TSTP Solution File: NUM507+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM507+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 11:31:01 EDT 2023
% Result : Theorem 16.81s 3.20s
% Output : CNFRefutation 16.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 21
% Syntax : Number of formulae : 136 ( 33 unt; 0 def)
% Number of atoms : 535 ( 171 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 687 ( 288 ~; 295 |; 81 &)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 153 ( 0 sgn; 107 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
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/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtlseqdt0(xr,xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(f50,axiom,
( sdtlseqdt0(xk,xp)
& xp != xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2377) ).
fof(f51,conjecture,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xr) ),
inference(negated_conjecture,[],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f56,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f58,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f57]) ).
fof(f72,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f73,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f72]) ).
fof(f85,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f86,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f88,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f90,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f92,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f91]) ).
fof(f103,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(f104,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,[],[f103]) ).
fof(f115,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(f116,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f115]) ).
fof(f122,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) ),
inference(ennf_transformation,[],[f52]) ).
fof(f133,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,[],[f104]) ).
fof(f134,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,[],[f133]) ).
fof(f135,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,[],[f116]) ).
fof(f136,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,[],[f135]) ).
fof(f137,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,[],[f136]) ).
fof(f138,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(f139,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])],[f137,f138]) ).
fof(f142,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f145,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f146,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f159,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f173,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f174,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f176,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f178,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f180,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f192,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f200,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f210,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f211,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f212,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f214,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f215,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f222,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f227,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f230,plain,
sdtlseqdt0(xr,xk),
inference(cnf_transformation,[],[f49]) ).
fof(f232,plain,
xp != xk,
inference(cnf_transformation,[],[f50]) ).
fof(f233,plain,
sdtlseqdt0(xk,xp),
inference(cnf_transformation,[],[f50]) ).
fof(f234,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) ),
inference(cnf_transformation,[],[f122]) ).
fof(f244,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f192]) ).
fof(f246,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f200]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f142]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f145]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_67,plain,
( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_81,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_82,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f176]) ).
cnf(c_84,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f180]) ).
cnf(c_86,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1)) ),
inference(cnf_transformation,[],[f178]) ).
cnf(c_100,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(cnf_transformation,[],[f244]) ).
cnf(c_112,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(cnf_transformation,[],[f246]) ).
cnf(c_116,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f212]) ).
cnf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f211]) ).
cnf(c_118,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f210]) ).
cnf(c_120,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f215]) ).
cnf(c_121,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f214]) ).
cnf(c_128,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnf_transformation,[],[f222]) ).
cnf(c_135,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f227]) ).
cnf(c_137,plain,
sdtlseqdt0(xr,xk),
inference(cnf_transformation,[],[f230]) ).
cnf(c_138,plain,
sdtlseqdt0(xk,xp),
inference(cnf_transformation,[],[f233]) ).
cnf(c_139,plain,
xp != xk,
inference(cnf_transformation,[],[f232]) ).
cnf(c_140,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) ),
inference(cnf_transformation,[],[f234]) ).
cnf(c_184,plain,
~ isPrime0(sz00),
inference(global_subsumption_just,[status(thm)],[c_112,c_49,c_112]) ).
cnf(c_1173,plain,
sz00 != xp,
inference(resolution_lifted,[status(thm)],[c_184,c_121]) ).
cnf(c_2533,plain,
X0 = X0,
theory(equality) ).
cnf(c_2535,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_2537,plain,
( X0 != X1
| X2 != X3
| sdtpldt0(X0,X2) = sdtpldt0(X1,X3) ),
theory(equality) ).
cnf(c_3815,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xr)
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_3850,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_3993,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_5613,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_5621,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(superposition,[status(thm)],[c_82,c_140]) ).
cnf(c_6948,plain,
( X0 != X1
| X1 = X0 ),
inference(resolution,[status(thm)],[c_2535,c_2533]) ).
cnf(c_7896,plain,
( sdtpldt0(xn,xm) != sdtpldt0(xn,xm)
| xp != xr
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) ),
inference(instantiation,[status(thm)],[c_2537]) ).
