%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG048+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 : n010.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 02:38:18 PM UTC 2026
% Result : Theorem 6.96s 16.77s
% Output : CNFRefutation 6.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 21
% Syntax : Number of formulae : 165 ( 25 unt; 2 def)
% Number of atoms : 714 ( 211 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 766 ( 325 ~; 344 |; 62 &)
% ( 3 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 201 ( 0 sgn 196 !; 5 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> iLess0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(f13,axiom,
! [X0] :
( aScalar0(X0)
=> ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(X0)) = X0
& sdtpldt0(smndt0(X0),X0) = sz0z00
& sdtpldt0(X0,smndt0(X0)) = sz0z00
& sdtasdt0(sz0z00,X0) = sz0z00
& sdtasdt0(X0,sz0z00) = sz0z00
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
fof(f20,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
fof(f21,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEASm) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
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/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
fof(f27,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
fof(f30,axiom,
! [X0] :
( aVector0(X0)
=> aNaturalNumber0(aDimensionOf0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aVector0(X0) )
=> aScalar0(sdtlbdtrb0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
fof(f32,axiom,
! [X0] :
( aVector0(X0)
=> ( aDimensionOf0(X0) != sz00
=> ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( ! [X2] :
( aNaturalNumber0(X2)
=> sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
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/sandbox2/benchmark/theBenchmark.p',mEqInit) ).
fof(f34,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( aDimensionOf0(X0) = aDimensionOf0(X1)
=> aScalar0(sdtasasdt0(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
fof(f35,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( aDimensionOf0(X1) = sz00
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> sdtasasdt0(X0,X1) = sz0z00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).
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/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).
fof(f37,conjecture,
! [X0] :
( aVector0(X0)
=> ( ! [X1] :
( aVector0(X1)
=> ( iLess0(aDimensionOf0(X1),aDimensionOf0(X0))
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ) )
=> sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( aVector0(X0)
=> ( ! [X1] :
( aVector0(X1)
=> ( iLess0(aDimensionOf0(X1),aDimensionOf0(X0))
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ) )
=> sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f49,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f53,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f52]) ).
fof(f55,plain,
! [X0] :
( ~ aScalar0(X0)
| ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(X0)) = X0
& sdtpldt0(smndt0(X0),X0) = sz0z00
& sdtpldt0(X0,smndt0(X0)) = sz0z00
& sdtasdt0(sz0z00,X0) = sz0z00
& sdtasdt0(X0,sz0z00) = sz0z00
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f66,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(X0,X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f67,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f67]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ),
inference(flattening,[],[f71]) ).
fof(f77,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(f78,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,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f82,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(X0)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aVector0(X0)
| aScalar0(sdtlbdtrb0(X0,X1)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aVector0(X0)
| aScalar0(sdtlbdtrb0(X0,X1)) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f86,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) ) ),
inference(flattening,[],[f85]) ).
fof(f87,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(f88,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f90,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X0,X1)) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sz0z00 ),
inference(ennf_transformation,[],[f35]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sz0z00 ),
inference(flattening,[],[f91]) ).
fof(f93,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(f94,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,[],[f93]) ).
fof(f95,plain,
? [X0] :
( aVector0(X0)
& ! [X1] :
( ~ aVector0(X1)
| ~ iLess0(aDimensionOf0(X1),aDimensionOf0(X0))
| sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) )
& ~ sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
inference(ennf_transformation,[],[f38]) ).
fof(f96,plain,
? [X0] :
( aVector0(X0)
& ! [X1] :
( ~ aVector0(X1)
| ~ iLess0(aDimensionOf0(X1),aDimensionOf0(X0))
| sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) )
& ~ sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
inference(flattening,[],[f95]) ).
fof(f98,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(nnf_transformation,[],[f86]) ).
fof(f99,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X3] :
( ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X3] :
( ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtlbdtrb0(X1,sK1(X0,X1)) != sdtlbdtrb0(X0,sK1(X0,X1)) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f100]) ).
