TSTP Solution File: NUM512+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM512+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 11:31:03 EDT 2023
% Result : Theorem 9.42s 2.20s
% Output : CNFRefutation 9.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 132 ( 48 unt; 0 def)
% Number of atoms : 425 ( 173 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 508 ( 215 ~; 216 |; 60 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn; 81 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f36,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtlseqdt0(xr,xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(f52,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(f54,conjecture,
( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
& sdtasdt0(xn,xm) = sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f55,negated_conjecture,
~ ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
& sdtasdt0(xn,xm) = sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) ),
inference(negated_conjecture,[],[f54]) ).
fof(f60,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f61,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f60]) ).
fof(f67,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f68,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f70,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f69]) ).
fof(f106,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f107,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f106]) ).
fof(f116,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f117,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f116]) ).
fof(f118,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f119,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f118]) ).
fof(f125,plain,
( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
| sdtasdt0(xn,xm) != sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) ),
inference(ennf_transformation,[],[f55]) ).
fof(f136,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f107]) ).
fof(f137,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f136]) ).
fof(f138,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f139,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f139]) ).
fof(f141,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK2(X0) != X0
& sz10 != sK2(X0)
& doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f142,plain,
! [X0] :
( ( ( isPrime0(X0)
| ( sK2(X0) != X0
& sz10 != sK2(X0)
& doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0)) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f140,f141]) ).
fof(f145,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f149,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f154,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f155,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f195,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f196,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f202,plain,
! [X2,X0,X1] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f203,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f213,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f214,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f215,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f217,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f218,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f225,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f230,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f231,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f48]) ).
fof(f232,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f234,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f49]) ).
fof(f238,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f52]) ).
fof(f241,plain,
( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
| sdtasdt0(xn,xm) != sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) ),
inference(cnf_transformation,[],[f125]) ).
fof(f250,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f196]) ).
fof(f251,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f195]) ).
fof(f253,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f203]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f145]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_58,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_59,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_99,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| X0 = sz00 ),
inference(cnf_transformation,[],[f250]) ).
cnf(c_100,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(cnf_transformation,[],[f251]) ).
cnf(c_105,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| X0 = sz00 ),
inference(cnf_transformation,[],[f202]) ).
cnf(c_112,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(cnf_transformation,[],[f253]) ).
cnf(c_116,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f215]) ).
cnf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f214]) ).
cnf(c_118,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f213]) ).
cnf(c_120,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f218]) ).
cnf(c_121,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f217]) ).
cnf(c_128,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnf_transformation,[],[f225]) ).
cnf(c_133,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f232]) ).
cnf(c_134,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f231]) ).
cnf(c_135,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f230]) ).
cnf(c_136,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f234]) ).
cnf(c_141,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f238]) ).
cnf(c_144,negated_conjecture,
( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm)
| sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) != sdtasdt0(xn,xm) ),
inference(cnf_transformation,[],[f241]) ).
cnf(c_190,plain,
~ isPrime0(sz00),
inference(global_subsumption_just,[status(thm)],[c_112,c_49,c_112]) ).
cnf(c_1693,plain,
sz00 != xp,
inference(resolution_lifted,[status(thm)],[c_190,c_121]) ).
cnf(c_1697,plain,
sz00 != xr,
inference(resolution_lifted,[status(thm)],[c_190,c_133]) ).
cnf(c_4896,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xn) = sdtasdt0(xn,X0) ),
inference(superposition,[status(thm)],[c_118,c_58]) ).
cnf(c_4897,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xr) = sdtasdt0(xr,X0) ),
inference(superposition,[status(thm)],[c_135,c_58]) ).
cnf(c_4933,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sz00 = xp
| aNaturalNumber0(xk) ),
inference(superposition,[status(thm)],[c_128,c_100]) ).
cnf(c_4935,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sdtsldt0(X1,X0),X2) = sdtasdt0(X2,sdtsldt0(X1,X0))
| X0 = sz00 ),
inference(superposition,[status(thm)],[c_100,c_58]) ).
cnf(c_4957,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(sdtasdt0(X2,sdtsldt0(X1,X0)),X3) = sdtasdt0(X2,sdtasdt0(sdtsldt0(X1,X0),X3))
| X0 = sz00 ),
inference(superposition,[status(thm)],[c_100,c_59]) ).
cnf(c_4977,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm)
| sz00 = xp ),
inference(superposition,[status(thm)],[c_120,c_99]) ).
cnf(c_4979,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm)
| sz00 = xr ),
inference(superposition,[status(thm)],[c_136,c_99]) ).
cnf(c_4980,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sdtasdt0(xr,sdtsldt0(xn,xr)) = xn
| sz00 = xr ),
inference(superposition,[status(thm)],[c_141,c_99]) ).
