%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM462+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 02:24:32 PM UTC 2026
% Result : Theorem 1.34s 24.06s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 101 ( 23 unt; 0 def)
% Number of atoms : 360 ( 159 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 474 ( 215 ~; 206 |; 43 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 120 !; 7 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
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/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f25,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__897) ).
fof(f26,axiom,
( sdtlseqdt0(xl,xn)
& ? [X0] :
( sdtpldt0(xl,X0) = xn
& aNaturalNumber0(X0) )
& xl != xn
& xm != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__897_03) ).
fof(f27,conjecture,
( ( sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ? [X0] :
( sdtpldt0(sdtasdt0(xl,xm),X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ? [X0] :
( sdtpldt0(sdtasdt0(xm,xl),X0) = sdtasdt0(xm,xn)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ( ( sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ? [X0] :
( sdtpldt0(sdtasdt0(xl,xm),X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ? [X0] :
( sdtpldt0(sdtasdt0(xm,xl),X0) = sdtasdt0(xm,xn)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f30,plain,
~ ( ( sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ? [X1] :
( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xl,xm),X1)
& aNaturalNumber0(X1) ) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ? [X0] :
( sdtpldt0(sdtasdt0(xm,xl),X0) = sdtasdt0(xm,xn)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ),
inference(rectify,[],[f28]) ).
fof(f33,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f34,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f33]) ).
fof(f39,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f40,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f41,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f40]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(flattening,[],[f46]) ).
fof(f50,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(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f53,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f52]) ).
fof(f69,plain,
( ( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
& ! [X1] :
( sdtasdt0(xn,xm) != sdtpldt0(sdtasdt0(xl,xm),X1)
| ~ aNaturalNumber0(X1) ) )
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ( ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
& ! [X0] :
( sdtasdt0(xm,xn) != sdtpldt0(sdtasdt0(xm,xl),X0)
| ~ aNaturalNumber0(X0) ) )
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(ennf_transformation,[],[f30]) ).
fof(f75,plain,
( sdtlseqdt0(xl,xn)
& xn = sdtpldt0(xl,sK1)
& aNaturalNumber0(sK1)
& xl != xn
& xm != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f26]) ).
fof(f76,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f84,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f51]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f51]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X0 ),
inference(cnf_transformation,[],[f53]) ).
fof(f115,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f25]) ).
fof(f116,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f25]) ).
fof(f117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f119,plain,
xn = sdtpldt0(xl,sK1),
inference(cnf_transformation,[],[f75]) ).
fof(f120,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f75]) ).
fof(f121,plain,
xl != xn,
inference(cnf_transformation,[],[f75]) ).
fof(f122,plain,
sz00 != xm,
inference(cnf_transformation,[],[f75]) ).
fof(f124,plain,
! [X1] :
( sdtasdt0(xn,xm) != sdtpldt0(sdtasdt0(xl,xm),X1)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(cnf_transformation,[],[f69]) ).
fof(f125,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtpldt0(sdtasdt0(xm,xl),X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(cnf_transformation,[],[f69]) ).
fof(f126,plain,
! [X0,X1] :
( sdtasdt0(xn,xm) != sdtpldt0(sdtasdt0(xl,xm),X1)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtpldt0(sdtasdt0(xm,xl),X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f76]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_56,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) = sdtasdt0(X0,sdtpldt0(X1,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) = sdtasdt0(sdtpldt0(X1,X2),X0) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f91]) ).
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,[],[f96]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sz00 )
| ( X0 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X2,X1) ) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_88,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f117]) ).
tcf(c_89,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f116]) ).
tcf(c_90,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f115]) ).
tcf(c_91,plain,
sz00 != xm,
inference(cnf_transformation,[],[f122]) ).
tcf(c_92,plain,
xl != xn,
inference(cnf_transformation,[],[f121]) ).
tcf(c_93,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f120]) ).
tcf(c_94,plain,
sdtpldt0(xl,sK1) = xn,
inference(cnf_transformation,[],[f119]) ).