fof(f102,plain,
( aVector0(sK2)
& ! [X1] :
( ~ aVector0(X1)
| ~ iLess0(aDimensionOf0(X1),aDimensionOf0(sK2))
| sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) )
& ~ sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f96]) ).
fof(f109,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f110,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f112,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f117,plain,
! [X0] :
( ~ aScalar0(X0)
| sz0z00 = sdtpldt0(X0,smndt0(X0)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f132,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f133,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f139,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f140,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f142,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(X0)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f143,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aVector0(X0)
| aScalar0(sdtlbdtrb0(X0,X1)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f144,plain,
! [X3,X0,X1] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| sziznziztdt0(X0) != X1
| ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3) ),
inference(cnf_transformation,[],[f101]) ).
fof(f145,plain,
! [X0,X1] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| sziznziztdt0(X0) != X1
| aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f146,plain,
! [X0,X1] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| sziznziztdt0(X0) != X1
| aVector0(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f149,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f150,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f151,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz0z00 = sdtasasdt0(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f152,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,[],[f94]) ).
fof(f153,plain,
aVector0(sK2),
inference(cnf_transformation,[],[f102]) ).
fof(f154,plain,
! [X1] :
( ~ aVector0(X1)
| ~ iLess0(aDimensionOf0(X1),aDimensionOf0(sK2))
| sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f155,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2)),
inference(cnf_transformation,[],[f102]) ).
fof(f156,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| aVector0(sziznziztdt0(X0)) ),
inference(equality_resolution,[],[f146]) ).
fof(f157,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) ),
inference(equality_resolution,[],[f145]) ).
fof(f158,plain,
! [X3,X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X0,X3) = sdtlbdtrb0(sziznziztdt0(X0),X3) ),
inference(equality_resolution,[],[f144]) ).
tcf(c_55,plain,
! [X0: $i] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_56,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f110]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_64,plain,
! [X0: $i] :
( ( sdtpldt0(X0,smndt0(X0)) = sz0z00 )
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_78,plain,
! [X0: $i] :
( sdtlseqdt0(X0,X0)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
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,[],[f139]) ).
tcf(c_86,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_88,plain,
! [X0: $i] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtlbdtrb0(X1,X0))
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_92,plain,
! [X0: $i] :
( aVector0(sziznziztdt0(X0))
| ( aDimensionOf0(X0) = sz00 )
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_93,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = sz00 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) = aDimensionOf0(X0) )
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = sz00 )
| ( sdtlbdtrb0(sziznziztdt0(X1),X0) = sdtlbdtrb0(X1,X0) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f158]) ).
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,[],[f149]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasasdt0(X0,X1))
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( ( sdtasasdt0(X0,X1) = sz0z00 )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X1) != sz00 )
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(cnf_transformation,[],[f151]) ).
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,[],[f152]) ).
tcf(c_99,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2)),
inference(cnf_transformation,[],[f155]) ).
tcf(c_100,negated_conjecture,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0)
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(sK2)) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_101,negated_conjecture,
aVector0(sK2),
inference(cnf_transformation,[],[f153]) ).
tcf(c_103,plain,
( sdtlseqdt0(sz0z00,sz0z00)
| ~ aScalar0(sz0z00) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_130,plain,
( ( sz0z00 = sz0z00 )
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sz0z00,sz0z00) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0)
| ( aDimensionOf0(X1) != X0 )
| ( szszuzczcdt0(X0) != aDimensionOf0(sK2) ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_100]) ).
tcf(c_873,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0)
| ~ aNaturalNumber0(aDimensionOf0(X0))
| ( szszuzczcdt0(aDimensionOf0(X0)) != aDimensionOf0(sK2) ) ),
inference(unflattening,[status(thm)],[c_872]) ).
tcf(c_875,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0)
| ( szszuzczcdt0(aDimensionOf0(X0)) != aDimensionOf0(sK2) ) ),
inference(global_subsumption_just,[status(thm)],[c_873,c_88,c_873]) ).
tcf(c_1609,definition,
iPr_def_13 = aDimensionOf0(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1610,definition,
iPr_def_14 = sdtasasdt0(sK2,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1611,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0)
| ( szszuzczcdt0(aDimensionOf0(X0)) != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_875,c_1609]) ).
