%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG049+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 : n007.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 02:38:19 PM UTC 2026
% Result : Theorem 6.32s 1.76s
% Output : CNFRefutation 6.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 139 ( 34 unt; 0 def)
% Number of atoms : 437 ( 114 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 534 ( 236 ~; 240 |; 36 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 163 ( 0 sgn 163 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( szszuzczcdt0(X0) != sz00
& aNaturalNumber0(szszuzczcdt0(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).
fof(f7,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> iLess0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETrn) ).
fof(f25,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
fof(f26,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X0) )
=> ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPosMon) ).
fof(f30,axiom,
! [X0] :
( aVector0(X0)
=> aNaturalNumber0(aDimensionOf0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aVector0(X0) )
=> aScalar0(sdtlbdtrb0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).
fof(f33,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( aDimensionOf0(X1) != sz00
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEqInit) ).
fof(f34,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( aDimensionOf0(X0) = aDimensionOf0(X1)
=> aScalar0(sdtasasdt0(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).
fof(f36,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( aDimensionOf0(X1) != sz00
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPN) ).
fof(f37,axiom,
aVector0(xs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1542) ).
fof(f38,axiom,
! [X0] :
( aVector0(X0)
=> ( iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
=> sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1516) ).
fof(f39,axiom,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1542_01) ).
fof(f41,axiom,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs))
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1590) ).
fof(f42,conjecture,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f50,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs))
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
inference(rectify,[],[f41]) ).
fof(f51,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(flattening,[],[f43]) ).
fof(f52,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(X0) != sz00
& aNaturalNumber0(szszuzczcdt0(X0)) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f57,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f60,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f61,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f60]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f77]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ) ),
inference(flattening,[],[f85]) ).
fof(f90,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(X0)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aVector0(X0)
| aScalar0(sdtlbdtrb0(X0,X1)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aVector0(X0)
| aScalar0(sdtlbdtrb0(X0,X1)) ),
inference(flattening,[],[f91]) ).
fof(f95,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f96,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X0,X1)) ),
inference(flattening,[],[f97]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ),
inference(ennf_transformation,[],[f36]) ).
fof(f102,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
! [X0] :
( ~ aVector0(X0)
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
inference(ennf_transformation,[],[f38]) ).
fof(f104,plain,
! [X0] :
( ~ aVector0(X0)
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
inference(flattening,[],[f103]) ).
fof(f106,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
& ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs))
& ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
inference(ennf_transformation,[],[f50]) ).
fof(f114,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f118,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f119,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f121,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f146,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f148,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f151,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(X0)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f152,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aVector0(X0)
| aScalar0(sdtlbdtrb0(X0,X1)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f158,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f159,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f98]) ).
fof(f161,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ),
inference(cnf_transformation,[],[f102]) ).
fof(f162,plain,
aVector0(xs),
inference(cnf_transformation,[],[f37]) ).
fof(f163,plain,
! [X0] :
( ~ aVector0(X0)
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f164,plain,
sz00 != aDimensionOf0(xs),
inference(cnf_transformation,[],[f39]) ).
fof(f171,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(cnf_transformation,[],[f106]) ).
fof(f172,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f173,plain,
aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))),
inference(cnf_transformation,[],[f106]) ).
fof(f174,plain,
aVector0(sziznziztdt0(xs)),
inference(cnf_transformation,[],[f106]) ).
fof(f178,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_50,plain,
! [X0: $i] :
( aNaturalNumber0(szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_55,plain,
! [X0: $i] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_56,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f119]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X0,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_88,plain,
! [X0: $i] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtlbdtrb0(X1,X0))
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasasdt0(X0,X1))
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = sz00 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) = sdtasasdt0(X0,X1) )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_99,plain,
aVector0(xs),
inference(cnf_transformation,[],[f162]) ).
tcf(c_100,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0)
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_101,plain,
aDimensionOf0(xs) != sz00,
inference(cnf_transformation,[],[f164]) ).
tcf(c_111,plain,
aVector0(sziznziztdt0(xs)),
inference(cnf_transformation,[],[f174]) ).
tcf(c_112,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(cnf_transformation,[],[f173]) ).
tcf(c_113,plain,
! [X0: $i] :
( ( sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_114,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(cnf_transformation,[],[f171]) ).