cnf(c_5052,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr)
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr)
| sz00 = xr ),
inference(superposition,[status(thm)],[c_134,c_105]) ).
cnf(c_5255,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtsldt0(X1,X0),xr) = sdtasdt0(xr,sdtsldt0(X1,X0))
| X0 = sz00 ),
inference(superposition,[status(thm)],[c_100,c_4897]) ).
cnf(c_5268,plain,
sdtasdt0(xm,xn) = sdtasdt0(xn,xm),
inference(superposition,[status(thm)],[c_117,c_4896]) ).
cnf(c_5271,plain,
( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xm,xn)
| sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) != sdtasdt0(xm,xn) ),
inference(demodulation,[status(thm)],[c_144,c_5268]) ).
cnf(c_5272,plain,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(demodulation,[status(thm)],[c_128,c_5268]) ).
cnf(c_5274,plain,
doDivides0(xr,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm)],[c_136,c_5268]) ).
cnf(c_5526,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| aNaturalNumber0(xk) ),
inference(global_subsumption_just,[status(thm)],[c_4933,c_116,c_120,c_1693,c_4933]) ).
cnf(c_5532,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(xk) ),
inference(superposition,[status(thm)],[c_53,c_5526]) ).
cnf(c_5581,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sdtasdt0(sdtsldt0(xn,xr),X0) = sdtasdt0(X0,sdtsldt0(xn,xr))
| sz00 = xr ),
inference(superposition,[status(thm)],[c_141,c_4935]) ).
cnf(c_5748,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sdtasdt0(sdtasdt0(X0,sdtsldt0(xn,xr)),X1) = sdtasdt0(X0,sdtasdt0(sdtsldt0(xn,xr),X1))
| sz00 = xr ),
inference(superposition,[status(thm)],[c_141,c_4957]) ).
cnf(c_5751,plain,
sdtasdt0(xr,sdtsldt0(xn,xr)) = xn,
inference(global_subsumption_just,[status(thm)],[c_4980,c_135,c_118,c_1697,c_4980]) ).
cnf(c_5813,plain,
( sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_4979,c_135,c_1697,c_4979]) ).
cnf(c_5814,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm) ),
inference(renaming,[status(thm)],[c_5813]) ).
cnf(c_5819,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm) ),
inference(superposition,[status(thm)],[c_53,c_5814]) ).
cnf(c_5820,plain,
( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_4977,c_116,c_1693,c_4977]) ).
cnf(c_5821,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm) ),
inference(renaming,[status(thm)],[c_5820]) ).
cnf(c_5826,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm) ),
inference(superposition,[status(thm)],[c_53,c_5821]) ).
cnf(c_5851,plain,
( sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_5052,c_135,c_118,c_117,c_1697,c_5052,c_5532]) ).
cnf(c_5852,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr) ),
inference(renaming,[status(thm)],[c_5851]) ).
cnf(c_5860,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(xp,xk),xr),
inference(superposition,[status(thm)],[c_116,c_5852]) ).
cnf(c_6633,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xr)
| sdtasdt0(sdtsldt0(sdtasdt0(xm,xn),xr),xr) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xm,xn),xr))
| sz00 = xr ),
inference(superposition,[status(thm)],[c_5274,c_5255]) ).
cnf(c_6695,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_5268,c_53]) ).
cnf(c_7825,plain,
( sdtasdt0(sdtsldt0(xn,xr),X0) = sdtasdt0(X0,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_5581,c_135,c_118,c_1697,c_5581]) ).
cnf(c_7826,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtsldt0(xn,xr),X0) = sdtasdt0(X0,sdtsldt0(xn,xr)) ),
inference(renaming,[status(thm)],[c_7825]) ).
cnf(c_7835,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xm,sdtsldt0(xn,xr)),
inference(superposition,[status(thm)],[c_117,c_7826]) ).
cnf(c_7837,plain,
sdtasdt0(sdtsldt0(xn,xr),xr) = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(superposition,[status(thm)],[c_135,c_7826]) ).
cnf(c_7839,plain,
( sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) != sdtasdt0(xm,xn)
| sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) != sdtasdt0(xm,xn) ),
inference(demodulation,[status(thm)],[c_5271,c_7835]) ).
cnf(c_8612,plain,
( sdtasdt0(sdtasdt0(X0,sdtsldt0(xn,xr)),X1) = sdtasdt0(X0,sdtasdt0(sdtsldt0(xn,xr),X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_5748,c_135,c_118,c_1697,c_5748]) ).
cnf(c_8613,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X0,sdtsldt0(xn,xr)),X1) = sdtasdt0(X0,sdtasdt0(sdtsldt0(xn,xr),X1)) ),
inference(renaming,[status(thm)],[c_8612]) ).
