%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM461+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 : n006.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 119.00s 44.54s
% Output : CNFRefutation 119.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 143 ( 32 unt; 0 def)
% Number of atoms : 516 ( 155 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 652 ( 279 ~; 308 |; 51 &)
% ( 3 <=>; 11 =>; 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 156 ( 0 sgn 144 !; 12 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
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(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
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)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f24,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__840) ).
fof(f25,axiom,
( sdtlseqdt0(xl,xn)
& ? [X0] :
( sdtpldt0(xl,X0) = xn
& aNaturalNumber0(X0) )
& xl != xn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__840_03) ).
fof(f26,axiom,
aNaturalNumber0(xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__873) ).
fof(f27,conjecture,
( ( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| ? [X0] :
( sdtpldt0(sdtpldt0(xl,xm),X0) = sdtpldt0(xn,xm)
& aNaturalNumber0(X0) ) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| ? [X0] :
( sdtpldt0(sdtpldt0(xm,xl),X0) = sdtpldt0(xm,xn)
& aNaturalNumber0(X0) ) )
& sdtpldt0(xm,xl) != sdtpldt0(xm,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ( ( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| ? [X0] :
( sdtpldt0(sdtpldt0(xl,xm),X0) = sdtpldt0(xn,xm)
& aNaturalNumber0(X0) ) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| ? [X0] :
( sdtpldt0(sdtpldt0(xm,xl),X0) = sdtpldt0(xm,xn)
& aNaturalNumber0(X0) ) )
& sdtpldt0(xm,xl) != sdtpldt0(xm,xn) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
~ ( ( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| ? [X1] :
( sdtpldt0(xn,xm) = sdtpldt0(sdtpldt0(xl,xm),X1)
& aNaturalNumber0(X1) ) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| ? [X0] :
( sdtpldt0(sdtpldt0(xm,xl),X0) = sdtpldt0(xm,xn)
& aNaturalNumber0(X0) ) )
& sdtpldt0(xm,xl) != sdtpldt0(xm,xn) ),
inference(rectify,[],[f28]) ).
fof(f31,plain,
( ( ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
& ! [X1] :
( sdtpldt0(xn,xm) != sdtpldt0(sdtpldt0(xl,xm),X1)
| ~ aNaturalNumber0(X1) ) )
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ( ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
& ! [X0] :
( sdtpldt0(xm,xn) != sdtpldt0(sdtpldt0(xm,xl),X0)
| ~ aNaturalNumber0(X0) ) )
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn) ),
inference(ennf_transformation,[],[f29]) ).
fof(f32,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f33,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f37,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f40,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f39]) ).
fof(f41,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(f42,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,[],[f41]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f50,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f49]) ).
fof(f65,plain,
( sdtlseqdt0(xl,xn)
& xn = sdtpldt0(xl,sK0)
& aNaturalNumber0(sK0)
& xl != xn ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f25]) ).
fof(f66,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f67,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f67]) ).
fof(f69,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f24]) ).
fof(f70,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f24]) ).
fof(f72,plain,
xn = sdtpldt0(xl,sK0),
inference(cnf_transformation,[],[f65]) ).
fof(f73,plain,
aNaturalNumber0(sK0),
inference(cnf_transformation,[],[f65]) ).
fof(f74,plain,
xl != xn,
inference(cnf_transformation,[],[f65]) ).
fof(f75,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f26]) ).
fof(f76,plain,
( ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn) ),
inference(cnf_transformation,[],[f31]) ).
fof(f77,plain,
! [X1] :
( sdtpldt0(xn,xm) != sdtpldt0(sdtpldt0(xl,xm),X1)
| ~ aNaturalNumber0(X1)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn) ),
inference(cnf_transformation,[],[f31]) ).
fof(f78,plain,
! [X0] :
( ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(xm,xn) != sdtpldt0(sdtpldt0(xm,xl),X0)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn) ),
inference(cnf_transformation,[],[f31]) ).
fof(f79,plain,
! [X0,X1] :
( sdtpldt0(xn,xm) != sdtpldt0(sdtpldt0(xl,xm),X1)
| ~ aNaturalNumber0(X1)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(xm,xn) != sdtpldt0(sdtpldt0(xm,xl),X0)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn) ),
inference(cnf_transformation,[],[f31]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f37]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sK1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f42]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f42]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f93,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_49,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f70]) ).
tcf(c_50,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f69]) ).
