%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM480+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 : n008.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 02:25:10 PM UTC 2026
% Result : Theorem 264.24s 39.07s
% Output : CNFRefutation 264.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 119 ( 28 unt; 0 def)
% Number of atoms : 427 ( 152 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 550 ( 242 ~; 250 |; 37 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 168 ( 0 sgn 163 !; 5 ?; 60 :)
% 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(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
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(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
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(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(f36,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524) ).
fof(f37,axiom,
( doDivides0(xl,xm)
& xl != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524_04) ).
fof(f38,axiom,
aNaturalNumber0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1553) ).
fof(f39,axiom,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1594) ).
fof(f40,conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f41,negated_conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f44,plain,
sdtsldt0(sdtasdt0(xn,xm),xl) != sdtasdt0(xn,sdtsldt0(xm,xl)),
inference(flattening,[],[f41]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f48]) ).
fof(f54,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(flattening,[],[f57]) ).
fof(f65,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f66,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f67]) ).
fof(f90,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f90]) ).
fof(f92,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(f93,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,[],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(flattening,[],[f94]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f108,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f108]) ).
fof(f110,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,[],[f93]) ).
fof(f111,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,[],[f110]) ).
fof(f112,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f116,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f119,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f54]) ).
fof(f121,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f66]) ).
fof(f133,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f168,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f36]) ).
fof(f169,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f36]) ).
fof(f170,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f37]) ).
fof(f171,plain,
sz00 != xl,
inference(cnf_transformation,[],[f37]) ).
fof(f172,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f38]) ).
fof(f173,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnf_transformation,[],[f39]) ).
fof(f174,plain,
sdtsldt0(sdtasdt0(xn,xm),xl) != sdtasdt0(xn,sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f44]) ).
fof(f181,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f160]) ).
fof(f183,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f162]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f112]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_104,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f169]) ).
tcf(c_105,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f168]) ).
tcf(c_106,plain,
sz00 != xl,
inference(cnf_transformation,[],[f171]) ).
tcf(c_107,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f170]) ).
tcf(c_108,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f172]) ).
tcf(c_109,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnf_transformation,[],[f173]) ).
tcf(c_110,negated_conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(cnf_transformation,[],[f174]) ).
tcf(c_115,plain,
( ( sdtpldt0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_127,plain,
( ( sz00 = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_94,c_53,c_94]) ).
tcf(c_1008,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1010,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1011,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtsldt0(X0,X2) = sdtsldt0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1960,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xm) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_105,c_58]) ).
tcf(c_1984,plain,
! [X0: $i] :
( ( sz00 = xl )
| ( xl != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_1010]) ).
tcf(c_1985,plain,
( ( sz00 = xl )
| ( xl != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_1984]) ).
tcf(c_1998,plain,
! [X0: $i,X1: $i] :
( ( sdtsldt0(sdtasdt0(xn,xm),xl) = sdtsldt0(X0,X1) )
| ( xl != X1 )
| ( sdtasdt0(xn,xm) != X0 ) ),
inference(instantiation,[status(thm)],[c_1017]) ).
tcf(c_2021,plain,
! [X0: $i] :
( aNaturalNumber0(sdtsldt0(X0,xl))
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xl,X0) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_2054,plain,
sdtasdt0(xm,xn) = sdtasdt0(xn,xm),
inference(superposition,[status(thm)],[c_108,c_1960]) ).
tcf(c_2067,plain,
xl = xl,
inference(instantiation,[status(thm)],[c_1008]) ).
tcf(c_2071,plain,
( aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_2054,c_53]) ).
tcf(c_2080,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm) ),
inference(instantiation,[status(thm)],[c_2021]) ).
tcf(c_2102,plain,
! [X0: $i] :
( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
| ~ aNaturalNumber0(X0)
| ( sdtsldt0(sdtasdt0(xn,xm),xl) != X0 ) ),
inference(instantiation,[status(thm)],[c_1011]) ).
