%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG056+1 : 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 : n008.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 02:06:12 PM UTC 2026
% Result : Theorem 2.61s 1.08s
% Output : CNFRefutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 25
% Syntax : Number of formulae : 114 ( 54 unt; 0 def)
% Number of atoms : 285 ( 135 equ)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 278 ( 107 ~; 104 |; 49 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 16 con; 0-2 aty)
% Number of variables : 76 ( 2 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefInit,axiom,
! [X1] :
( aVector0(X1)
=> ( aDimensionOf0(X1) != sz00
=> ! [X2] :
( X2 = sziznziztdt0(X1)
<=> ( ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) )
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& aVector0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
fof(m__1692,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
fof(mSuccEqu,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( szszuzczcdt0(X1) = szszuzczcdt0(X2)
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
fof(m__1726,hypothesis,
( xq = sziznziztdt0(xt)
& aVector0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
fof(m__1678,hypothesis,
( aVector0(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
fof(m__1709,hypothesis,
( xp = sziznziztdt0(xs)
& aVector0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
fof(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
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(mMNeg,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
& sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
fof(mArith,axiom,
! [X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
& sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
& sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
& sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(m__1873,hypothesis,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
fof(m__1766,hypothesis,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
fof(m__1746,hypothesis,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
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(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
fof(m__1854,hypothesis,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
fof(m__1930,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
fof(m__1800,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
fof(m__1837,hypothesis,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m__,conjecture,
xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1892,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
fof(m__1783,hypothesis,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
fof(m__1949,hypothesis,
( xN = sdtasdt0(xR,xS)
& aScalar0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
fof(c_0_25,plain,
! [X1] :
( aVector0(X1)
=> ( aDimensionOf0(X1) != sz00
=> ! [X2] :
( X2 = sziznziztdt0(X1)
<=> ( ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) )
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& aVector0(X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefInit]) ).
fof(c_0_26,plain,
! [X62,X63,X64,X65] :
( ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X65 = sziznziztdt0(X62)
| szszuzczcdt0(aDimensionOf0(X65)) != aDimensionOf0(X62)
| ~ aVector0(X65)
| sdtlbdtrb0(X65,esk2_2(X62,X65)) != sdtlbdtrb0(X62,esk2_2(X62,X65)) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X65 = sziznziztdt0(X62)
| szszuzczcdt0(aDimensionOf0(X65)) != aDimensionOf0(X62)
| ~ aVector0(X65)
| aNaturalNumber0(esk2_2(X62,X65)) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X63 != sziznziztdt0(X62)
| sdtlbdtrb0(X63,X64) = sdtlbdtrb0(X62,X64)
| ~ aNaturalNumber0(X64) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X63 != sziznziztdt0(X62)
| szszuzczcdt0(aDimensionOf0(X63)) = aDimensionOf0(X62) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X63 != sziznziztdt0(X62)
| aVector0(X63) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])])])]) ).
fof(c_0_27,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_simplification,[status(thm)],[m__1692]) ).
cnf(c_0_28,plain,
( ~ aVector0(X2)
| X1 != sziznziztdt0(X2)
| aDimensionOf0(X2) = sz00
| szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_29,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[c_0_27]) ).
fof(c_0_30,plain,
! [X9,X10] :
( X9 = X10
| szszuzczcdt0(X9) != szszuzczcdt0(X10)
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccEqu])])]) ).
cnf(c_0_31,plain,
( ~ aVector0(X1)
| aDimensionOf0(X1) = sz00
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(X1))) = aDimensionOf0(X1) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_32,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_33,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
cnf(c_0_34,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_35,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( szszuzczcdt0(X1) != szszuzczcdt0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,hypothesis,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xs),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_38,hypothesis,
xp = sziznziztdt0(xs),
inference(split_conjunct,[status(thm)],[m__1709]) ).
cnf(c_0_39,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_40,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(aDimensionOf0(xq))
| szszuzczcdt0(X1) != aDimensionOf0(xs)
| aDimensionOf0(xq) = X1 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,hypothesis,
szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_38]),c_0_39])]),c_0_35]) ).
fof(c_0_42,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_43,hypothesis,
( ~ aNaturalNumber0(aDimensionOf0(xp))
| ~ aNaturalNumber0(aDimensionOf0(xq))
| aDimensionOf0(xp) = aDimensionOf0(xq) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
( ~ aVector0(X1)
| aNaturalNumber0(aDimensionOf0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_45,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[m__1726]) ).
fof(c_0_46,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])])]) ).
cnf(c_0_47,hypothesis,
( ~ aNaturalNumber0(aDimensionOf0(xp))
| aDimensionOf0(xp) = aDimensionOf0(xq) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_48,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[m__1709]) ).
cnf(c_0_49,plain,
( aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| aScalar0(sdtasasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_50,hypothesis,
aDimensionOf0(xp) = aDimensionOf0(xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_44]),c_0_48])]) ).
