%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG049+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 : Thu Sep 24 02:05:38 PM UTC 2026
% Result : Theorem 3.69s 0.99s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 77 ( 24 unt; 0 def)
% Number of atoms : 259 ( 74 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 292 ( 110 ~; 97 |; 57 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEqInit,axiom,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( ( aDimensionOf0(X2) != sz00
& aDimensionOf0(X1) = aDimensionOf0(X2) )
=> aDimensionOf0(sziznziztdt0(X1)) = aDimensionOf0(sziznziztdt0(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEqInit) ).
fof(m__1542_01,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542_01) ).
fof(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(m__1542,hypothesis,
aVector0(xs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542) ).
fof(m__1568,hypothesis,
( ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs))
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1568) ).
fof(mDefSPN,axiom,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( ( aDimensionOf0(X2) != sz00
& aDimensionOf0(X1) = aDimensionOf0(X2) )
=> sdtasasdt0(X1,X2) = sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(X2)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(X2,aDimensionOf0(X2)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).
fof(mIH,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> iLess0(X1,szszuzczcdt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(m__,conjecture,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mPosMon,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(sz0z00,X2)
& sdtlseqdt0(sz0z00,X1) )
=> ( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
& sdtlseqdt0(sz0z00,sdtpldt0(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
fof(mLETrn,axiom,
! [X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETrn) ).
fof(m__1590,hypothesis,
( 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))
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1590) ).
fof(m__1516,hypothesis,
! [X1] :
( aVector0(X1)
=> ( iLess0(aDimensionOf0(X1),aDimensionOf0(xs))
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1516) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
fof(mScZero,axiom,
! [X1] :
( aScalar0(X1)
=> ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(X1)) = X1
& sdtpldt0(smndt0(X1),X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtpldt0(sz0z00,X1) = X1
& sdtpldt0(X1,sz0z00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(mSuccNat,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( szszuzczcdt0(X1) != sz00
& aNaturalNumber0(szszuzczcdt0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNat) ).
fof(mScPr,axiom,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( aDimensionOf0(X1) = aDimensionOf0(X2)
=> aScalar0(sdtasasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(mElmSc,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aVector0(X1) )
=> aScalar0(sdtlbdtrb0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
fof(c_0_19,plain,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( ( aDimensionOf0(X2) != sz00
& aDimensionOf0(X1) = aDimensionOf0(X2) )
=> aDimensionOf0(sziznziztdt0(X1)) = aDimensionOf0(sziznziztdt0(X2)) ) ),
inference(fof_simplification,[status(thm)],[mEqInit]) ).
fof(c_0_20,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_simplification,[status(thm)],[m__1542_01]) ).
fof(c_0_21,plain,
! [X67,X68] :
( aDimensionOf0(sziznziztdt0(X67)) = aDimensionOf0(sziznziztdt0(X68))
| aDimensionOf0(X68) = sz00
| aDimensionOf0(X67) != aDimensionOf0(X68)
| ~ aVector0(X68)
| ~ aVector0(X67) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_22,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X59] :
( aNaturalNumber0(aDimensionOf0(X59))
| ~ aVector0(X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDimNat])])]) ).
cnf(c_0_24,plain,
( aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| aDimensionOf0(sziznziztdt0(X1)) = aDimensionOf0(sziznziztdt0(X2))
| aDimensionOf0(X2) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1542]) ).
cnf(c_0_26,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_27,hypothesis,
! [X76,X77] :
( ( sdtlbdtrb0(sziznziztdt0(xs),X77) = sdtlbdtrb0(xs,X77)
| ~ aNaturalNumber0(X77) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs))
& ( sdtlbdtrb0(sziznziztdt0(xs),X76) = sdtlbdtrb0(xs,X76)
| ~ aNaturalNumber0(X76) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1568])])])]) ).
cnf(c_0_28,plain,
( ~ aVector0(X1)
| aNaturalNumber0(aDimensionOf0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,hypothesis,
( ~ aVector0(X1)
| aDimensionOf0(X1) != aDimensionOf0(xs)
| aDimensionOf0(sziznziztdt0(X1)) = aDimensionOf0(sziznziztdt0(xs)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,hypothesis,
aVector0(sziznziztdt0(xs)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,hypothesis,
( ~ aVector0(X1)
| aDimensionOf0(X1) != aDimensionOf0(xs)
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
fof(c_0_32,plain,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( ( aDimensionOf0(X2) != sz00
& aDimensionOf0(X1) = aDimensionOf0(X2) )
=> sdtasasdt0(X1,X2) = sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(X2)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(X2,aDimensionOf0(X2)))) ) ),
inference(fof_simplification,[status(thm)],[mDefSPN]) ).