tcf(c_2124,plain,
sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtasdt0(xn,sdtsldt0(xm,xl)),
inference(instantiation,[status(thm)],[c_1008]) ).
tcf(c_2126,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(xn,sdtsldt0(xm,xl)) = X1 )
| ( X1 != X0 )
| ( sdtasdt0(xn,sdtsldt0(xm,xl)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1010]) ).
tcf(c_2148,plain,
! [X0: $i] :
( ( sdtsldt0(sdtasdt0(xn,xm),xl) = sdtsldt0(X0,xl) )
| ( xl != xl )
| ( sdtasdt0(xn,xm) != X0 ) ),
inference(instantiation,[status(thm)],[c_1998]) ).
tcf(c_2208,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_1010,c_1008]) ).
tcf(c_2218,plain,
! [X0: $i] :
( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
| ~ aNaturalNumber0(sdtsldt0(X0,xl))
| ( sdtsldt0(sdtasdt0(xn,xm),xl) != sdtsldt0(X0,xl) ) ),
inference(instantiation,[status(thm)],[c_2102]) ).
tcf(c_2267,plain,
( ( sdtsldt0(sdtasdt0(xn,xm),xl) = sdtsldt0(sdtasdt0(xm,xn),xl) )
| ( xl != xl )
| ( sdtasdt0(xn,xm) != sdtasdt0(xm,xn) ) ),
inference(instantiation,[status(thm)],[c_2148]) ).
tcf(c_2268,plain,
( ( sdtasdt0(xn,xm) = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_2294,plain,
sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) = sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)),
inference(resolution,[status(thm)],[c_109,c_2208]) ).
tcf(c_2329,plain,
( aNaturalNumber0(sdtasdt0(xn,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_2473,plain,
! [X0: $i] :
( ( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) = X0 )
| ( X0 != sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) ) ),
inference(resolution,[status(thm)],[c_2294,c_1010]) ).
tcf(c_2895,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[c_59,c_2208]) ).
tcf(c_2981,plain,
! [X0: $i] :
( ( sdtasdt0(xn,sdtsldt0(xm,xl)) = X0 )
| ( X0 != sdtasdt0(xn,sdtsldt0(xm,xl)) )
| ( sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtasdt0(xn,sdtsldt0(xm,xl)) ) ),
inference(instantiation,[status(thm)],[c_2126]) ).
tcf(c_5978,plain,
( ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) )
| ( sdtsldt0(sdtasdt0(xn,xm),xl) != sdtasdt0(xn,sdtsldt0(xm,xl)) )
| ( sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtasdt0(xn,sdtsldt0(xm,xl)) ) ),
inference(instantiation,[status(thm)],[c_2981]) ).
tcf(c_7733,plain,
( ( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(resolution,[status(thm)],[c_2895,c_2473]) ).
tcf(c_30590,plain,
( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xm,xn),xl))
| ( sdtsldt0(sdtasdt0(xn,xm),xl) != sdtsldt0(sdtasdt0(xm,xn),xl) ) ),
inference(instantiation,[status(thm)],[c_2218]) ).
tcf(c_161880,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_161922,plain,
! [X0: $i] :
( aNaturalNumber0(sdtsldt0(X0,xl))
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xl,X0) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_161964,plain,
! [X0: $i,X1: $i] :
( doDivides0(xl,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xl,X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(instantiation,[status(thm)],[c_161880]) ).
tcf(c_162443,plain,
! [X0: $i] :
( doDivides0(xl,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ doDivides0(xm,sdtasdt0(xm,X0)) ),
inference(instantiation,[status(thm)],[c_161964]) ).
tcf(c_162662,plain,
! [X0: $i] :
( doDivides0(xm,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(instantiation,[status(thm)],[c_144]) ).
tcf(c_162782,plain,
! [X0: $i] :
( aNaturalNumber0(sdtsldt0(sdtasdt0(xm,X0),xl))
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ doDivides0(xl,sdtasdt0(xm,X0)) ),
inference(instantiation,[status(thm)],[c_161922]) ).