tcf(c_115,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(cnf_transformation,[],[f178]) ).
tcf(c_116,plain,
( aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_549,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0)
| ( aDimensionOf0(X1) != X0 )
| ( szszuzczcdt0(X0) != aDimensionOf0(xs) ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_100]) ).
tcf(c_550,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0)
| ~ aNaturalNumber0(aDimensionOf0(X0))
| ( szszuzczcdt0(aDimensionOf0(X0)) != aDimensionOf0(xs) ) ),
inference(unflattening,[status(thm)],[c_549]) ).
tcf(c_552,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0)
| ( szszuzczcdt0(aDimensionOf0(X0)) != aDimensionOf0(xs) ) ),
inference(global_subsumption_just,[status(thm)],[c_550,c_88,c_550]) ).
tcf(c_952,plain,
! [X0_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0_iProver_aDimensionOf0_1,X0_iProver_aDimensionOf0_1))
| ~ aVector0(X0_iProver_aDimensionOf0_1)
| ( szszuzczcdt0(aDimensionOf0(X0_iProver_aDimensionOf0_1)) != aDimensionOf0(xs) ) ),
inference(subtyping,[status(esa)],[c_552]) ).
tcf(c_953,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(subtyping,[status(esa)],[c_115]) ).
tcf(c_954,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(subtyping,[status(esa)],[c_114]) ).
tcf(c_955,plain,
! [X0_iProver_szszuzczcdt0_0: iProver_szszuzczcdt0_0] :
( ( sdtlbdtrb0(sziznziztdt0(xs),X0_iProver_szszuzczcdt0_0) = sdtlbdtrb0(xs,X0_iProver_szszuzczcdt0_0) )
| ~ aNaturalNumber0(X0_iProver_szszuzczcdt0_0) ),
inference(subtyping,[status(esa)],[c_113]) ).
tcf(c_956,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(subtyping,[status(esa)],[c_112]) ).
tcf(c_958,plain,
aDimensionOf0(xs) != sz00,
inference(subtyping,[status(esa)],[c_101]) ).
tcf(c_960,plain,
! [X0_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1,X1_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1] :
( ( aDimensionOf0(X1_iProver_aDimensionOf0_1) = sz00 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0_iProver_aDimensionOf0_1),sziznziztdt0(X1_iProver_aDimensionOf0_1)),sdtasdt0(sdtlbdtrb0(X0_iProver_aDimensionOf0_1,aDimensionOf0(X0_iProver_aDimensionOf0_1)),sdtlbdtrb0(X1_iProver_aDimensionOf0_1,aDimensionOf0(X1_iProver_aDimensionOf0_1)))) = sdtasasdt0(X0_iProver_aDimensionOf0_1,X1_iProver_aDimensionOf0_1) )
| ~ aVector0(X1_iProver_aDimensionOf0_1)
| ~ aVector0(X0_iProver_aDimensionOf0_1)
| ( aDimensionOf0(X0_iProver_aDimensionOf0_1) != aDimensionOf0(X1_iProver_aDimensionOf0_1) ) ),
inference(subtyping,[status(esa)],[c_98]) ).
tcf(c_962,plain,
! [X0_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1,X1_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1] :
( aScalar0(sdtasasdt0(X0_iProver_aDimensionOf0_1,X1_iProver_aDimensionOf0_1))
| ~ aVector0(X1_iProver_aDimensionOf0_1)
| ~ aVector0(X0_iProver_aDimensionOf0_1)
| ( aDimensionOf0(X0_iProver_aDimensionOf0_1) != aDimensionOf0(X1_iProver_aDimensionOf0_1) ) ),
inference(subtyping,[status(esa)],[c_96]) ).
tcf(c_963,plain,
! [X0_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1,X1_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1] :
( ( aDimensionOf0(X1_iProver_aDimensionOf0_1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(X0_iProver_aDimensionOf0_1)) = aDimensionOf0(sziznziztdt0(X1_iProver_aDimensionOf0_1)) )
| ~ aVector0(X1_iProver_aDimensionOf0_1)
| ~ aVector0(X0_iProver_aDimensionOf0_1)
| ( aDimensionOf0(X0_iProver_aDimensionOf0_1) != aDimensionOf0(X1_iProver_aDimensionOf0_1) ) ),
inference(subtyping,[status(esa)],[c_95]) ).
