TSTP Solution File: NUM516+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 : Tue Apr 30 20:34:59 EDT 2024
% Result : Theorem 34.43s 4.73s
% Output : CNFRefutation 34.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 30
% Syntax : Number of formulae : 118 ( 21 unt; 2 def)
% Number of atoms : 386 ( 90 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 448 ( 180 ~; 184 |; 50 &)
% ( 20 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 73 ( 72 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
| sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
=> W1 = W2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( W1 != W0
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != W1
& sdtlseqdt0(W0,W1) )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00
& doDivides0(W0,W1) )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( W1 = sz10
| W1 = W0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,conjecture,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
~ ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f60,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f63,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f64,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f67,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f87,plain,
! [W0,W1,W2] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W1) != sdtpldt0(W0,W2)
& sdtpldt0(W1,W0) != sdtpldt0(W2,W0) )
| W1 = W2 ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[status(esa)],[f87]) ).
fof(f112,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f113,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f112]) ).
fof(f116,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| sdtlseqdt0(W0,W1)
| ( W1 != W0
& sdtlseqdt0(W1,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f23]) ).
fof(f118,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f116]) ).
fof(f119,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| W0 = W1
| ~ sdtlseqdt0(W0,W1)
| ! [W2] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f24]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f119]) ).
fof(f144,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| W0 = sz00
| ~ doDivides0(W0,W1)
| ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f145,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| W0 = sz00
| ~ doDivides0(W0,W1)
| ! [W2] :
( ( W2 != sdtsldt0(W1,W0)
| ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) )
& ( W2 = sdtsldt0(W1,W0)
| ~ aNaturalNumber0(W2)
| W1 != sdtasdt0(W0,W2) ) ) ),
inference(NNF_transformation,[status(esa)],[f144]) ).
fof(f146,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| W0 = sz00
| ~ doDivides0(W0,W1)
| ( ! [W2] :
( W2 != sdtsldt0(W1,W0)
| ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) )
& ! [W2] :
( W2 = sdtsldt0(W1,W0)
| ~ aNaturalNumber0(W2)
| W1 != sdtasdt0(W0,W2) ) ) ),
inference(miniscoping,[status(esa)],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ doDivides0(X0,X1)
| X2 != sdtsldt0(X1,X0)
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f160,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0)
| W1 = sz10
| W1 = W0 ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f161,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0)
| W1 = sz10
| W1 = W0 ) ) )
& ( isPrime0(W0)
| W0 = sz00
| W0 = sz10
| ? [W1] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& W1 != sz10
& W1 != W0 ) ) ) ),
inference(NNF_transformation,[status(esa)],[f160]) ).
fof(f162,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0)
| W1 = sz10
| W1 = W0 ) ) )
& ( isPrime0(W0)
| W0 = sz00
| W0 = sz10
| ( aNaturalNumber0(sk0_2(W0))
& doDivides0(sk0_2(W0),W0)
& sk0_2(W0) != sz10
& sk0_2(W0) != W0 ) ) ) ),
inference(skolemization,[status(esa)],[f161]) ).
fof(f163,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| X0 != sz00 ),
inference(cnf_transformation,[status(esa)],[f162]) ).
fof(f175,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f176,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f177,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f194,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f196,plain,
isPrime0(xr),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f202,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f203,plain,
sdtsldt0(xn,xr) != xn,
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f204,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f206,plain,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(pre_NNF_transformation,[status(esa)],[f56]) ).
fof(f207,plain,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cnf_transformation,[status(esa)],[f206]) ).
fof(f208,plain,
( spl0_0
<=> doDivides0(xr,xn) ),
introduced(split_symbol_definition) ).
fof(f210,plain,
( ~ doDivides0(xr,xn)
| spl0_0 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f215,plain,
( spl0_2
<=> sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
introduced(split_symbol_definition) ).
fof(f216,plain,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( spl0_3
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(split_symbol_definition) ).
fof(f220,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| spl0_3 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f207,f215,f218]) ).
fof(f229,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ doDivides0(X0,X1)
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f147]) ).
fof(f232,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(destructive_equality_resolution,[status(esa)],[f163]) ).
