%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM507+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 : Fri Sep 25 02:25:22 PM UTC 2026
% Result : Theorem 21.47s 3.81s
% Output : CNFRefutation 21.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 20
% Syntax : Number of formulae : 133 ( 33 unt; 0 def)
% Number of atoms : 515 ( 165 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 658 ( 276 ~; 285 |; 75 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 145 ( 0 sgn 142 !; 3 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/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(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X1 = X0
| X1 = sz10 ) )
& X0 != sz10
& X0 != sz00 ) ) ),
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(f50,axiom,
( sdtlseqdt0(xk,xp)
& xk != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2377) ).
fof(f51,conjecture,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f58,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f57]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(ennf_transformation,[],[f14]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(flattening,[],[f72]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f90,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ! [X2] :
( ~ aNaturalNumber0(X2)
| ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ! [X2] :
( ~ aNaturalNumber0(X2)
| ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ),
inference(flattening,[],[f91]) ).
fof(f103,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f104,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f103]) ).
fof(f115,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f116,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
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(f131,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f104]) ).
fof(f132,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(nnf_transformation,[],[f116]) ).
fof(f134,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(rectify,[],[f134]) ).
fof(f136,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ( doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0))
& sK2(X0) != X0
& sz10 != sK2(X0) )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f135]) ).
fof(f138,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f141,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f142,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f73]) ).
fof(f169,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f86]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f171,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f132]) ).
fof(f198,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz00 != X0 ),
inference(cnf_transformation,[],[f136]) ).
fof(f206,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f207,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f208,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f210,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f211,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f218,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f225,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f227,plain,
sdtlseqdt0(xr,xk),
inference(cnf_transformation,[],[f49]) ).
fof(f228,plain,
sdtlseqdt0(xk,xp),
inference(cnf_transformation,[],[f50]) ).
fof(f229,plain,
xp != xk,
inference(cnf_transformation,[],[f50]) ).
fof(f230,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(f239,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f189]) ).
fof(f241,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f198]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f138]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2) ) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_110,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f208]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f207]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f206]) ).
tcf(c_120,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f211]) ).
tcf(c_121,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f210]) ).
tcf(c_128,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnf_transformation,[],[f218]) ).
tcf(c_133,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f225]) ).
tcf(c_136,plain,
sdtlseqdt0(xr,xk),
inference(cnf_transformation,[],[f227]) ).
tcf(c_138,plain,
xp != xk,
inference(cnf_transformation,[],[f229]) ).
tcf(c_139,plain,
sdtlseqdt0(xk,xp),
inference(cnf_transformation,[],[f228]) ).
tcf(c_140,negated_conjecture,
( ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_186,plain,
~ isPrime0(sz00),
inference(global_subsumption_just,[status(thm)],[c_110,c_49,c_110]) ).
tcf(c_1087,plain,
sz00 != xp,
inference(resolution_lifted,[status(thm)],[c_186,c_120]) ).
tcf(c_2533,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2535,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(X0,X2) = sdtpldt0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3815,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_3850,plain,
( aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_3993,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_5601,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr))
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(superposition,[status(thm)],[c_83,c_140]) ).
tcf(c_5830,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_6969,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_2535,c_2533]) ).
tcf(c_8933,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr))
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(superposition,[status(thm)],[c_83,c_140]) ).
tcf(c_8968,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr))
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) ) ),
inference(global_subsumption_just,[status(thm)],[c_8933,c_133,c_118,c_117,c_116,c_3815,c_3850,c_3993,c_5601]) ).
tcf(c_10322,plain,
( ( xp = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xk) ),
inference(superposition,[status(thm)],[c_139,c_80]) ).
tcf(c_10946,plain,
( aNaturalNumber0(xk)
| ( sz00 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_128,c_99]) ).
tcf(c_12860,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),X0)
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0) ),
inference(superposition,[status(thm)],[c_8968,c_81]) ).