tcf(c_96,negated_conjecture,
! [X0: $i,X1: $i] :
( ( sdtasdt0(xl,xm) = sdtasdt0(xn,xm) )
| ( sdtasdt0(xm,xl) = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtasdt0(xl,xm),X1) != sdtasdt0(xn,xm) )
| ( sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xm,xn) ) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_97,negated_conjecture,
! [X0: $i] :
( ( sdtasdt0(xl,xm) = sdtasdt0(xn,xm) )
| ( sdtasdt0(xm,xl) = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ( sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xm,xn) ) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_98,negated_conjecture,
! [X0: $i] :
( ( sdtasdt0(xl,xm) = sdtasdt0(xn,xm) )
| ( sdtasdt0(xm,xl) = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ( sdtpldt0(sdtasdt0(xl,xm),X0) != sdtasdt0(xn,xm) ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_1364,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( sdtpldt0(sdtasdt0(xl,xm),X0) != sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_98]) ).
tcf(c_1366,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_97]) ).
tcf(c_1368,negated_conjecture,
( iPr_def_11
| iPr_def_10
| ( sdtasdt0(xl,xm) = sdtasdt0(xn,xm) )
| ( sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_96]) ).
tcf(c_1369,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1371,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(X0,X2) = sdtasdt0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2098,plain,
( ( sz00 = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_2099,plain,
( ( sdtpldt0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_2114,plain,
! [X0: $i] :
( ( sz00 = xm )
| ( xm != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_1371]) ).
tcf(c_2211,plain,
! [X0: $i] :
( ( xl = xn )
| ( X0 = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xl) != sdtasdt0(X0,xn) ) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_2212,plain,
( ( xl = xn )
| ( xm = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ( sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ) ),
inference(instantiation,[status(thm)],[c_2211]) ).
tcf(c_2229,plain,
! [X0: $i] :
( ( xl = xn )
| ( X0 = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xl,X0) != sdtasdt0(xn,X0) ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_2230,plain,
( ( xl = xn )
| ( xm = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ( sdtasdt0(xl,xm) != sdtasdt0(xn,xm) ) ),
inference(instantiation,[status(thm)],[c_2229]) ).
tcf(c_2329,plain,
( ( sz00 = xm )
| ( xm != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_2114]) ).
tcf(c_2451,negated_conjecture,
( iPr_def_11
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1368,c_90,c_89,c_88,c_49,c_92,c_91,c_1368,c_2098,c_2099,c_2212,c_2230,c_2329]) ).
tcf(c_3224,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_1371,c_1369]) ).
tcf(c_3419,plain,
xn = sdtpldt0(xl,sK1),
inference(resolution,[status(thm)],[c_3224,c_94]) ).
tcf(c_7362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) = X0 )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( X0 != sdtasdt0(X1,sdtpldt0(X2,X3)) ) ),
inference(resolution,[status(thm)],[c_64,c_1371]) ).
tcf(c_8193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) = X0 )
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( X0 != sdtasdt0(sdtpldt0(X1,X2),X3) ) ),
inference(resolution,[status(thm)],[c_65,c_1371]) ).
tcf(c_47570,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ( sdtasdt0(xm,xn) != sdtasdt0(xm,sdtpldt0(xl,X0)) ) ),
inference(resolution,[status(thm)],[c_7362,c_1366]) ).
tcf(c_48184,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ( sdtasdt0(xn,xm) != sdtasdt0(sdtpldt0(xl,X0),xm) ) ),
inference(resolution,[status(thm)],[c_8193,c_1364]) ).
tcf(c_49111,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xm) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_88,c_58]) ).
tcf(c_49610,plain,
sdtasdt0(xm,sK1) = sdtasdt0(sK1,xm),
inference(superposition,[status(thm)],[c_93,c_49111]) ).
tcf(c_55771,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ( sdtasdt0(xm,xn) != sdtasdt0(xm,sdtpldt0(xl,X0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_47570,c_89,c_88,c_47570]) ).
tcf(c_55796,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ( xn != sdtpldt0(xl,X0) )
| ( xm != xm ) ),
inference(resolution,[status(thm)],[c_55771,c_1374]) ).
tcf(c_55797,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ( xn != sdtpldt0(xl,X0) ) ),
inference(equality_resolution_simp,[status(thm)],[c_55796]) ).