fof(f242,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,xm) = sdtpldt0(xm,X0) ),
inference(resolution,[status(thm)],[f68,f176]) ).
fof(f248,plain,
( spl0_4
<=> aNaturalNumber0(xr) ),
introduced(split_symbol_definition) ).
fof(f250,plain,
( ~ aNaturalNumber0(xr)
| spl0_4 ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,plain,
( spl0_5
<=> aNaturalNumber0(xp) ),
introduced(split_symbol_definition) ).
fof(f253,plain,
( ~ aNaturalNumber0(xp)
| spl0_5 ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f259,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f177]) ).
fof(f260,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f261,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f250,f194]) ).
fof(f262,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f261]) ).
fof(f263,plain,
( spl0_7
<=> aNaturalNumber0(xm) ),
introduced(split_symbol_definition) ).
fof(f265,plain,
( ~ aNaturalNumber0(xm)
| spl0_7 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f271,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f176]) ).
fof(f272,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f271]) ).
fof(f273,plain,
( spl0_9
<=> aNaturalNumber0(xn) ),
introduced(split_symbol_definition) ).
fof(f275,plain,
( ~ aNaturalNumber0(xn)
| spl0_9 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f281,plain,
( $false
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f275,f175]) ).
fof(f282,plain,
spl0_9,
inference(contradiction_clause,[status(thm)],[f281]) ).
fof(f374,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(resolution,[status(thm)],[f242,f175]) ).
fof(f377,plain,
( spl0_20
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(split_symbol_definition) ).
fof(f380,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(paramodulation,[status(thm)],[f374,f64]) ).
fof(f381,plain,
( ~ spl0_7
| ~ spl0_9
| spl0_20 ),
inference(split_clause,[status(thm)],[f380,f263,f273,f377]) ).
fof(f395,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xn)
| sdtlseqdt0(xn,X0) ),
inference(resolution,[status(thm)],[f118,f175]) ).
fof(f460,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(xn,X0)
| X0 = xn ),
inference(resolution,[status(thm)],[f113,f175]) ).
fof(f767,plain,
( spl0_72
<=> aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
introduced(split_symbol_definition) ).
fof(f769,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| spl0_72 ),
inference(component_clause,[status(thm)],[f767]) ).
fof(f770,plain,
( spl0_73
<=> sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ),
introduced(split_symbol_definition) ).
fof(f771,plain,
( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ spl0_73 ),
inference(component_clause,[status(thm)],[f770]) ).
fof(f773,plain,
( spl0_74
<=> sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm)) ),
introduced(split_symbol_definition) ).
fof(f775,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
| spl0_74 ),
inference(component_clause,[status(thm)],[f773]) ).
fof(f776,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| spl0_3 ),
inference(resolution,[status(thm)],[f123,f220]) ).
fof(f777,plain,
( ~ spl0_72
| ~ spl0_20
| spl0_73
| ~ spl0_74
| ~ spl0_5
| spl0_3 ),
inference(split_clause,[status(thm)],[f776,f767,f377,f770,f773,f251,f218]) ).
fof(f838,plain,
( spl0_87
<=> aNaturalNumber0(sdtsldt0(xn,xr)) ),
introduced(split_symbol_definition) ).
fof(f840,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl0_87 ),
inference(component_clause,[status(thm)],[f838]) ).
fof(f841,plain,
( spl0_88
<=> sdtsldt0(xn,xr) = xn ),
introduced(split_symbol_definition) ).
fof(f842,plain,
( sdtsldt0(xn,xr) = xn
| ~ spl0_88 ),
inference(component_clause,[status(thm)],[f841]) ).
fof(f844,plain,
( spl0_89
<=> sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
introduced(split_symbol_definition) ).
fof(f846,plain,
( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| spl0_89 ),
inference(component_clause,[status(thm)],[f844]) ).
fof(f847,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ~ aNaturalNumber0(xm)
| spl0_74 ),
inference(resolution,[status(thm)],[f775,f123]) ).
fof(f848,plain,
( ~ spl0_87
| ~ spl0_9
| spl0_88
| ~ spl0_89
| ~ spl0_7
| spl0_74 ),
inference(split_clause,[status(thm)],[f847,f838,f273,f841,f844,f263,f773]) ).