cnf(c_8941,plain,
sdtpldt0(xn,xm) = sdtpldt0(xn,xm),
inference(instantiation,[status(thm)],[c_2533]) ).
cnf(c_9521,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(superposition,[status(thm)],[c_82,c_140]) ).
cnf(c_9556,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(global_subsumption_just,[status(thm)],[c_9521,c_135,c_118,c_117,c_116,c_3815,c_3850,c_3993,c_5621]) ).
cnf(c_12349,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xp = xk ),
inference(superposition,[status(thm)],[c_138,c_80]) ).
cnf(c_13154,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_16149,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),X0) ),
inference(superposition,[status(thm)],[c_9556,c_81]) ).
cnf(c_19929,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(superposition,[status(thm)],[c_82,c_140]) ).
cnf(c_19964,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(global_subsumption_just,[status(thm)],[c_19929,c_135,c_118,c_117,c_116,c_3815,c_3850,c_3993,c_5621]) ).
cnf(c_20507,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),X0) ),
inference(superposition,[status(thm)],[c_19964,c_81]) ).
cnf(c_20572,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),X0) ),
inference(global_subsumption_just,[status(thm)],[c_20507,c_135,c_118,c_117,c_116,c_3815,c_3850,c_3993,c_16149]) ).
cnf(c_22241,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| xp = xr ),
inference(resolution,[status(thm)],[c_67,c_140]) ).
cnf(c_23059,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| xp = xr ),
inference(global_subsumption_just,[status(thm)],[c_22241,c_135,c_118,c_117,c_116,c_3850,c_22241]) ).
cnf(c_23234,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| xp = xr
| xr = xp ),
inference(resolution,[status(thm)],[c_86,c_23059]) ).
cnf(c_24299,plain,
( ~ sdtlseqdt0(xr,xp)
| xp = xr
| xr = xp ),
inference(global_subsumption_just,[status(thm)],[c_23234,c_135,c_118,c_117,c_116,c_3850,c_23234]) ).
cnf(c_24304,plain,
( ~ sdtlseqdt0(xr,xp)
| xr = xp ),
inference(forward_subsumption_resolution,[status(thm)],[c_24299,c_6948]) ).
cnf(c_29113,plain,
( ~ sdtlseqdt0(sdtpldt0(xn,xm),X0)
| ~ aNaturalNumber0(sdtpldt0(X0,xr))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| sdtpldt0(xn,xm) = X0
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(X0,xr)) ),
inference(superposition,[status(thm)],[c_84,c_20572]) ).
cnf(c_30958,plain,
( ~ sdtlseqdt0(xr,xp)
| xp = xr ),
inference(resolution,[status(thm)],[c_6948,c_24304]) ).
cnf(c_31568,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| xp = xr ),
inference(superposition,[status(thm)],[c_86,c_140]) ).
cnf(c_35555,plain,
( ~ sdtlseqdt0(xr,xp)
| xp = xr ),
inference(global_subsumption_just,[status(thm)],[c_31568,c_30958]) ).
cnf(c_35557,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| xp = xr
| sdtlseqdt0(xp,xr) ),
inference(superposition,[status(thm)],[c_82,c_35555]) ).
cnf(c_35559,plain,
( xp = xr
| sdtlseqdt0(xp,xr) ),
inference(global_subsumption_just,[status(thm)],[c_35557,c_135,c_116,c_35557]) ).
cnf(c_35561,plain,
( ~ sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| xp = xr
| sdtlseqdt0(xp,X0) ),
inference(superposition,[status(thm)],[c_35559,c_81]) ).
cnf(c_36695,plain,
( ~ sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(X0)
| xp = xr
| sdtlseqdt0(xp,X0) ),
inference(global_subsumption_just,[status(thm)],[c_35561,c_135,c_116,c_35561]) ).
cnf(c_36703,plain,
( ~ aNaturalNumber0(xk)
| xp = xr
| sdtlseqdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_137,c_36695]) ).