tcf(c_1612,negated_conjecture,
aVector0(sK2),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_1613,negated_conjecture,
~ sdtlseqdt0(sz0z00,iPr_def_14),
inference(demodulation,[status(thm)],[c_99,c_1610]) ).
tcf(c_1614,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2536,plain,
( aNaturalNumber0(iPr_def_13)
| ~ aVector0(sK2) ),
inference(superposition,[status(thm)],[c_1609,c_88]) ).
tcf(c_2537,plain,
aNaturalNumber0(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_2536,c_1612]) ).
tcf(c_2947,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = sz00 )
| ( sdtlbdtrb0(sziznziztdt0(X0),iPr_def_13) = sdtlbdtrb0(X0,iPr_def_13) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_2537,c_94]) ).
tcf(c_2972,plain,
( aVector0(sziznziztdt0(sK2))
| ( aDimensionOf0(sK2) = sz00 )
| ~ aVector0(sK2) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_3055,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = sz00 )
| ( aDimensionOf0(sziznziztdt0(sK2)) = aDimensionOf0(sziznziztdt0(X0)) )
| ~ aVector0(sK2)
| ~ aVector0(X0)
| ( aDimensionOf0(sK2) != aDimensionOf0(X0) ) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_3057,plain,
! [X0: $i] :
( ( sdtasasdt0(sK2,X0) = sz0z00 )
| ~ aVector0(sK2)
| ~ aVector0(X0)
| ( aDimensionOf0(sK2) != aDimensionOf0(X0) )
| ( aDimensionOf0(X0) != sz00 ) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_3059,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,iPr_def_14)
| ~ sdtlseqdt0(X0,X1)
| ( iPr_def_14 != X1 )
| ( sz0z00 != X0 ) ),
inference(instantiation,[status(thm)],[c_1623]) ).
tcf(c_3175,plain,
( ( aDimensionOf0(sK2) = sz00 )
| ( sdtlbdtrb0(sziznziztdt0(sK2),iPr_def_13) = sdtlbdtrb0(sK2,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_1612,c_2947]) ).
tcf(c_3176,plain,
( ( sz00 = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sK2),iPr_def_13) = sdtlbdtrb0(sK2,iPr_def_13) ) ),
inference(light_normalisation,[status(thm)],[c_3175,c_1609]) ).
tcf(c_3193,plain,
( aScalar0(sdtlbdtrb0(sK2,iPr_def_13))
| ( sz00 = iPr_def_13 )
| ~ aNaturalNumber0(iPr_def_13)
| ~ aVector0(sziznziztdt0(sK2)) ),
inference(superposition,[status(thm)],[c_3176,c_89]) ).
tcf(c_3194,plain,
( aScalar0(sdtlbdtrb0(sK2,iPr_def_13))
| ( sz00 = iPr_def_13 )
| ~ aVector0(sziznziztdt0(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3193,c_2537]) ).
tcf(c_3404,plain,
( ( aDimensionOf0(sK2) = sz00 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sK2))) = aDimensionOf0(sK2) ) ),
inference(superposition,[status(thm)],[c_1612,c_93]) ).
tcf(c_3405,plain,
( ( sz00 = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sK2))) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3404,c_1609]) ).
tcf(c_3440,plain,
! [X0: $i] :
( aScalar0(sdtasasdt0(X0,X0))
| ~ aVector0(X0) ),
inference(equality_resolution,[status(thm)],[c_96]) ).
tcf(c_3458,plain,
( aScalar0(iPr_def_14)
| ~ aVector0(sK2) ),
inference(superposition,[status(thm)],[c_1610,c_3440]) ).
tcf(c_3477,plain,
aScalar0(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_3458,c_1612]) ).
tcf(c_3538,plain,
( ( aDimensionOf0(sK2) = sz00 )
| ( aDimensionOf0(sziznziztdt0(sK2)) = aDimensionOf0(sziznziztdt0(sK2)) )
| ~ aVector0(sK2)
| ( aDimensionOf0(sK2) != aDimensionOf0(sK2) ) ),
inference(instantiation,[status(thm)],[c_3055]) ).