fof(f849,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| spl0_72 ),
inference(resolution,[status(thm)],[f769,f64]) ).
fof(f850,plain,
( ~ spl0_87
| ~ spl0_7
| spl0_72 ),
inference(split_clause,[status(thm)],[f849,f838,f263,f767]) ).
fof(f853,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtsldt0(xn,xr) = xn
| ~ spl0_73 ),
inference(resolution,[status(thm)],[f771,f89]) ).
fof(f854,plain,
( ~ spl0_7
| ~ spl0_87
| ~ spl0_9
| spl0_88
| ~ spl0_73 ),
inference(split_clause,[status(thm)],[f853,f263,f838,f273,f841,f770]) ).
fof(f1111,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f216,f89]) ).
fof(f1112,plain,
( ~ spl0_5
| ~ spl0_72
| ~ spl0_20
| spl0_73
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f1111,f251,f767,f377,f770,f215]) ).
fof(f2016,plain,
( spl0_199
<=> xr = sz00 ),
introduced(split_symbol_definition) ).
fof(f2017,plain,
( xr = sz00
| ~ spl0_199 ),
inference(component_clause,[status(thm)],[f2016]) ).
fof(f2034,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| xr = sz00
| ~ doDivides0(xr,xn)
| spl0_87 ),
inference(resolution,[status(thm)],[f840,f229]) ).
fof(f2035,plain,
( ~ spl0_4
| ~ spl0_9
| spl0_199
| ~ spl0_0
| spl0_87 ),
inference(split_clause,[status(thm)],[f2034,f248,f273,f2016,f208,f838]) ).
fof(f2140,plain,
( spl0_216
<=> sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
introduced(split_symbol_definition) ).
fof(f2143,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtlseqdt0(xn,sdtsldt0(xn,xr))
| spl0_89 ),
inference(resolution,[status(thm)],[f846,f395]) ).
fof(f2144,plain,
( ~ spl0_87
| spl0_216
| spl0_89 ),
inference(split_clause,[status(thm)],[f2143,f838,f2140,f844]) ).
fof(f6426,plain,
~ isPrime0(sz00),
inference(forward_subsumption_resolution,[status(thm)],[f232,f60]) ).
fof(f7960,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f202,f210]) ).
fof(f7961,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f7960]) ).
fof(f8604,plain,
( isPrime0(sz00)
| ~ spl0_199 ),
inference(forward_demodulation,[status(thm)],[f2017,f196]) ).
fof(f8605,plain,
( $false
| ~ spl0_199 ),
inference(forward_subsumption_resolution,[status(thm)],[f8604,f6426]) ).
fof(f8606,plain,
~ spl0_199,
inference(contradiction_clause,[status(thm)],[f8605]) ).
fof(f16423,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| sdtsldt0(xn,xr) = xn ),
inference(resolution,[status(thm)],[f460,f204]) ).
fof(f16424,plain,
( ~ spl0_87
| ~ spl0_216
| spl0_88 ),
inference(split_clause,[status(thm)],[f16423,f838,f2140,f841]) ).
fof(f16495,plain,
( $false
| ~ spl0_88 ),
inference(forward_subsumption_resolution,[status(thm)],[f842,f203]) ).
fof(f16496,plain,
~ spl0_88,
inference(contradiction_clause,[status(thm)],[f16495]) ).
fof(f16497,plain,
$false,
inference(sat_refutation,[status(thm)],[f221,f260,f262,f272,f282,f381,f777,f848,f850,f854,f1112,f2035,f2144,f7961,f8606,f16424,f16496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33 % Computer : n005.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Mon Apr 29 20:52:11 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.10/0.34 % Drodi V3.6.0
% 34.43/4.73 % Refutation found
% 34.43/4.73 % SZS status Theorem for theBenchmark: Theorem is valid
% 34.43/4.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 34.97/4.79 % Elapsed time: 4.442597 seconds
% 34.97/4.79 % CPU time: 35.012001 seconds
% 34.97/4.79 % Total memory used: 217.033 MB
% 34.97/4.79 % Net memory used: 206.862 MB
%------------------------------------------------------------------------------