tcf(c_15328,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr))
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(superposition,[status(thm)],[c_83,c_140]) ).
tcf(c_15363,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr))
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) ) ),
inference(global_subsumption_just,[status(thm)],[c_15328,c_133,c_118,c_117,c_116,c_3815,c_3850,c_3993,c_5601]) ).
tcf(c_15909,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),X0)
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0) ),
inference(superposition,[status(thm)],[c_15363,c_81]) ).
tcf(c_15974,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),X0)
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0) ),
inference(global_subsumption_just,[status(thm)],[c_15909,c_133,c_118,c_117,c_116,c_3815,c_3850,c_3993,c_12860]) ).
tcf(c_16901,plain,
( ( xp = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolution,[status(thm)],[c_66,c_140]) ).
tcf(c_16904,plain,
( ( xp = xr )
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(global_subsumption_just,[status(thm)],[c_16901,c_133,c_118,c_117,c_116,c_3850,c_16901]) ).
tcf(c_17212,plain,
( ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ( xp != xr )
| ( sdtpldt0(xn,xm) != sdtpldt0(xn,xm) ) ),
inference(instantiation,[status(thm)],[c_2537]) ).
tcf(c_18021,plain,
( ( xr = xp )
| ( xp = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[c_85,c_16904]) ).
tcf(c_18487,plain,
( ( xr = xp )
| ( xp = xr )
| ~ sdtlseqdt0(xr,xp) ),
inference(global_subsumption_just,[status(thm)],[c_18021,c_133,c_118,c_117,c_116,c_3850,c_18021]) ).
tcf(c_18492,plain,
( ( xr = xp )
| ~ sdtlseqdt0(xr,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18487,c_6969]) ).
tcf(c_21695,plain,
sdtpldt0(xn,xm) = sdtpldt0(xn,xm),
inference(instantiation,[status(thm)],[c_2533]) ).
tcf(c_22431,plain,
( ( xp = xr )
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_85,c_140]) ).
tcf(c_22432,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),X0))
| ( X0 = xr )
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xr,X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),X0)) ),
inference(superposition,[status(thm)],[c_85,c_15974]) ).
tcf(c_23829,plain,
( ( xp = xr )
| ~ sdtlseqdt0(xr,xp) ),
inference(resolution,[status(thm)],[c_6969,c_18492]) ).
tcf(c_27489,plain,
( ( xp = xr )
| ~ sdtlseqdt0(xr,xp) ),
inference(global_subsumption_just,[status(thm)],[c_22431,c_23829]) ).
tcf(c_27491,plain,
( sdtlseqdt0(xp,xr)
| ( xp = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_83,c_27489]) ).
tcf(c_27503,plain,
( sdtlseqdt0(xp,xr)
| ( xp = xr ) ),
inference(global_subsumption_just,[status(thm)],[c_27491,c_133,c_118,c_27491]) ).
tcf(c_27505,plain,
! [X0: $i] :
( sdtlseqdt0(xp,X0)
| ( xp = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xr,X0) ),
inference(superposition,[status(thm)],[c_27503,c_81]) ).
tcf(c_28491,plain,
! [X0: $i] :
( sdtlseqdt0(xp,X0)
| ( xp = xr )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xr,X0) ),
inference(global_subsumption_just,[status(thm)],[c_27505,c_133,c_118,c_27505]) ).
tcf(c_28499,plain,
( sdtlseqdt0(xp,xk)
| ( xp = xr )
| ~ aNaturalNumber0(xk) ),
inference(superposition,[status(thm)],[c_136,c_28491]) ).
tcf(c_28626,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr),
inference(global_subsumption_just,[status(thm)],[c_22432,c_118,c_117,c_116,c_138,c_121,c_1087,c_5830,c_10322,c_10946,c_17212,c_21695,c_28499]) ).
tcf(c_28638,plain,
! [X0: $i] :
( ( X0 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ( sdtpldt0(sdtpldt0(xn,xm),X0) != sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(superposition,[status(thm)],[c_28626,c_66]) ).