cnf(c_8626,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,sdtsldt0(xn,xr)),xr) = sdtasdt0(X0,sdtasdt0(sdtsldt0(xn,xr),xr)) ),
inference(superposition,[status(thm)],[c_135,c_8613]) ).
cnf(c_8891,plain,
sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm),
inference(global_subsumption_just,[status(thm)],[c_5819,c_118,c_117,c_5819]) ).
cnf(c_8893,plain,
sdtasdt0(xr,sdtsldt0(sdtasdt0(xm,xn),xr)) = sdtasdt0(xm,xn),
inference(light_normalisation,[status(thm)],[c_8891,c_5268]) ).
cnf(c_8926,plain,
sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm),
inference(global_subsumption_just,[status(thm)],[c_5826,c_118,c_117,c_5826]) ).
cnf(c_8928,plain,
sdtasdt0(xp,xk) = sdtasdt0(xm,xn),
inference(light_normalisation,[status(thm)],[c_8926,c_5268,c_5272]) ).
cnf(c_11958,plain,
sdtasdt0(sdtsldt0(sdtasdt0(xm,xn),xr),xr) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xm,xn),xr)),
inference(global_subsumption_just,[status(thm)],[c_6633,c_135,c_118,c_117,c_1697,c_6633,c_6695]) ).
cnf(c_11960,plain,
sdtasdt0(sdtasdt0(xp,sdtsldt0(xk,xr)),xr) = sdtasdt0(xp,xk),
inference(light_normalisation,[status(thm)],[c_11958,c_5860,c_8893,c_8928]) ).
cnf(c_19265,plain,
sdtasdt0(sdtsldt0(xn,xr),xr) = xn,
inference(light_normalisation,[status(thm)],[c_7837,c_5751]) ).
cnf(c_19592,plain,
( sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) != sdtasdt0(xp,xk)
| sdtasdt0(xp,xk) != sdtasdt0(xp,xk) ),
inference(light_normalisation,[status(thm)],[c_7839,c_5860,c_8928,c_11960]) ).
cnf(c_19593,plain,
sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) != sdtasdt0(xp,xk),
inference(equality_resolution_simp,[status(thm)],[c_19592]) ).
cnf(c_27429,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,sdtsldt0(xn,xr)),xr) = sdtasdt0(X0,xn) ),
inference(light_normalisation,[status(thm)],[c_8626,c_19265]) ).
cnf(c_27437,plain,
sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) = sdtasdt0(xm,xn),
inference(superposition,[status(thm)],[c_117,c_27429]) ).
cnf(c_27447,plain,
sdtasdt0(xp,xk) != sdtasdt0(xm,xn),
inference(demodulation,[status(thm)],[c_19593,c_27437]) ).
cnf(c_27448,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_8928,c_27447]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM512+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 14:53:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.42/2.20 % SZS status Started for theBenchmark.p
% 9.42/2.20 % SZS status Theorem for theBenchmark.p
% 9.42/2.20
% 9.42/2.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 9.42/2.20
% 9.42/2.20 ------ iProver source info
% 9.42/2.20
% 9.42/2.20 git: date: 2023-05-31 18:12:56 +0000
% 9.42/2.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 9.42/2.20 git: non_committed_changes: false
% 9.42/2.20 git: last_make_outside_of_git: false
% 9.42/2.20
% 9.42/2.20 ------ Parsing...
% 9.42/2.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 9.42/2.20
% 9.42/2.20 ------ 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
% 9.42/2.20
% 9.42/2.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 9.42/2.20
% 9.42/2.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.42/2.20 ------ Proving...
% 9.42/2.20 ------ Problem Properties
% 9.42/2.20
% 9.42/2.20
% 9.42/2.20 clauses 88
% 9.42/2.20 conjectures 1
% 9.42/2.20 EPR 33
% 9.42/2.20 Horn 63
% 9.42/2.20 unary 29
% 9.42/2.20 binary 8
% 9.42/2.20 lits 284
% 9.42/2.20 lits eq 80
% 9.42/2.20 fd_pure 0
% 9.42/2.20 fd_pseudo 0
% 9.42/2.20 fd_cond 15
% 9.42/2.20 fd_pseudo_cond 11
% 9.42/2.20 AC symbols 0
% 9.42/2.20
% 9.42/2.20 ------ Input Options Time Limit: Unbounded
% 9.42/2.20
% 9.42/2.20
% 9.42/2.20 ------
% 9.42/2.20 Current options:
% 9.42/2.20 ------
% 9.42/2.20
% 9.42/2.20
% 9.42/2.20
% 9.42/2.20
% 9.42/2.20 ------ Proving...
% 9.42/2.20
% 9.42/2.20
% 9.42/2.20 % SZS status Theorem for theBenchmark.p
% 9.42/2.20
% 9.42/2.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.42/2.20
% 9.42/2.21
%------------------------------------------------------------------------------