tcf(c_3539,plain,
( ( sdtasasdt0(sK2,sK2) = sz0z00 )
| ~ aVector0(sK2)
| ( aDimensionOf0(sK2) != sz00 )
| ( aDimensionOf0(sK2) != aDimensionOf0(sK2) ) ),
inference(instantiation,[status(thm)],[c_3057]) ).
tcf(c_3544,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,iPr_def_14)
| ~ sdtlseqdt0(X0,iPr_def_14)
| ( iPr_def_14 != iPr_def_14 )
| ( sz0z00 != X0 ) ),
inference(instantiation,[status(thm)],[c_3059]) ).
tcf(c_3545,plain,
iPr_def_14 = iPr_def_14,
inference(instantiation,[status(thm)],[c_1614]) ).
tcf(c_3571,plain,
sdtpldt0(iPr_def_14,smndt0(iPr_def_14)) = sz0z00,
inference(superposition,[status(thm)],[c_3477,c_64]) ).
tcf(c_3642,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ( sz00 = iPr_def_13 )
| ~ aVector0(sziznziztdt0(sK2)) ),
inference(superposition,[status(thm)],[c_3405,c_1611]) ).
tcf(c_3883,plain,
aDimensionOf0(sK2) = aDimensionOf0(sK2),
inference(instantiation,[status(thm)],[c_1614]) ).
tcf(c_4666,plain,
( sdtlseqdt0(sz0z00,iPr_def_14)
| ~ sdtlseqdt0(iPr_def_14,iPr_def_14)
| ( iPr_def_14 != iPr_def_14 )
| ( sz0z00 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_3544]) ).
tcf(c_4667,plain,
( sdtlseqdt0(iPr_def_14,iPr_def_14)
| ~ aScalar0(iPr_def_14) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_4676,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X1,sdtasasdt0(sK2,sK2))
| ~ sdtlseqdt0(X2,X0)
| ( X1 != X2 )
| ( sdtasasdt0(sK2,sK2) != X0 ) ),
inference(instantiation,[status(thm)],[c_1623]) ).
tcf(c_4677,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2))
| ~ sdtlseqdt0(sz0z00,sz0z00)
| ( sz0z00 != sz0z00 )
| ( sdtasasdt0(sK2,sK2) != sz0z00 ) ),
inference(instantiation,[status(thm)],[c_4676]) ).
tcf(c_5038,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,sK2) = sz0z00 )
| ~ aVector0(sK2)
| ~ aVector0(X0)
| ( aDimensionOf0(sK2) != sz00 )
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1609,c_97]) ).
tcf(c_5043,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,sK2) = sz0z00 )
| ~ aVector0(sK2)
| ~ aVector0(X0)
| ( sz00 != iPr_def_13 )
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_5038,c_1609]) ).
tcf(c_5044,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,sK2) = sz0z00 )
| ~ aVector0(X0)
| ( sz00 != iPr_def_13 )
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5043,c_1612]) ).
tcf(c_5101,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,sdtpldt0(X1,X0))
| ~ aScalar0(iPr_def_14)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(smndt0(iPr_def_14))
| ~ sdtlseqdt0(iPr_def_14,X1)
| ~ sdtlseqdt0(smndt0(iPr_def_14),X0) ),
inference(superposition,[status(thm)],[c_3571,c_81]) ).
tcf(c_5163,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,sdtpldt0(X1,X0))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(smndt0(iPr_def_14))
| ~ sdtlseqdt0(iPr_def_14,X1)
| ~ sdtlseqdt0(smndt0(iPr_def_14),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5101,c_3477]) ).
tcf(c_5491,plain,
! [X0: $i] :
( aScalar0(sdtasasdt0(sziznziztdt0(sK2),X0))
| ~ aVector0(X0)
| ~ aVector0(sziznziztdt0(sK2))
| ( aDimensionOf0(sziznziztdt0(sK2)) != aDimensionOf0(X0) ) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_5740,plain,
( ( sdtasasdt0(sK2,sK2) = sz0z00 )
| ~ aVector0(sK2)
| ( sz00 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1609,c_5044]) ).