tcf(c_969,plain,
! [X0_iProver_szszuzczcdt0_0: iProver_szszuzczcdt0_0,X0_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1] :
( aScalar0(sdtlbdtrb0(X0_iProver_aDimensionOf0_1,X0_iProver_szszuzczcdt0_0))
| ~ aVector0(X0_iProver_aDimensionOf0_1)
| ~ aNaturalNumber0(X0_iProver_szszuzczcdt0_0) ),
inference(subtyping,[status(esa)],[c_89]) ).
tcf(c_974,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sz0z00,sdtpldt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2))
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(sz0z00,X1_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(sz0z00,X0_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_84]) ).
tcf(c_975,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(X1_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2)
| sdtlseqdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_83]) ).
tcf(c_978,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(X0_iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2)
| ~ aScalar0(X2_iProver_sdtlseqdt0_2)
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X1_iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_80]) ).
tcf(c_1000,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( aScalar0(sdtasdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2))
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(subtyping,[status(esa)],[c_58]) ).
tcf(c_1007,plain,
! [X0_iProver_szszuzczcdt0_0: iProver_szszuzczcdt0_0] :
( aNaturalNumber0(szszuzczcdt0(X0_iProver_szszuzczcdt0_0))
| ~ aNaturalNumber0(X0_iProver_szszuzczcdt0_0) ),
inference(subtyping,[status(esa)],[c_50]) ).
tcf(c_1016,plain,
! [X0_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1] : X0_iProver_aDimensionOf0_1 = X0_iProver_aDimensionOf0_1,
theory(equality) ).
tcf(c_1017,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] : X0_iProver_sdtlseqdt0_2 = X0_iProver_sdtlseqdt0_2,
theory(equality) ).
tcf(c_1020,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( X2_iProver_sdtlseqdt0_2 = X0_iProver_sdtlseqdt0_2 )
| ( X2_iProver_sdtlseqdt0_2 != X1_iProver_sdtlseqdt0_2 )
| ( X0_iProver_sdtlseqdt0_2 != X1_iProver_sdtlseqdt0_2 ) ),
theory(equality) ).
tcf(c_1027,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X3_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(X0_iProver_sdtlseqdt0_2,X2_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X1_iProver_sdtlseqdt0_2,X3_iProver_sdtlseqdt0_2)
| ( X2_iProver_sdtlseqdt0_2 != X3_iProver_sdtlseqdt0_2 )
| ( X0_iProver_sdtlseqdt0_2 != X1_iProver_sdtlseqdt0_2 ) ),
theory(equality) ).
tcf(c_1028,plain,
! [X0_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1,X1_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1] :
( ( aDimensionOf0(X0_iProver_aDimensionOf0_1) = aDimensionOf0(X1_iProver_aDimensionOf0_1) )
| ( X0_iProver_aDimensionOf0_1 != X1_iProver_aDimensionOf0_1 ) ),
theory(equality) ).
tcf(c_1032,plain,
! [X0_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1,X1_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1,X2_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1,X3_iProver_aDimensionOf0_1: iProver_aDimensionOf0_1] :
( ( sdtasasdt0(X0_iProver_aDimensionOf0_1,X2_iProver_aDimensionOf0_1) = sdtasasdt0(X1_iProver_aDimensionOf0_1,X3_iProver_aDimensionOf0_1) )
| ( X2_iProver_aDimensionOf0_1 != X3_iProver_aDimensionOf0_1 )
| ( X0_iProver_aDimensionOf0_1 != X1_iProver_aDimensionOf0_1 ) ),
theory(equality) ).
tcf(c_1037,plain,
( ( aDimensionOf0(xs) = aDimensionOf0(xs) )
| ( xs != xs ) ),
inference(instantiation,[status(thm)],[c_1028]) ).
tcf(c_1040,plain,
( ( sdtasasdt0(xs,xs) = sdtasasdt0(xs,xs) )
| ( xs != xs ) ),
inference(instantiation,[status(thm)],[c_1032]) ).
tcf(c_1043,plain,
xs = xs,
inference(instantiation,[status(thm)],[c_1016]) ).