tcf(c_51,plain,
xl != xn,
inference(cnf_transformation,[],[f74]) ).
tcf(c_52,plain,
aNaturalNumber0(sK0),
inference(cnf_transformation,[],[f73]) ).
tcf(c_53,plain,
sdtpldt0(xl,sK0) = xn,
inference(cnf_transformation,[],[f72]) ).
tcf(c_55,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f75]) ).
tcf(c_56,negated_conjecture,
! [X0: $i,X1: $i] :
( ( sdtpldt0(xm,xl) = sdtpldt0(xm,xn) )
| ( sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtpldt0(xm,xl),X1) != sdtpldt0(xm,xn) )
| ( sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xn,xm) ) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_57,negated_conjecture,
! [X0: $i] :
( ( sdtpldt0(xm,xl) = sdtpldt0(xm,xn) )
| ( sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| ( sdtpldt0(sdtpldt0(xm,xl),X0) != sdtpldt0(xm,xn) ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] :
( ( sdtpldt0(xm,xl) = sdtpldt0(xm,xn) )
| ( sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| ( sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xn,xm) ) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_59,negated_conjecture,
( ( sdtpldt0(xm,xl) = sdtpldt0(xm,xn) )
| ( sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_62,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,[],[f82]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sK1(X0,X1)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2) ) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X2,X1) ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_1109,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_58]) ).
tcf(c_1110,negated_conjecture,
( iPr_def_10
| ( sdtpldt0(xm,xl) = sdtpldt0(xm,xn) )
| ( sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_58]) ).
tcf(c_1111,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( sdtpldt0(sdtpldt0(xm,xl),X0) != sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_57]) ).
tcf(c_1113,negated_conjecture,
( iPr_def_11
| iPr_def_10
| ( sdtpldt0(xm,xl) = sdtpldt0(xm,xn) )
| ( sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_56]) ).
tcf(c_1959,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xl) = sdtpldt0(xl,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_73]) ).
tcf(c_2130,plain,
! [X0: $i] :
( ( xl = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,xl) != sdtpldt0(X0,xn) ) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_2131,plain,
( ( xl = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ( sdtpldt0(xm,xl) != sdtpldt0(xm,xn) ) ),
inference(instantiation,[status(thm)],[c_2130]) ).
tcf(c_2143,plain,
sdtpldt0(xl,xm) = sdtpldt0(xm,xl),
inference(superposition,[status(thm)],[c_55,c_1959]) ).
tcf(c_2164,plain,
( ( sdtpldt0(xm,xl) = sdtpldt0(xm,xn) )
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) )
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xn,xm)) ),
inference(demodulation,[status(thm)],[c_59,c_2143]) ).
tcf(c_2166,plain,
( iPr_def_10
| ( sdtpldt0(xm,xl) = sdtpldt0(xm,xn) )
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) )
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) ),
inference(demodulation,[status(thm)],[c_1110,c_2143]) ).
tcf(c_2167,plain,
( iPr_def_11
| iPr_def_10
| ( sdtpldt0(xm,xl) = sdtpldt0(xm,xn) )
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) ) ),
inference(demodulation,[status(thm)],[c_1113,c_2143]) ).
tcf(c_2168,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtpldt0(xm,xl),X0) != sdtpldt0(xn,xm) ) ),
inference(demodulation,[status(thm)],[c_1109,c_2143]) ).
tcf(c_2217,plain,
! [X0: $i] :
( ( xl = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xl,X0) != sdtpldt0(xn,X0) ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_2218,plain,
( ( xl = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ( sdtpldt0(xl,xm) != sdtpldt0(xn,xm) ) ),
inference(instantiation,[status(thm)],[c_2217]) ).
tcf(c_2465,plain,
( iPr_def_11
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_2167,c_55,c_50,c_49,c_51,c_1113,c_2131,c_2218]) ).
tcf(c_2486,plain,
( iPr_def_10
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) ),
inference(global_subsumption_just,[status(thm)],[c_2166,c_55,c_50,c_49,c_51,c_1110,c_2131,c_2218]) ).
tcf(c_2492,plain,
( iPr_def_10
| sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xl)) ),
inference(superposition,[status(thm)],[c_61,c_2486]) ).
tcf(c_2498,plain,
( ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) ) ),
inference(global_subsumption_just,[status(thm)],[c_2164,c_55,c_50,c_49,c_51,c_2131,c_2164]) ).
