f261,plain,
! [X0,X1] :
( aNaturalNumber0(sK14_skl(X0,X1))
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f262,plain,
! [X0,X1] :
( ~ sP1_prd(X0,X1)
| sdtasdt0(X0,sK14_skl(X0,X1)) = X1 ),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f270,plain,
! [X0,X1] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f99]) ).
fof(f326,plain,
( xk = sz00
| sdtlseqdt0(xr,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f153,f223]) ).
fof(f329,plain,
( ~ aNaturalNumber0(xk)
| sdtlseqdt0(xr,xk)
| xk = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f326,f220]) ).
fof(f335,plain,
( ~ aNaturalNumber0(xk)
| sdtlseqdt0(xr,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[f329,f214]) ).
fof(f644,plain,
( ~ aNaturalNumber0(sK14_skl(xr,xn))
| ~ sP1_prd(xr,xn) ),
inference(resolution,[status(thm)],[f262,f241]) ).
fof(f654,plain,
~ sP1_prd(xr,xn),
inference(forward_subsumption_resolution,[status(thm)],[f644,f261]) ).
fof(f820,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(xk,xr)
| xk = xr
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f109,f335]) ).
fof(f840,plain,
( ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(xk,xr)
| xk = xr
| ~ aNaturalNumber0(xk) ),
inference(duplicate_literals_removal,[status(thm)],[f820]) ).
fof(f841,plain,
( xk = xr
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(xk,xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f840,f210]) ).
fof(f868,plain,
( xk = xr
| ~ sdtlseqdt0(xk,xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f841,f220]) ).
fof(f909,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(resolution,[status(thm)],[f133,f114]) ).
fof(f919,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| iLess0(X1,X0)
| X1 = X0
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f909]) ).
fof(f1038,plain,
! [X0,X1] :
( ~ aNaturalNumber0(sK4_skl(xr,xm,X0))
| sdtasdt0(X0,xm) != sdtasdt0(xr,X1)
| sP1_prd(xr,X0)
| sP0_prd(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolution,[status(thm)],[f180,f243]) ).
fof(f1050,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK4_skl(xr,xm,X1))
| sP0_prd(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(X1,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1_prd(xr,X1)
| ~ aNaturalNumber0(xm)
| sdtasdt0(xr,X0) != sdtasdt0(X1,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[f1038,f220]) ).
fof(f1078,plain,
! [X0,X1] :
( ~ aNaturalNumber0(sK4_skl(xr,xm,X1))
| sdtasdt0(X1,xm) != sdtasdt0(xr,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X1,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1_prd(xr,X1)
| ~ aNaturalNumber0(X1)
| sP0_prd(xr)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1050,f172]) ).
fof(f1081,plain,
( ~ aNaturalNumber0(sK4_skl(xr,xm,xn))
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1_prd(xr,xn)
| ~ aNaturalNumber0(xn)
| sP0_prd(xr)
| ~ aNaturalNumber0(sK10_skl) ),
inference(resolution,[status(thm)],[f1078,f233]) ).
fof(f1098,plain,
( ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1_prd(xr,xn)
| sP0_prd(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK4_skl(xr,xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1081,f232]) ).
fof(f1131,plain,
( sP0_prd(xr)
| sP1_prd(xr,xn)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sK4_skl(xr,xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1098,f171]) ).
fof(f1239,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f60]) ).
fof(f1244,plain,
( ~ aNaturalNumber0(sK9_skl)
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(xr,xk) ),
inference(paramodulation,[status(thm)],[f231,f1239]) ).
fof(f1246,plain,
( sdtlseqdt0(xr,xk)
| ~ aNaturalNumber0(sK9_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1244,f220]) ).
fof(f1255,plain,
sdtlseqdt0(xr,xk),
inference(forward_subsumption_resolution,[status(thm)],[f1246,f230]) ).
fof(f1554,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sP0_prd(xr)
| ~ aNaturalNumber0(sK10_skl)
| sP1_prd(xr,xn)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| aNaturalNumber0(sK4_skl(xr,xm,xn)) ),
inference(resolution,[status(thm)],[f179,f233]) ).
fof(f1630,plain,
( ~ aNaturalNumber0(sK10_skl)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sP0_prd(xr)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| sP1_prd(xr,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[f1554,f1131]) ).
fof(f1635,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sK10_skl)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xn)
| sP0_prd(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f1630,f654]) ).