tcf(c_1044,plain,
sz0z00 = sz0z00,
inference(instantiation,[status(thm)],[c_1017]) ).
tcf(c_1047,plain,
( ( aDimensionOf0(xs) = sz00 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtasasdt0(xs,xs) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) ) ),
inference(instantiation,[status(thm)],[c_960]) ).
tcf(c_1048,plain,
( aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) ) ),
inference(instantiation,[status(thm)],[c_962]) ).
tcf(c_1049,plain,
( ( aDimensionOf0(xs) = sz00 )
| ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xs)) )
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != aDimensionOf0(xs) ) ),
inference(instantiation,[status(thm)],[c_963]) ).
tcf(c_2203,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ) ),
inference(instantiation,[status(thm)],[c_952]) ).
tcf(c_2207,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| sdtlseqdt0(sdtasasdt0(xs,xs),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(xs,xs)) ),
inference(instantiation,[status(thm)],[c_975]) ).
tcf(c_2218,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(X1_iProver_sdtlseqdt0_2,X0_iProver_sdtlseqdt0_2)
| ( sz0z00 != X1_iProver_sdtlseqdt0_2 )
| ( sdtasasdt0(xs,xs) != X0_iProver_sdtlseqdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1027]) ).
tcf(c_2390,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtasasdt0(xs,xs) = X1_iProver_sdtlseqdt0_2 )
| ( X1_iProver_sdtlseqdt0_2 != X0_iProver_sdtlseqdt0_2 )
| ( sdtasasdt0(xs,xs) != X0_iProver_sdtlseqdt0_2 ) ),
inference(instantiation,[status(thm)],[c_1020]) ).
tcf(c_2646,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( ( sdtasasdt0(xs,xs) = X0_iProver_sdtlseqdt0_2 )
| ( X0_iProver_sdtlseqdt0_2 != sdtasasdt0(xs,xs) )
| ( sdtasasdt0(xs,xs) != sdtasasdt0(xs,xs) ) ),
inference(instantiation,[status(thm)],[c_2390]) ).
tcf(c_3024,plain,
( aNaturalNumber0(aDimensionOf0(xs))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(superposition,[status(thm)],[c_956,c_1007]) ).
tcf(c_3029,plain,
aNaturalNumber0(aDimensionOf0(xs)),
inference(global_subsumption_just,[status(thm)],[c_3024,c_99,c_116]) ).
tcf(c_3216,plain,
( ( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) )
| ( sdtasasdt0(xs,xs) != sdtasasdt0(xs,xs) )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) != sdtasasdt0(xs,xs) ) ),
inference(instantiation,[status(thm)],[c_2646]) ).
tcf(c_3430,plain,
sdtlbdtrb0(sziznziztdt0(xs),aDimensionOf0(xs)) = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(superposition,[status(thm)],[c_3029,c_955]) ).
tcf(c_3745,plain,
( aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ~ aNaturalNumber0(aDimensionOf0(xs)) ),
inference(superposition,[status(thm)],[c_3430,c_969]) ).
tcf(c_4251,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ( sz0z00 != X0_iProver_sdtlseqdt0_2 )
| ( sdtasasdt0(xs,xs) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(instantiation,[status(thm)],[c_2218]) ).
tcf(c_4252,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ( sz0z00 != sz0z00 )
| ( sdtasasdt0(xs,xs) != sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ) ),
inference(instantiation,[status(thm)],[c_4251]) ).
tcf(c_4415,plain,
( aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)) ) ),
inference(instantiation,[status(thm)],[c_962]) ).
tcf(c_5710,plain,
( sdtlseqdt0(sdtasasdt0(xs,xs),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(xs,xs)) ),
inference(superposition,[status(thm)],[c_975,c_953]) ).
tcf(c_5728,plain,
sdtlseqdt0(sdtasasdt0(xs,xs),sz0z00),
inference(global_subsumption_just,[status(thm)],[c_5710,c_99,c_56,c_115,c_1037,c_1043,c_1048,c_2207]) ).
tcf(c_6283,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sdtasasdt0(xs,xs),X0_iProver_sdtlseqdt0_2)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(sz0z00,X0_iProver_sdtlseqdt0_2)
| ~ aScalar0(sdtasasdt0(xs,xs)) ),
inference(superposition,[status(thm)],[c_5728,c_978]) ).