fof(c_0_51,plain,
! [X31,X32] :
( ( ~ aScalar0(X32)
| ~ aScalar0(X31)
| sdtasdt0(smndt0(X31),X32) = smndt0(sdtasdt0(X31,X32)) )
& ( ~ aScalar0(X32)
| ~ aScalar0(X31)
| sdtasdt0(X31,smndt0(X32)) = smndt0(sdtasdt0(X31,X32)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])])]) ).
fof(c_0_52,plain,
! [X21,X22,X23] :
( ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtasdt0(X21,X22) = sdtasdt0(X22,X21) )
& ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtasdt0(sdtasdt0(X21,X22),X23) = sdtasdt0(X21,sdtasdt0(X22,X23)) )
& ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtpldt0(X21,X22) = sdtpldt0(X22,X21) )
& ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtpldt0(sdtpldt0(X21,X22),X23) = sdtpldt0(X21,sdtpldt0(X22,X23)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])])]) ).
cnf(c_0_53,hypothesis,
( ~ aVector0(X1)
| aDimensionOf0(X1) != aDimensionOf0(xq)
| aScalar0(sdtasasdt0(X1,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_48])]) ).
cnf(c_0_54,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_55,hypothesis,
xH = sdtasdt0(xA,xB),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_56,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_57,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_58,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,hypothesis,
aScalar0(sdtasasdt0(xq,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_53]),c_0_45])]) ).
fof(c_0_60,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_61,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_62,hypothesis,
sdtasdt0(smndt0(xA),xB) = smndt0(xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57])]) ).
cnf(c_0_63,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_64,plain,
! [X19] :
( aScalar0(smndt0(X19))
| ~ aScalar0(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])])]) ).
cnf(c_0_65,plain,
( ~ aScalar0(X1)
| smndt0(smndt0(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_67,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_68,hypothesis,
( ~ aScalar0(smndt0(xA))
| sdtasdt0(xB,smndt0(xA)) = smndt0(xH) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_56])]) ).
cnf(c_0_69,plain,
( ~ aScalar0(X1)
| aScalar0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_70,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_71,hypothesis,
sdtasdt0(xA,smndt0(xB)) = smndt0(xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_55]),c_0_56]),c_0_57])]) ).
cnf(c_0_72,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_73,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_74,hypothesis,
sdtasdt0(xB,smndt0(xA)) = smndt0(xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_57])]) ).
cnf(c_0_75,hypothesis,
smndt0(smndt0(xH)) = xH,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_55]),c_0_56]),c_0_57])]) ).
cnf(c_0_76,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xB,sdtasdt0(xB,X1)) = sdtasdt0(xG,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_56])]) ).
cnf(c_0_77,hypothesis,
sdtasdt0(xB,xA) = xH,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_74]),c_0_57]),c_0_56])]),c_0_75]) ).
cnf(c_0_78,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_79,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_80,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_81,hypothesis,
sdtasdt0(xG,xA) = sdtasdt0(xB,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_57])]) ).
cnf(c_0_82,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_83,hypothesis,
sdtasdt0(xF,smndt0(xD)) = smndt0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_78]),c_0_79]),c_0_80])]) ).
cnf(c_0_84,hypothesis,
sdtasdt0(xB,xH) = sdtasdt0(xA,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_81]),c_0_57]),c_0_82])]) ).
cnf(c_0_85,hypothesis,
aScalar0(xH),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_86,hypothesis,
( ~ aScalar0(smndt0(xD))
| aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_83]),c_0_80])]) ).
cnf(c_0_87,hypothesis,
sdtasdt0(xA,xG) = sdtasdt0(xH,xB),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_84]),c_0_85]),c_0_56])]) ).
fof(c_0_88,negated_conjecture,
xN != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_89,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xD,xF) = xS ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_58]),c_0_80]),c_0_79])]) ).
cnf(c_0_90,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_69]),c_0_79])]) ).
cnf(c_0_91,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_92,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xA,sdtasdt0(xB,X1)) = sdtasdt0(xH,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_55]),c_0_56]),c_0_57])]) ).
cnf(c_0_93,hypothesis,
sdtasdt0(xB,xH) = sdtasdt0(xH,xB),
inference(rw,[status(thm)],[c_0_84,c_0_87]) ).
fof(c_0_94,negated_conjecture,
xN != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
cnf(c_0_95,hypothesis,
sdtasdt0(xD,xF) = xS,
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_96,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xA,sdtasdt0(xA,X1)) = sdtasdt0(xF,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_91]),c_0_57])]) ).
cnf(c_0_97,hypothesis,
sdtasdt0(xA,sdtasdt0(xH,xB)) = sdtasdt0(xH,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_85])]) ).
fof(c_0_98,negated_conjecture,
xN != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
inference(fof_nnf,[status(thm)],[c_0_94]) ).
cnf(c_0_99,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xD,sdtasdt0(xF,X1)) = sdtasdt0(xS,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_95]),c_0_80]),c_0_79])]) ).
cnf(c_0_100,hypothesis,
sdtasdt0(xF,xG) = sdtasdt0(xH,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_87]),c_0_97]),c_0_82])]) ).
cnf(c_0_101,hypothesis,
aScalar0(sdtasdt0(xH,xB)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_87]),c_0_82]),c_0_57])]) ).