fof(c_0_33,plain,
! [X13] :
( iLess0(X13,szszuzczcdt0(X13))
| ~ aNaturalNumber0(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH])])]) ).
cnf(c_0_34,hypothesis,
( ~ aVector0(X1)
| aDimensionOf0(X1) != aDimensionOf0(xs)
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
fof(c_0_35,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_36,plain,
! [X53,X54] :
( ( ~ aScalar0(X54)
| ~ aScalar0(X53)
| ~ sdtlseqdt0(sz0z00,X54)
| ~ sdtlseqdt0(sz0z00,X53)
| sdtlseqdt0(sz0z00,sdtasdt0(X53,X54)) )
& ( ~ aScalar0(X54)
| ~ aScalar0(X53)
| ~ sdtlseqdt0(sz0z00,X54)
| ~ sdtlseqdt0(sz0z00,X53)
| sdtlseqdt0(sz0z00,sdtpldt0(X53,X54)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])])]) ).
fof(c_0_37,plain,
! [X73,X74] :
( sdtasasdt0(X73,X74) = sdtpldt0(sdtasasdt0(sziznziztdt0(X73),sziznziztdt0(X74)),sdtasdt0(sdtlbdtrb0(X73,aDimensionOf0(X73)),sdtlbdtrb0(X74,aDimensionOf0(X74))))
| aDimensionOf0(X74) = sz00
| aDimensionOf0(X73) != aDimensionOf0(X74)
| ~ aVector0(X74)
| ~ aVector0(X73) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
fof(c_0_38,plain,
! [X40,X41,X42] :
( sdtlseqdt0(X40,X42)
| ~ sdtlseqdt0(X41,X42)
| ~ sdtlseqdt0(X40,X41)
| ~ aScalar0(X42)
| ~ aScalar0(X41)
| ~ aScalar0(X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETrn])])]) ).
fof(c_0_39,hypothesis,
! [X78,X79] :
( sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
& ( sdtlbdtrb0(sziznziztdt0(xs),X79) = sdtlbdtrb0(xs,X79)
| ~ aNaturalNumber0(X79) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs))
& ( sdtlbdtrb0(sziznziztdt0(xs),X78) = sdtlbdtrb0(xs,X78)
| ~ aNaturalNumber0(X78) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1590])])])]) ).
fof(c_0_40,hypothesis,
! [X75] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X75,X75))
| ~ iLess0(aDimensionOf0(X75),aDimensionOf0(xs))
| ~ aVector0(X75) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1516])])]) ).
cnf(c_0_41,plain,
( ~ aNaturalNumber0(X1)
| iLess0(X1,szszuzczcdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,hypothesis,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_43,hypothesis,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_25])]) ).
fof(c_0_44,plain,
! [X55] :
( sdtlseqdt0(sz0z00,sdtasdt0(X55,X55))
| ~ aScalar0(X55) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])])]) ).
fof(c_0_45,plain,
! [X20] :
( ( ~ aScalar0(X20)
| smndt0(sz0z00) = sz0z00 )
& ( ~ aScalar0(X20)
| smndt0(smndt0(X20)) = X20 )
& ( ~ aScalar0(X20)
| sdtpldt0(smndt0(X20),X20) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtpldt0(X20,smndt0(X20)) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtasdt0(sz0z00,X20) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtasdt0(X20,sz0z00) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtpldt0(sz0z00,X20) = X20 )
& ( ~ aScalar0(X20)
| sdtpldt0(X20,sz0z00) = X20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])])]) ).
fof(c_0_46,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
cnf(c_0_47,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtlseqdt0(sz0z00,sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,plain,
( aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| sdtasasdt0(X1,X2) = sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(X2)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(X2,aDimensionOf0(X2))))
| aDimensionOf0(X2) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_49,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_50,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_51,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
cnf(c_0_52,hypothesis,
( ~ iLess0(aDimensionOf0(X1),aDimensionOf0(xs))
| ~ aVector0(X1)
| sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,hypothesis,
iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_54,plain,
( ~ aScalar0(X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
( ~ aScalar0(X1)
| sdtasdt0(sz0z00,X1) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_56,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(fof_nnf,[status(thm)],[c_0_46]) ).