tcf(c_2499,plain,
( ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) )
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xn,xm)) ),
inference(renaming,[status(thm)],[c_2498]) ).
tcf(c_2506,plain,
( sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xm,xl))
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) )
| ~ aNaturalNumber0(sdtpldt0(xm,xl))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_61,c_2499]) ).
tcf(c_2577,plain,
( sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl))
| sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xm,xl))
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xl))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_61,c_2506]) ).
tcf(c_2589,plain,
( aNaturalNumber0(sdtpldt0(xm,xl))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_2143,c_74]) ).
tcf(c_2591,plain,
aNaturalNumber0(sdtpldt0(xm,xl)),
inference(forward_subsumption_resolution,[status(thm)],[c_2589,c_55,c_49]) ).
tcf(c_2600,plain,
( iPr_def_10
| sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl))
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2492,c_2591]) ).
tcf(c_2987,plain,
! [X0: $i] :
( iPr_def_10
| sdtlseqdt0(sdtpldt0(xm,xn),X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xl))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),X0) ),
inference(superposition,[status(thm)],[c_2600,c_62]) ).
tcf(c_2990,plain,
! [X0: $i] :
( iPr_def_10
| sdtlseqdt0(sdtpldt0(xm,xn),X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2987,c_2591]) ).
tcf(c_3555,plain,
( sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl))
| sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xm,xl))
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_2577,c_2577,c_2591]) ).
tcf(c_3567,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xn,xm),X0)
| sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl))
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xl))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),X0) ),
inference(superposition,[status(thm)],[c_3555,c_62]) ).
tcf(c_3576,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xn,xm),X0)
| sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl))
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3567,c_2591]) ).
tcf(c_3622,plain,
! [X0: $i] :
( iPr_def_10
| sdtlseqdt0(X0,sdtpldt0(xm,xl))
| sdtlseqdt0(sdtpldt0(xm,xn),X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xl)) ),
inference(superposition,[status(thm)],[c_61,c_2990]) ).
tcf(c_3625,plain,
! [X0: $i] :
( iPr_def_10
| sdtlseqdt0(X0,sdtpldt0(xm,xl))
| sdtlseqdt0(sdtpldt0(xm,xn),X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3622,c_2591]) ).
tcf(c_4025,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl))
| ( sdtpldt0(xn,xm) = X0 )
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(X0,sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),X0) ),
inference(superposition,[status(thm)],[c_3576,c_63]) ).
tcf(c_4287,plain,
( iPr_def_10
| sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl))
| sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xm,xl))
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xn) )
| ( sdtpldt0(xn,xm) = sdtpldt0(xm,xl) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_3625,c_4025]) ).
tcf(c_4858,plain,
( ( sdtpldt0(xn,xm) = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_4937,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(global_subsumption_just,[status(thm)],[c_4287,c_55,c_50,c_4858]) ).
tcf(c_4951,plain,
( sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl))
| ( sdtpldt0(xm,xl) = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(demodulation,[status(thm)],[c_3555,c_4937]) ).
tcf(c_4954,plain,
( ( sdtpldt0(xm,xl) = sdtpldt0(xm,xn) )
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) ),
inference(demodulation,[status(thm)],[c_2499,c_4937]) ).
tcf(c_4956,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtpldt0(xm,xl),X0) != sdtpldt0(xm,xn) ) ),
inference(demodulation,[status(thm)],[c_2168,c_4937]) ).
tcf(c_5038,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_4937,c_74]) ).
tcf(c_5041,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(forward_subsumption_resolution,[status(thm)],[c_5038,c_55,c_50]) ).
tcf(c_5060,plain,
( iPr_def_10
| sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2600,c_5041]) ).
tcf(c_5166,plain,
sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl)),
inference(global_subsumption_just,[status(thm)],[c_5060,c_55,c_50,c_49,c_51,c_2131,c_4951,c_5041]) ).
tcf(c_5169,plain,
( ( sdtpldt0(sdtpldt0(xm,xn),sK1(sdtpldt0(xm,xn),sdtpldt0(xm,xl))) = sdtpldt0(xm,xl) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xl)) ),
inference(superposition,[status(thm)],[c_5166,c_67]) ).
tcf(c_5175,plain,
sdtpldt0(sdtpldt0(xm,xn),sK1(sdtpldt0(xm,xn),sdtpldt0(xm,xl))) = sdtpldt0(xm,xl),
inference(forward_subsumption_resolution,[status(thm)],[c_5169,c_5041,c_2591]) ).