tcf(c_166509,plain,
( aNaturalNumber0(sdtsldt0(sdtasdt0(xm,xn),xl))
| ( xl = sz00 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ doDivides0(xl,sdtasdt0(xm,xn)) ),
inference(instantiation,[status(thm)],[c_162782]) ).
tcf(c_169210,plain,
( doDivides0(xl,sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ doDivides0(xm,sdtasdt0(xm,xn)) ),
inference(instantiation,[status(thm)],[c_162443]) ).
tcf(c_179062,plain,
( doDivides0(xm,sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(instantiation,[status(thm)],[c_162662]) ).
tcf(c_287395,plain,
! [X0: $i,X1: $i] :
( ( xl = sz00 )
| ( X0 = X1 )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xl,X0) != sdtasdt0(xl,X1) ) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_288181,plain,
( ( xl = sz00 )
| ( sdtsldt0(sdtasdt0(xn,xm),xl) = sdtasdt0(xn,sdtsldt0(xm,xl)) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
| ~ aNaturalNumber0(sdtasdt0(xn,sdtsldt0(xm,xl)))
| ( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ) ),
inference(instantiation,[status(thm)],[c_287395]) ).
tcf(c_288182,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_288181,c_179062,c_169210,c_166509,c_30590,c_7733,c_5978,c_2329,c_2268,c_2267,c_2124,c_2080,c_2071,c_2067,c_1985,c_127,c_110,c_115,c_106,c_107,c_49,c_104,c_105,c_108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM480+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 04:12:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 264.24/39.07 % SZS status Started for theBenchmark.p
% 264.24/39.07 % SZS status Theorem for theBenchmark.p
% 264.24/39.07
% 264.24/39.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 264.24/39.07
% 264.24/39.07 % ------ iProver source info
% 264.24/39.07
% 264.24/39.07 % git: date: 2026-07-19 20:42:38 +0200
% 264.24/39.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 264.24/39.07 % git: non_committed_changes: false
% 264.24/39.07
% 264.24/39.07 % ------ Parsing...
% 264.24/39.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 264.24/39.07
% 264.24/39.07 % ------ 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 %
% 264.24/39.07
% 264.24/39.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 264.24/39.07
% 264.24/39.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 264.24/39.07 % ------ Proving...
% 264.24/39.07 % ------ Problem Properties
% 264.24/39.07
% 264.24/39.07 %
% 264.24/39.07 % clauses 57
% 264.24/39.07 % conjectures 1
% 264.24/39.07 % EPR 15
% 264.24/39.07 % Horn 43
% 264.24/39.07 % unary 10
% 264.24/39.07 % binary 7
% 264.24/39.07 % lits 206
% 264.24/39.07 % lits eq 53
% 264.24/39.07 % fd_pure 0
% 264.24/39.07 % fd_pseudo 0
% 264.24/39.07 % fd_cond 7
% 264.24/39.07 % fd_pseudo_cond 9
% 264.24/39.07 % AC symbols 0
% 264.24/39.07
% 264.24/39.07 % ------ Input Options Time Limit: Unbounded
% 264.24/39.07
% 264.24/39.07
% 264.24/39.07 % ------
% 264.24/39.07 % Current options:
% 264.24/39.07 % ------
% 264.24/39.07
% 264.24/39.07
% 264.24/39.07 %
% 264.24/39.07
% 264.24/39.07 % ------ Proving...
% 264.24/39.07 %
% 264.24/39.07
% 264.24/39.07 % ------ Proving...
% 264.24/39.07 %
% 264.24/39.07
% 264.24/39.07 % ------ Proving...
% 264.24/39.07 %
% 264.24/39.07
% 264.24/39.07 % SZS status Theorem for theBenchmark.p
% 264.24/39.07
% 264.24/39.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 264.24/39.07
% 264.24/39.07
%------------------------------------------------------------------------------