fof(f1636,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sK10_skl)
| ~ aNaturalNumber0(xn)
| sP0_prd(xr) ),
inference(resolution,[status(thm)],[f1635,f919]) ).
fof(f1637,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sK10_skl)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr))
| sP0_prd(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f1636,f171]) ).
fof(f1653,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,xk) ),
inference(resolution,[status(thm)],[f111,f239]) ).
fof(f1670,plain,
! [X0] :
( ~ aNaturalNumber0(xk)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[f1653,f173]) ).
fof(f2091,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f1670,f210]) ).
fof(f2097,plain,
( ~ aNaturalNumber0(xr)
| sdtlseqdt0(xr,xp) ),
inference(resolution,[status(thm)],[f2091,f1255]) ).
fof(f2106,plain,
sdtlseqdt0(xr,xp),
inference(forward_subsumption_resolution,[status(thm)],[f2097,f220]) ).
fof(f3073,plain,
( ~ aNaturalNumber0(xm)
| sP0_prd(xr)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1637,f232]) ).
fof(f3076,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(xm)
| sP0_prd(xr)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f3073,f109]) ).
fof(f3077,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| sP0_prd(xr)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(xr) ),
inference(duplicate_literals_removal,[status(thm)],[f3076]) ).
fof(f3078,plain,
( ~ aNaturalNumber0(xm)
| sP0_prd(xr)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3077,f220]) ).
fof(f5701,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sP0_prd(xr)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3078,f172]) ).
fof(f5702,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xr = xp
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sP0_prd(xr)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(resolution,[status(thm)],[f5701,f117]) ).
fof(f5711,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| sP0_prd(xr)
| xr = xp ),
inference(forward_subsumption_resolution,[status(thm)],[f5702,f60]) ).
fof(f5712,plain,
( sP0_prd(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = xr
| ~ aNaturalNumber0(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f5711,f84]) ).
fof(f5713,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sP0_prd(xr)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = xr
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f5712,f60]) ).
fof(f5714,plain,
( sP0_prd(xr)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = xr
| ~ aNaturalNumber0(xr) ),
inference(duplicate_literals_removal,[status(thm)],[f5713]) ).
fof(f5715,plain,
( xr = xp
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sP0_prd(xr)
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f5714,f220]) ).
fof(f5922,plain,
( sP0_prd(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xr = xp
| ~ sdtlseqdt0(xr,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f5715,f173]) ).
fof(f5923,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sP0_prd(xr)
| xr = xp
| ~ sdtlseqdt0(xr,xp) ),
inference(resolution,[status(thm)],[f5922,f60]) ).
fof(f5924,plain,
( ~ aNaturalNumber0(xm)
| xr = xp
| ~ aNaturalNumber0(xn)
| sP0_prd(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f5923,f2106]) ).
fof(f5937,plain,
( ~ aNaturalNumber0(xm)
| sP0_prd(xr)
| xp = xr ),
inference(forward_subsumption_resolution,[status(thm)],[f5924,f171]) ).
fof(f5938,plain,
( xr = xp
| sP0_prd(xr) ),
inference(resolution,[status(thm)],[f5937,f172]) ).
fof(f6068,plain,
( sP0_prd(xr)
| sdtlseqdt0(xk,xr) ),
inference(paramodulation,[status(thm)],[f5938,f239]) ).
fof(f6082,plain,
( sP0_prd(xr)
| xk != xr ),
inference(paramodulation,[status(thm)],[f5938,f236]) ).
fof(f6372,plain,
( xk = xr
| sP0_prd(xr) ),
inference(resolution,[status(thm)],[f6068,f868]) ).
fof(f6382,plain,
sP0_prd(xr),
inference(forward_subsumption_resolution,[status(thm)],[f6372,f6082]) ).
fof(f6386,plain,
~ isPrime0(xr),
inference(resolution,[status(thm)],[f6382,f254]) ).
fof(f6387,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6386,f228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM506+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 02:35:40 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 107.85/14.10 % Refutation found
% 107.85/14.10 % SZS status Theorem for theBenchmark: Theorem is valid
% 107.85/14.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 38.65/14.16 % Elapsed time: 13.777570 seconds
% 38.65/14.16 % CPU time: 108.752191 seconds
% 38.65/14.16 % Total memory used: 337.734 MB
% 38.65/14.16 % Net memory used: 313.745 MB
%------------------------------------------------------------------------------