fof(c_0_57,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( szszuzczcdt0(X1) != sz00
& aNaturalNumber0(szszuzczcdt0(X1)) ) ),
inference(fof_simplification,[status(thm)],[mSuccNat]) ).
cnf(c_0_58,plain,
( ~ aScalar0(sdtasasdt0(sziznziztdt0(X2),sziznziztdt0(X1)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(X2,aDimensionOf0(X2)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(X2),sziznziztdt0(X1)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(X2,aDimensionOf0(X2)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| ~ aVector0(X2)
| ~ aVector0(X1)
| aDimensionOf0(X2) != aDimensionOf0(X1)
| sdtlseqdt0(sz0z00,sdtasasdt0(X2,X1))
| aDimensionOf0(X1) = sz00 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_59,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ sdtlseqdt0(X1,sz0z00)
| sdtlseqdt0(X1,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_60,hypothesis,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_30])]) ).
cnf(c_0_61,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_51])]) ).
cnf(c_0_62,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
fof(c_0_63,plain,
! [X69,X70] :
( aScalar0(sdtasasdt0(X69,X70))
| aDimensionOf0(X69) != aDimensionOf0(X70)
| ~ aVector0(X70)
| ~ aVector0(X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScPr])])]) ).
fof(c_0_64,plain,
! [X6] :
( ( ~ aNaturalNumber0(X6)
| szszuzczcdt0(X6) != sz00 )
& ( ~ aNaturalNumber0(X6)
| aNaturalNumber0(szszuzczcdt0(X6)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
cnf(c_0_65,hypothesis,
( ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_25]),c_0_60]),c_0_61]),c_0_51])]),c_0_26]),c_0_62]) ).
cnf(c_0_66,plain,
( aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| aScalar0(sdtasasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_67,plain,
! [X17,X18] :
( aScalar0(sdtasdt0(X17,X18))
| ~ aScalar0(X18)
| ~ aScalar0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])])]) ).
cnf(c_0_68,plain,
( ~ aNaturalNumber0(X1)
| aNaturalNumber0(szszuzczcdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,hypothesis,
~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_30])]) ).
cnf(c_0_70,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
fof(c_0_71,plain,
! [X60,X61] :
( aScalar0(sdtlbdtrb0(X60,X61))
| ~ aNaturalNumber0(X61)
| ~ aVector0(X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mElmSc])])]) ).
cnf(c_0_72,hypothesis,
( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| aNaturalNumber0(aDimensionOf0(xs)) ),
inference(spm,[status(thm)],[c_0_68,c_0_42]) ).
cnf(c_0_73,hypothesis,
~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,plain,
( ~ aNaturalNumber0(X2)
| ~ aVector0(X1)
| aScalar0(sdtlbdtrb0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_75,hypothesis,
aNaturalNumber0(aDimensionOf0(xs)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_31]),c_0_25])]) ).
cnf(c_0_76,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_25]),c_0_75])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG049+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:15:42 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.69/0.99 % Version: 3.5.1
% 3.69/0.99 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.69/0.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.69/0.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.69/0.99 % Starting new_bool_3 with 300s (1) cores
% 3.69/0.99 % Starting new_bool_1 with 300s (1) cores
% 3.69/0.99 % Starting sh5l with 300s (1) cores
% 3.69/0.99 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 824309 completed with status 0
% 3.69/0.99 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.69/0.99 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.69/0.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.69/0.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.69/0.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.69/0.99 % No SInE strategy applied
% 3.69/0.99 % Search class: FGHSF-FFMM21-MFFFFFNN
% 3.69/0.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.69/0.99 % Starting SubtermCWHack with 136s (1) cores
% 3.69/0.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.69/0.99 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 3.69/0.99 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 3.69/0.99 % Starting new_bool_3 with 136s (1) cores
% 3.69/0.99 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 824321 completed with status 0
% 3.69/0.99 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 3.69/0.99 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.69/0.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.69/0.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.69/0.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.69/0.99 % No SInE strategy applied
% 3.69/0.99 % Search class: FGHSF-FFMM21-MFFFFFNN
% 3.69/0.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.69/0.99 % Starting SubtermCWHack with 136s (1) cores
% 3.69/0.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.69/0.99 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 3.69/0.99 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 3.69/0.99 % Preprocessing time : 0.002 s
% 3.69/0.99 % Presaturation interreduction done
% 3.69/0.99
% 3.69/0.99 % Proof found!