tcf(c_33998,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_138,c_121,c_1087,c_5830,c_10322,c_10946,c_17212,c_21695,c_28499]) ).
tcf(c_34968,plain,
! [X0: $i] :
( ( X0 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ( sdtpldt0(sdtpldt0(xn,xm),X0) != sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(superposition,[status(thm)],[c_33998,c_66]) ).
tcf(c_35127,plain,
! [X0: $i] :
( ( X0 = xr )
| ( sdtpldt0(sdtpldt0(xn,xm),X0) != sdtpldt0(sdtpldt0(xn,xm),xp) )
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_34968,c_133,c_117,c_116,c_3850,c_28638]) ).
tcf(c_35128,plain,
! [X0: $i] :
( ( X0 = xr )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtpldt0(xn,xm),X0) != sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(renaming,[status(thm)],[c_35127]) ).
tcf(c_35133,plain,
( ( xp = xr )
| ~ aNaturalNumber0(xp) ),
inference(equality_resolution,[status(thm)],[c_35128]) ).
tcf(c_35139,plain,
xp = xr,
inference(global_subsumption_just,[status(thm)],[c_35133,c_118,c_117,c_116,c_138,c_121,c_1087,c_5830,c_10322,c_10946,c_28499]) ).
tcf(c_35153,plain,
sdtlseqdt0(xp,xk),
inference(superposition,[status(thm)],[c_35139,c_136]) ).
tcf(c_35157,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_35153,c_10946,c_10322,c_5830,c_1087,c_121,c_138,c_116,c_117,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM507+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n002.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 04:23:34 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.44 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.45
% 0.12/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.45
% 0.12/0.45 % Detected problem language: tptp
% 0.19/0.46 % Proving...
% 21.47/3.81 % SZS status Started for theBenchmark.p
% 21.47/3.81 % SZS status Theorem for theBenchmark.p
% 21.47/3.81
% 21.47/3.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.47/3.81
% 21.47/3.81 % ------ iProver source info
% 21.47/3.81
% 21.47/3.81 % git: date: 2026-07-19 20:42:38 +0200
% 21.47/3.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.47/3.81 % git: non_committed_changes: false
% 21.47/3.81
% 21.47/3.81 % ------ Parsing...
% 21.47/3.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.47/3.81
% 21.47/3.81 % ------ 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 %
% 21.47/3.81
% 21.47/3.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.47/3.81
% 21.47/3.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 21.47/3.81 % ------ Proving...
% 21.47/3.81 % ------ Problem Properties
% 21.47/3.81
% 21.47/3.81 %
% 21.47/3.81 % clauses 85
% 21.47/3.81 % conjectures 1
% 21.47/3.81 % EPR 32
% 21.47/3.81 % Horn 60
% 21.47/3.81 % unary 26
% 21.47/3.81 % binary 8
% 21.47/3.81 % lits 281
% 21.47/3.81 % lits eq 78
% 21.47/3.81 % fd_pure 0
% 21.47/3.81 % fd_pseudo 0
% 21.47/3.81 % fd_cond 15
% 21.47/3.81 % fd_pseudo_cond 11
% 21.47/3.81 % AC symbols 0
% 21.47/3.81
% 21.47/3.81 % ------ Input Options Time Limit: Unbounded
% 21.47/3.81
% 21.47/3.81
% 21.47/3.81 % ------
% 21.47/3.81 % Current options:
% 21.47/3.81 % ------
% 21.47/3.81
% 21.47/3.81
% 21.47/3.81 %
% 21.47/3.81
% 21.47/3.81 % ------ Proving...
% 21.47/3.81 %
% 21.47/3.81
% 21.47/3.81 % SZS status Theorem for theBenchmark.p
% 21.47/3.81
% 21.47/3.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.47/3.82
% 21.47/3.82
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