tcf(c_5741,plain,
( ( sz0z00 = iPr_def_14 )
| ~ aVector0(sK2)
| ( sz00 != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_5740,c_1610]) ).
tcf(c_5742,plain,
( ( sz0z00 = iPr_def_14 )
| ( sz00 != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5741,c_1612]) ).
tcf(c_5745,plain,
sz00 != iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_5742,c_1613,c_3477,c_3545,c_4666,c_4667,c_5742]) ).
tcf(c_5747,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(sK2))) = iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_3405,c_5745]) ).
tcf(c_5751,plain,
( aScalar0(sdtlbdtrb0(sK2,iPr_def_13))
| ~ aVector0(sziznziztdt0(sK2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3194,c_5745]) ).
tcf(c_5789,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ~ aVector0(sziznziztdt0(sK2)) ),
inference(superposition,[status(thm)],[c_5747,c_1611]) ).
tcf(c_5806,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2))),
inference(global_subsumption_just,[status(thm)],[c_5789,c_101,c_56,c_99,c_103,c_130,c_1613,c_2972,c_3477,c_3539,c_3545,c_3642,c_3883,c_4666,c_4667,c_4677,c_5742]) ).
tcf(c_6212,plain,
! [X0: $i] :
( ( aDimensionOf0(sK2) = sz00 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(sK2,aDimensionOf0(sK2)))) = sdtasasdt0(X0,sK2) )
| ~ aVector0(sK2)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1609,c_98]) ).
tcf(c_6217,plain,
! [X0: $i] :
( ( sz00 = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(sK2,iPr_def_13))) = sdtasasdt0(X0,sK2) )
| ~ aVector0(sK2)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_6212,c_1609]) ).
tcf(c_6218,plain,
! [X0: $i] :
( ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(sK2,iPr_def_13))) = sdtasasdt0(X0,sK2) )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6217,c_5745,c_1612]) ).
tcf(c_6294,plain,
aScalar0(sdtlbdtrb0(sK2,iPr_def_13)),
inference(global_subsumption_just,[status(thm)],[c_5751,c_101,c_56,c_99,c_103,c_130,c_1613,c_2972,c_3194,c_3477,c_3539,c_3545,c_3883,c_4666,c_4667,c_4677,c_5742]) ).
tcf(c_6451,plain,
( ( sdtpldt0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)),sdtlbdtrb0(sK2,iPr_def_13))) = sdtasasdt0(sK2,sK2) )
| ~ aVector0(sK2) ),
inference(superposition,[status(thm)],[c_1609,c_6218]) ).
tcf(c_6452,plain,
( ( sdtpldt0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13))) = iPr_def_14 )
| ~ aVector0(sK2) ),
inference(light_normalisation,[status(thm)],[c_6451,c_1609,c_1610]) ).
tcf(c_6453,plain,
sdtpldt0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13))) = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_6452,c_1612]) ).
tcf(c_6454,plain,
( sdtlseqdt0(sz0z00,iPr_def_14)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13))) ),
inference(superposition,[status(thm)],[c_6453,c_84]) ).
tcf(c_6458,plain,
( ~ aScalar0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6454,c_1613,c_5806]) ).
tcf(c_6522,plain,
( ~ aScalar0(sdtlbdtrb0(sK2,iPr_def_13))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13))) ),
inference(superposition,[status(thm)],[c_86,c_6458]) ).
tcf(c_6523,plain,
( ~ aScalar0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6522,c_6294]) ).
tcf(c_9512,plain,
( aScalar0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ~ aVector0(sziznziztdt0(sK2))
| ( aDimensionOf0(sziznziztdt0(sK2)) != aDimensionOf0(sziznziztdt0(sK2)) ) ),
inference(instantiation,[status(thm)],[c_5491]) ).