% 3.69/0.99 % SZS status Theorem
% 3.69/0.99 % SZS output start CNFRefutation
% See solution above
% 3.69/0.99 % Parsed axioms : 42
% 3.69/0.99 % Removed by relevancy pruning/SinE : 0
% 3.69/0.99 % Initial clauses : 72
% 3.69/0.99 % Removed in clause preprocessing : 5
% 3.69/0.99 % Initial clauses in saturation : 67
% 3.69/0.99 % Processed clauses : 1891
% 3.69/0.99 % ...of these trivial : 16
% 3.69/0.99 % ...subsumed : 1354
% 3.69/0.99 % ...remaining for further processing : 521
% 3.69/0.99 % Other redundant clauses eliminated : 11
% 3.69/0.99 % Clauses deleted for lack of memory : 0
% 3.69/0.99 % Backward-subsumed : 45
% 3.69/0.99 % Backward-rewritten : 8
% 3.69/0.99 % Generated clauses : 20050
% 3.69/0.99 % ...of the previous two non-redundant : 17800
% 3.69/0.99 % ...aggressively subsumed : 0
% 3.69/0.99 % Contextual simplify-reflections : 160
% 3.69/0.99 % Paramodulations : 20017
% 3.69/0.99 % Factorizations : 1
% 3.69/0.99 % NegExts : 0
% 3.69/0.99 % Equation resolutions : 32
% 3.69/0.99 % Disequality decompositions : 0
% 3.69/0.99 % Total rewrite steps : 14939
% 3.69/0.99 % ...of those cached : 14924
% 3.69/0.99 % Propositional unsat checks : 0
% 3.69/0.99 % Propositional check models : 0
% 3.69/0.99 % Propositional check unsatisfiable : 0
% 3.69/0.99 % Propositional clauses : 0
% 3.69/0.99 % Propositional clauses after purity: 0
% 3.69/0.99 % Propositional unsat core size : 0
% 3.69/0.99 % Propositional preprocessing time : 0.000
% 3.69/0.99 % Propositional encoding time : 0.000
% 3.69/0.99 % Propositional solver time : 0.000
% 3.69/0.99 % Success case prop preproc time : 0.000
% 3.69/0.99 % Success case prop encoding time : 0.000
% 3.69/0.99 % Success case prop solver time : 0.000
% 3.69/0.99 % Current number of processed clauses : 407
% 3.69/0.99 % Positive orientable unit clauses : 15
% 3.69/0.99 % Positive unorientable unit clauses: 0
% 3.69/0.99 % Negative unit clauses : 4
% 3.69/0.99 % Non-unit-clauses : 388
% 3.69/0.99 % Current number of unprocessed clauses: 15965
% 3.69/0.99 % ...number of literals in the above : 104211
% 3.69/0.99 % Current number of archived formulas : 0
% 3.69/0.99 % Current number of archived clauses : 111
% 3.69/0.99 % Clause-clause subsumption calls (NU) : 29699
% 3.69/0.99 % Rec. Clause-clause subsumption calls : 13274
% 3.69/0.99 % Non-unit clause-clause subsumptions : 1549
% 3.69/0.99 % Unit Clause-clause subsumption calls : 40
% 3.69/0.99 % Rewrite failures with RHS unbound : 0
% 3.69/0.99 % BW rewrite match attempts : 7
% 3.69/0.99 % BW rewrite match successes : 6
% 3.69/0.99 % Condensation attempts : 0
% 3.69/0.99 % Condensation successes : 0
% 3.69/0.99 % Termbank termtop insertions : 485565
% 3.69/0.99 % Search garbage collected termcells : 902
% 3.69/0.99
% 3.69/0.99 % -------------------------------------------------
% 3.69/0.99 % User time : 0.448 s
% 3.69/0.99 % System time : 0.025 s
% 3.69/0.99 % Total time : 0.473 s
% 3.69/0.99 % Maximum resident set size: 3656 pages
% 3.69/0.99
% 3.69/0.99 % -------------------------------------------------
% 3.69/0.99 % User time : 2.462 s
% 3.69/0.99 % System time : 0.120 s
% 3.69/0.99 % Total time : 2.582 s
% 3.69/0.99 % Maximum resident set size: 4864 pages
% 3.69/0.99 % E exiting
%------------------------------------------------------------------------------