tcf(c_5269,plain,
! [X0: $i] :
( ( sdtpldt0(sdtpldt0(xm,xl),X0) != sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_4956,c_1111,c_2465,c_4956]) ).
tcf(c_5270,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtpldt0(xm,xl),X0) != sdtpldt0(xm,xn) ) ),
inference(renaming,[status(thm)],[c_5269]) ).
tcf(c_22235,negated_conjecture,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtpldt0(sdtpldt0(xm,xl),X0) != sdtpldt0(xm,xn) ) ),
inference(global_subsumption_just,[status(thm)],[c_1111,c_5270]) ).
tcf(c_22247,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)),
inference(global_subsumption_just,[status(thm)],[c_1110,c_55,c_50,c_49,c_51,c_2131,c_4954]) ).
tcf(c_22575,plain,
( sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xl)) ),
inference(superposition,[status(thm)],[c_61,c_22247]) ).
tcf(c_22656,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sK0) = sdtpldt0(sK0,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_52,c_73]) ).
tcf(c_22756,plain,
sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xl)),
inference(global_subsumption_just,[status(thm)],[c_22575,c_55,c_50,c_49,c_51,c_2131,c_4951,c_5041]) ).
tcf(c_23022,plain,
( ( sdtpldt0(sdtpldt0(xm,xn),sK1(sdtpldt0(xm,xn),sdtpldt0(xm,xl))) = sdtpldt0(xm,xl) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xl)) ),
inference(superposition,[status(thm)],[c_22756,c_67]) ).
tcf(c_23306,plain,
sdtpldt0(sdtpldt0(xm,xn),sK1(sdtpldt0(xm,xn),sdtpldt0(xm,xl))) = sdtpldt0(xm,xl),
inference(global_subsumption_just,[status(thm)],[c_23022,c_5175]) ).
tcf(c_23311,plain,
( aNaturalNumber0(sdtpldt0(xm,xl))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sK1(sdtpldt0(xm,xn),sdtpldt0(xm,xl))) ),
inference(superposition,[status(thm)],[c_23306,c_74]) ).
tcf(c_23370,plain,
aNaturalNumber0(sdtpldt0(xm,xl)),
inference(global_subsumption_just,[status(thm)],[c_23311,c_2591]) ).
tcf(c_23380,plain,
sdtpldt0(sdtpldt0(xm,xl),sK0) = sdtpldt0(sK0,sdtpldt0(xm,xl)),
inference(superposition,[status(thm)],[c_23370,c_22656]) ).
tcf(c_24271,plain,
( ~ aNaturalNumber0(sK0)
| ( sdtpldt0(sK0,sdtpldt0(xm,xl)) != sdtpldt0(xm,xn) ) ),
inference(superposition,[status(thm)],[c_23380,c_22235]) ).
tcf(c_24281,plain,
sdtpldt0(sK0,sdtpldt0(xm,xl)) != sdtpldt0(xm,xn),
inference(forward_subsumption_resolution,[status(thm)],[c_24271,c_52]) ).
tcf(c_401633,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(sK0,X0),X1) = sdtpldt0(sK0,sdtpldt0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_52,c_72]) ).
tcf(c_401664,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xl) = sdtpldt0(xl,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_73]) ).
tcf(c_401665,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xn) = sdtpldt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_73]) ).
tcf(c_404172,plain,
! [X0: $i] :
( ( sdtpldt0(sdtpldt0(sK0,xl),X0) = sdtpldt0(sK0,sdtpldt0(xl,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_401633]) ).
tcf(c_404640,plain,
sdtpldt0(xl,sK0) = sdtpldt0(sK0,xl),
inference(superposition,[status(thm)],[c_52,c_401664]) ).
tcf(c_404641,plain,
sdtpldt0(xl,xm) = sdtpldt0(xm,xl),
inference(superposition,[status(thm)],[c_55,c_401664]) ).
tcf(c_404647,plain,
sdtpldt0(sK0,xl) = xn,
inference(light_normalisation,[status(thm)],[c_404640,c_53]) ).
tcf(c_404679,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(superposition,[status(thm)],[c_55,c_401665]) ).
tcf(c_441786,plain,
! [X0: $i] :
( ( sdtpldt0(sK0,sdtpldt0(xl,X0)) = sdtpldt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_404172,c_404647]) ).