tcf(c_56005,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ( sdtasdt0(xn,xm) != sdtasdt0(sdtpldt0(xl,X0),xm) ) ),
inference(global_subsumption_just,[status(thm)],[c_48184,c_89,c_88,c_48184]) ).
tcf(c_56031,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ( xn != sdtpldt0(xl,X0) )
| ( xm != xm ) ),
inference(resolution,[status(thm)],[c_56005,c_1374]) ).
tcf(c_56032,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ( xn != sdtpldt0(xl,X0) ) ),
inference(equality_resolution_simp,[status(thm)],[c_56031]) ).
tcf(c_61354,plain,
( aNaturalNumber0(sdtasdt0(xm,sK1))
| ~ aNaturalNumber0(sK1)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_49610,c_53]) ).
tcf(c_61357,plain,
aNaturalNumber0(sdtasdt0(xm,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_61354,c_93,c_88]) ).
tcf(c_61636,plain,
( ~ iPr_def_11
| ~ aNaturalNumber0(sK1)
| ~ aNaturalNumber0(sdtasdt0(xm,sK1)) ),
inference(resolution,[status(thm)],[c_55797,c_3419]) ).
tcf(c_61638,plain,
! [X0: $i] :
( ( xn != sdtpldt0(xl,X0) )
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_56032,c_93,c_2451,c_56032,c_61357,c_61636]) ).
tcf(c_61639,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ( xn != sdtpldt0(xl,X0) ) ),
inference(renaming,[status(thm)],[c_61638]) ).
tcf(c_61661,plain,
( ~ aNaturalNumber0(sK1)
| ~ aNaturalNumber0(sdtasdt0(sK1,xm)) ),
inference(resolution,[status(thm)],[c_61639,c_3419]) ).
tcf(c_192584,plain,
~ aNaturalNumber0(sdtasdt0(sK1,xm)),
inference(global_subsumption_just,[status(thm)],[c_61661,c_93,c_61661]) ).
tcf(c_192590,plain,
( ~ aNaturalNumber0(sK1)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_192584,c_53]) ).
tcf(c_192591,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_192590,c_88,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM462+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 04:05:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 1.34/24.06 % SZS status Started for theBenchmark.p
% 1.34/24.06 % SZS status Theorem for theBenchmark.p
% 1.34/24.06
% 1.34/24.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.34/24.06
% 1.34/24.06 % ------ iProver source info
% 1.34/24.06
% 1.34/24.06 % git: date: 2026-07-19 20:42:38 +0200
% 1.34/24.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.34/24.06 % git: non_committed_changes: false
% 1.34/24.06
% 1.34/24.06 % ------ Parsing...
% 1.34/24.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.34/24.06
% 1.34/24.06 % ------ 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 %
% 1.34/24.06
% 1.34/24.06 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.34/24.06
% 1.34/24.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.34/24.06 % ------ Proving...
% 1.34/24.06 % ------ Problem Properties
% 1.34/24.06
% 1.34/24.06 %
% 1.34/24.06 % clauses 50
% 1.34/24.06 % conjectures 6
% 1.34/24.06 % EPR 14
% 1.34/24.06 % Horn 40
% 1.34/24.06 % unary 11
% 1.34/24.06 % binary 7
% 1.34/24.06 % lits 159
% 1.34/24.06 % lits eq 49
% 1.34/24.06 % fd_pure 0
% 1.34/24.06 % fd_pseudo 0
% 1.34/24.06 % fd_cond 3
% 1.34/24.06 % fd_pseudo_cond 7
% 1.34/24.06 % AC symbols 0
% 1.34/24.06
% 1.34/24.06 % ------ Input Options Time Limit: Unbounded
% 1.34/24.06
% 1.34/24.06
% 1.34/24.06 % ------
% 1.34/24.06 % Current options:
% 1.34/24.06 % ------
% 1.34/24.06
% 1.34/24.06
% 1.34/24.06 %
% 1.34/24.06
% 1.34/24.06 % ------ Proving...
% 1.34/24.06 %
% 1.34/24.06
% 1.34/24.06 % SZS status Theorem for theBenchmark.p
% 1.34/24.06
% 1.34/24.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.34/24.06
% 1.34/24.06
%------------------------------------------------------------------------------