tcf(c_10305,plain,
( sdtlseqdt0(sz0z00,iPr_def_14)
| ~ aScalar0(smndt0(iPr_def_14))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ~ sdtlseqdt0(iPr_def_14,sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13)))
| ~ sdtlseqdt0(smndt0(iPr_def_14),sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13))) ),
inference(superposition,[status(thm)],[c_6453,c_5163]) ).
tcf(c_10359,plain,
( ~ aScalar0(smndt0(iPr_def_14))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ~ sdtlseqdt0(iPr_def_14,sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13)))
| ~ sdtlseqdt0(smndt0(iPr_def_14),sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10305,c_1613]) ).
tcf(c_10402,plain,
~ aScalar0(sdtasdt0(sdtlbdtrb0(sK2,iPr_def_13),sdtlbdtrb0(sK2,iPr_def_13))),
inference(global_subsumption_just,[status(thm)],[c_10359,c_101,c_56,c_99,c_103,c_130,c_2972,c_3538,c_3539,c_3883,c_4677,c_6523,c_9512]) ).
tcf(c_10404,plain,
~ aScalar0(sdtlbdtrb0(sK2,iPr_def_13)),
inference(superposition,[status(thm)],[c_58,c_10402]) ).
tcf(c_10405,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10404,c_6294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/15.40 % Computer : n010.cluster.edu
% 0.02/15.40 % Model : x86_64 x86_64
% 0.02/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/15.40 % Memory : 8046.5625MB
% 0.02/15.40 % OS : Linux 6.8.0-71-generic
% 0.02/15.40 % CPULimit : 300
% 0.02/15.40 % WCLimit : 300
% 0.02/15.40 % DateTime : Thu Sep 24 07:58:02 UTC 2026
% 0.02/15.40 % CPUTime :
% 0.02/15.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/15.44 Running first-order theorem proving
% 0.02/15.44 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/15.45
% 0.02/15.45 % ======== iProver multi-core TPTP/SMT =========
% 0.02/15.45
% 0.02/15.45 % Detected problem language: tptp
% 0.02/15.46 % Proving...
% 6.96/16.77 % SZS status Started for theBenchmark.p
% 6.96/16.77 % SZS status Theorem for theBenchmark.p
% 6.96/16.77
% 6.96/16.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.96/16.77
% 6.96/16.77 % ------ iProver source info
% 6.96/16.77
% 6.96/16.77 % git: date: 2026-07-19 20:42:38 +0200
% 6.96/16.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.96/16.77 % git: non_committed_changes: false
% 6.96/16.77
% 6.96/16.77 % ------ Parsing...
% 6.96/16.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.96/16.77
% 6.96/16.77 % ------ 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 %
% 6.96/16.77
% 6.96/16.77 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.96/16.77
% 6.96/16.77 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 6.96/16.77 % ------ Proving...
% 6.96/16.77 % ------ Problem Properties
% 6.96/16.77
% 6.96/16.77 %
% 6.96/16.77 % clauses 57
% 6.96/16.77 % conjectures 2
% 6.96/16.77 % EPR 11
% 6.96/16.77 % Horn 45
% 6.96/16.77 % unary 7
% 6.96/16.77 % binary 16
% 6.96/16.77 % lits 186
% 6.96/16.77 % lits eq 52
% 6.96/16.77 % fd_pure 0
% 6.96/16.77 % fd_pseudo 0
% 6.96/16.77 % fd_cond 1
% 6.96/16.77 % fd_pseudo_cond 5
% 6.96/16.77 % AC symbols 0
% 6.96/16.77
% 6.96/16.77 % ------ Schedule dynamic 5 is on
% 6.96/16.77
% 6.96/16.77 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.96/16.77
% 6.96/16.77
% 6.96/16.77 % ------
% 6.96/16.77 % Current options:
% 6.96/16.77 % ------
% 6.96/16.77
% 6.96/16.77
% 6.96/16.77 %
% 6.96/16.77
% 6.96/16.77 % ------ Proving...
% 6.96/16.77 %
% 6.96/16.77
% 6.96/16.77 % SZS status Theorem for theBenchmark.p
% 6.96/16.77
% 6.96/16.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.96/16.77
% 6.96/16.77
%------------------------------------------------------------------------------