cnf(c_37382,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr),
inference(global_subsumption_just,[status(thm)],[c_29113,c_118,c_117,c_116,c_139,c_120,c_1173,c_5613,c_7896,c_8941,c_12349,c_13154,c_36703]) ).
cnf(c_37397,plain,
( sdtpldt0(sdtpldt0(xn,xm),X0) != sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| X0 = xr ),
inference(superposition,[status(thm)],[c_37382,c_67]) ).
cnf(c_42883,negated_conjecture,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr),
inference(global_subsumption_just,[status(thm)],[c_140,c_118,c_117,c_116,c_139,c_120,c_1173,c_5613,c_7896,c_8941,c_12349,c_13154,c_36703]) ).
cnf(c_43908,plain,
( sdtpldt0(sdtpldt0(xn,xm),X0) != sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| X0 = xr ),
inference(superposition,[status(thm)],[c_42883,c_67]) ).
cnf(c_44013,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),X0) != sdtpldt0(sdtpldt0(xn,xm),xp)
| X0 = xr ),
inference(global_subsumption_just,[status(thm)],[c_43908,c_135,c_118,c_117,c_3850,c_37397]) ).
cnf(c_44014,plain,
( sdtpldt0(sdtpldt0(xn,xm),X0) != sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(X0)
| X0 = xr ),
inference(renaming,[status(thm)],[c_44013]) ).
cnf(c_44019,plain,
( ~ aNaturalNumber0(xp)
| xp = xr ),
inference(equality_resolution,[status(thm)],[c_44014]) ).
cnf(c_44020,plain,
xp = xr,
inference(global_subsumption_just,[status(thm)],[c_44019,c_118,c_117,c_116,c_139,c_120,c_1173,c_5613,c_12349,c_13154,c_36703]) ).
cnf(c_44034,plain,
sdtlseqdt0(xp,xk),
inference(superposition,[status(thm)],[c_44020,c_137]) ).
cnf(c_44038,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_44034,c_13154,c_12349,c_5613,c_1173,c_120,c_139,c_116,c_117,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM507+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 10:27:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.81/3.20 % SZS status Started for theBenchmark.p
% 16.81/3.20 % SZS status Theorem for theBenchmark.p
% 16.81/3.20
% 16.81/3.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 16.81/3.20
% 16.81/3.20 ------ iProver source info
% 16.81/3.20
% 16.81/3.20 git: date: 2023-05-31 18:12:56 +0000
% 16.81/3.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 16.81/3.20 git: non_committed_changes: false
% 16.81/3.20 git: last_make_outside_of_git: false
% 16.81/3.20
% 16.81/3.20 ------ Parsing...
% 16.81/3.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 16.81/3.20
% 16.81/3.20 ------ 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
% 16.81/3.20
% 16.81/3.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 16.81/3.20
% 16.81/3.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.81/3.20 ------ Proving...
% 16.81/3.20 ------ Problem Properties
% 16.81/3.20
% 16.81/3.20
% 16.81/3.20 clauses 85
% 16.81/3.20 conjectures 1
% 16.81/3.20 EPR 32
% 16.81/3.20 Horn 60
% 16.81/3.20 unary 26
% 16.81/3.20 binary 8
% 16.81/3.20 lits 281
% 16.81/3.20 lits eq 78
% 16.81/3.20 fd_pure 0
% 16.81/3.20 fd_pseudo 0
% 16.81/3.20 fd_cond 15
% 16.81/3.20 fd_pseudo_cond 11
% 16.81/3.20 AC symbols 0
% 16.81/3.20
% 16.81/3.20 ------ Input Options Time Limit: Unbounded
% 16.81/3.20
% 16.81/3.20
% 16.81/3.20 ------
% 16.81/3.20 Current options:
% 16.81/3.20 ------
% 16.81/3.20
% 16.81/3.20
% 16.81/3.20
% 16.81/3.20
% 16.81/3.20 ------ Proving...
% 16.81/3.20
% 16.81/3.20
% 16.81/3.20 % SZS status Theorem for theBenchmark.p
% 16.81/3.20
% 16.81/3.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.81/3.20
% 16.81/3.20
%------------------------------------------------------------------------------