tcf(c_6728,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sdtasasdt0(xs,xs),X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(sz0z00,X0_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2) ),
inference(global_subsumption_just,[status(thm)],[c_6283,c_99,c_56,c_1037,c_1043,c_1048,c_6283]) ).
tcf(c_6729,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sdtasasdt0(xs,xs),X0_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(sz0z00,X0_iProver_sdtlseqdt0_2) ),
inference(renaming,[status(thm)],[c_6728]) ).
tcf(c_6730,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sdtasasdt0(xs,xs),X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(sz0z00,X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(sdtasasdt0(xs,xs)) ),
inference(superposition,[status(thm)],[c_6729,c_978]) ).
tcf(c_6739,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sdtasasdt0(xs,xs),X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X1_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(sz0z00,X0_iProver_sdtlseqdt0_2)
| ~ sdtlseqdt0(X0_iProver_sdtlseqdt0_2,X1_iProver_sdtlseqdt0_2) ),
inference(global_subsumption_just,[status(thm)],[c_6730,c_99,c_1037,c_1043,c_1048,c_6730]) ).
tcf(c_6741,plain,
! [X0_iProver_sdtlseqdt0_2: iProver_sdtlseqdt0_2] :
( sdtlseqdt0(sdtasasdt0(xs,xs),X0_iProver_sdtlseqdt0_2)
| ~ aScalar0(X0_iProver_sdtlseqdt0_2)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),X0_iProver_sdtlseqdt0_2) ),
inference(superposition,[status(thm)],[c_954,c_6739]) ).
tcf(c_6798,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(instantiation,[status(thm)],[c_974]) ).
tcf(c_6944,plain,
~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(global_subsumption_just,[status(thm)],[c_6741,c_99,c_111,c_115,c_114,c_1037,c_1040,c_1043,c_1044,c_956,c_958,c_1047,c_1049,c_2203,c_3216,c_4252,c_4415,c_6798]) ).
tcf(c_6946,plain,
~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(superposition,[status(thm)],[c_1000,c_6944]) ).
tcf(c_6947,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6946,c_3745,c_116,c_111,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG049+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 07:56:23 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 6.32/1.76 % SZS status Started for theBenchmark.p
% 6.32/1.76 % SZS status Theorem for theBenchmark.p
% 6.32/1.76
% 6.32/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.32/1.76
% 6.32/1.76 % ------ iProver source info
% 6.32/1.76
% 6.32/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 6.32/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.32/1.76 % git: non_committed_changes: false
% 6.32/1.76
% 6.32/1.76 % ------ Parsing...
% 6.32/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.32/1.76
% 6.32/1.76 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 6.32/1.76
% 6.32/1.76 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.32/1.76
% 6.32/1.76 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 6.32/1.76 % ------ Proving...
% 6.32/1.76 % ------ Problem Properties
% 6.32/1.76
% 6.32/1.76 %
% 6.32/1.76 % clauses 60
% 6.32/1.76 % conjectures 1
% 6.32/1.76 % EPR 10
% 6.32/1.76 % Horn 48
% 6.32/1.76 % unary 8
% 6.32/1.76 % binary 18
% 6.32/1.76 % lits 191
% 6.32/1.76 % lits eq 53
% 6.32/1.76 % fd_pure 0
% 6.32/1.76 % fd_pseudo 0
% 6.32/1.76 % fd_cond 1
% 6.32/1.76 % fd_pseudo_cond 5
% 6.32/1.76 % AC symbols 0
% 6.32/1.76
% 6.32/1.76 % ------ Input Options Time Limit: Unbounded
% 6.32/1.76
% 6.32/1.76
% 6.32/1.76 % ------
% 6.32/1.76 % Current options:
% 6.32/1.76 % ------
% 6.32/1.76
% 6.32/1.76
% 6.32/1.76 %
% 6.32/1.76
% 6.32/1.76 % ------ Proving...
% 6.32/1.76 %
% 6.32/1.76
% 6.32/1.76 % SZS status Theorem for theBenchmark.p
% 6.32/1.76
% 6.32/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.32/1.76
% 6.32/1.76
%------------------------------------------------------------------------------