tcf(c_441796,plain,
sdtpldt0(sK0,sdtpldt0(xl,xm)) = sdtpldt0(xn,xm),
inference(superposition,[status(thm)],[c_55,c_441786]) ).
tcf(c_441814,plain,
sdtpldt0(sK0,sdtpldt0(xm,xl)) = sdtpldt0(xm,xn),
inference(light_normalisation,[status(thm)],[c_441796,c_404641,c_404679]) ).
tcf(c_441831,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_441814,c_24281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM461+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/15.39 % Computer : n006.cluster.edu
% 0.12/15.39 % Model : x86_64 x86_64
% 0.12/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.39 % Memory : 8046.5625MB
% 0.12/15.39 % OS : Linux 6.8.0-71-generic
% 0.12/15.39 % CPULimit : 300
% 0.12/15.39 % WCLimit : 300
% 0.12/15.39 % DateTime : Thu Sep 24 04:05:48 UTC 2026
% 0.12/15.40 % CPUTime :
% 0.14/15.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/15.43 Running first-order theorem proving
% 0.14/15.44 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
% 0.14/15.45
% 0.14/15.45 % ======== iProver multi-core TPTP/SMT =========
% 0.14/15.45
% 0.14/15.45 % Detected problem language: tptp
% 0.14/15.46 % Proving...
% 119.00/44.54 % SZS status Started for theBenchmark.p
% 119.00/44.54 % SZS status Theorem for theBenchmark.p
% 119.00/44.54
% 119.00/44.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 119.00/44.54
% 119.00/44.54 % ------ iProver source info
% 119.00/44.54
% 119.00/44.54 % git: date: 2026-07-19 20:42:38 +0200
% 119.00/44.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 119.00/44.54 % git: non_committed_changes: false
% 119.00/44.54
% 119.00/44.54 % ------ Parsing...
% 119.00/44.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 119.00/44.54
% 119.00/44.54 % ------ 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 %
% 119.00/44.54
% 119.00/44.54 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 119.00/44.54
% 119.00/44.54 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 119.00/44.54 % ------ Proving...
% 119.00/44.54 % ------ Problem Properties
% 119.00/44.54
% 119.00/44.54 %
% 119.00/44.54 % clauses 40
% 119.00/44.54 % conjectures 6
% 119.00/44.54 % EPR 11
% 119.00/44.54 % Horn 32
% 119.00/44.54 % unary 8
% 119.00/44.54 % binary 5
% 119.00/44.54 % lits 129
% 119.00/44.54 % lits eq 41
% 119.00/44.54 % fd_pure 0
% 119.00/44.54 % fd_pseudo 0
% 119.00/44.54 % fd_cond 3
% 119.00/44.54 % fd_pseudo_cond 5
% 119.00/44.54 % AC symbols 0
% 119.00/44.54
% 119.00/44.54 % ------ Schedule dynamic 5 is on
% 119.00/44.54
% 119.00/44.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 119.00/44.54
% 119.00/44.54
% 119.00/44.54 % ------
% 119.00/44.54 % Current options:
% 119.00/44.54 % ------
% 119.00/44.54
% 119.00/44.54
% 119.00/44.54 %
% 119.00/44.54
% 119.00/44.54 % ------ Proving...
% 119.00/44.54 % Proof_search_loop: time out after: 7409 full_loop iterations
% 119.00/44.54
% 119.00/44.54 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 119.00/44.54
% 119.00/44.54
% 119.00/44.54 % ------
% 119.00/44.54 % Current options:
% 119.00/44.54 % ------
% 119.00/44.54
% 119.00/44.54
% 119.00/44.54 %
% 119.00/44.54
% 119.00/44.54 % ------ Proving...
% 119.00/44.54 % Proof_search_loop: time out after: 8583 full_loop iterations
% 119.00/44.54
% 119.00/44.54 % ------ Option_1: Negative Selections Time Limit: 35.
% 119.00/44.54
% 119.00/44.54
% 119.00/44.54 % ------
% 119.00/44.54 % Current options:
% 119.00/44.54 % ------
% 119.00/44.54
% 119.00/44.54
% 119.00/44.54 %
% 119.00/44.54
% 119.00/44.54 % ------ Proving...
% 119.00/44.54 %
% 119.00/44.54
% 119.00/44.54 % SZS status Theorem for theBenchmark.p
% 119.00/44.54
% 119.00/44.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 119.00/44.54
% 119.00/44.54
%------------------------------------------------------------------------------