cnf(c_0_102,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_103,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_104,negated_conjecture,
xN != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_105,hypothesis,
( ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X1)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X2,sdtasdt0(X3,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_63]),c_0_67]) ).
cnf(c_0_106,hypothesis,
sdtasdt0(xD,sdtasdt0(xH,xH)) = sdtasdt0(xS,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_82])]) ).
cnf(c_0_107,hypothesis,
aScalar0(sdtasdt0(xH,xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_97]),c_0_101]),c_0_57])]) ).
cnf(c_0_108,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xC,sdtasdt0(xG,X1)) = sdtasdt0(xR,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_102]),c_0_82]),c_0_103])]) ).
cnf(c_0_109,negated_conjecture,
sdtasdt0(xC,sdtasdt0(xS,xG)) != xN,
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_104,c_0_105]),c_0_106]),c_0_107]),c_0_79]),c_0_103])]) ).
cnf(c_0_110,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xC,sdtasdt0(X1,xG)) = sdtasdt0(xR,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_63]),c_0_82])]) ).
cnf(c_0_111,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_112,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_113,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111]),c_0_112])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG056+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:16:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 2.61/1.08 % Version: 3.5.1
% 2.61/1.08 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.61/1.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.61/1.08 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.61/1.08 % Starting new_bool_3 with 300s (1) cores
% 2.61/1.08 % Starting new_bool_1 with 300s (1) cores
% 2.61/1.08 % Starting sh5l with 300s (1) cores
% 2.61/1.08 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 119782 completed with status 0
% 2.61/1.08 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 2.61/1.08 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.61/1.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.61/1.08 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.61/1.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.61/1.08 % No SInE strategy applied
% 2.61/1.08 % Search class: FGHSF-FFMM21-MFFFFFNN
% 2.61/1.08 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.61/1.08 % Starting SubtermCWHack with 136s (1) cores
% 2.61/1.08 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.61/1.08 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 2.61/1.08 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 2.61/1.08 % Starting new_bool_3 with 136s (1) cores
% 2.61/1.08 % new_bool_3 with pid 119791 completed with status 0
% 2.61/1.08 % Result found by new_bool_3
% 2.61/1.08 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.61/1.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.61/1.08 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.61/1.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.61/1.08 % No SInE strategy applied
% 2.61/1.08 % Search class: FGHSF-FFMM21-MFFFFFNN
% 2.61/1.08 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.61/1.08 % Starting SubtermCWHack with 136s (1) cores
% 2.61/1.08 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.61/1.08 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 2.61/1.08 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 2.61/1.08 % Starting new_bool_3 with 136s (1) cores
% 2.61/1.08 % Preprocessing time : 0.002 s
% 2.61/1.08 % Presaturation interreduction done
% 2.61/1.08
% 2.61/1.08 % Proof found!
% 2.61/1.08 % SZS status Theorem
% 2.61/1.08 % SZS output start CNFRefutation
% See solution above
% 2.61/1.08 % Parsed axioms : 58
% 2.61/1.08 % Removed by relevancy pruning/SinE : 0
% 2.61/1.08 % Initial clauses : 92
% 2.61/1.08 % Removed in clause preprocessing : 5
% 2.61/1.08 % Initial clauses in saturation : 87
% 2.61/1.08 % Processed clauses : 1966
% 2.61/1.08 % ...of these trivial : 458
% 2.61/1.08 % ...subsumed : 418
% 2.61/1.08 % ...remaining for further processing : 1090
% 2.61/1.08 % Other redundant clauses eliminated : 7
% 2.61/1.08 % Clauses deleted for lack of memory : 0
% 2.61/1.08 % Backward-subsumed : 15
% 2.61/1.08 % Backward-rewritten : 171
% 2.61/1.08 % Generated clauses : 19282
% 2.61/1.08 % ...of the previous two non-redundant : 15266
% 2.61/1.08 % ...aggressively subsumed : 0
% 2.61/1.08 % Contextual simplify-reflections : 51
% 2.61/1.08 % Paramodulations : 19261
% 2.61/1.08 % Factorizations : 2
% 2.61/1.08 % NegExts : 0
% 2.61/1.08 % Equation resolutions : 19
% 2.61/1.08 % Disequality decompositions : 0
% 2.61/1.08 % Total rewrite steps : 37893
% 2.61/1.08 % ...of those cached : 37330
% 2.61/1.08 % Propositional unsat checks : 0
% 2.61/1.08 % Propositional check models : 0
% 2.61/1.08 % Propositional check unsatisfiable : 0
% 2.61/1.08 % Propositional clauses : 0
% 2.61/1.08 % Propositional clauses after purity: 0
% 2.61/1.08 % Propositional unsat core size : 0
% 2.61/1.08 % Propositional preprocessing time : 0.000
% 2.61/1.08 % Propositional encoding time : 0.000
% 2.61/1.08 % Propositional solver time : 0.000
% 2.61/1.08 % Success case prop preproc time : 0.000
% 2.61/1.08 % Success case prop encoding time : 0.000
% 2.61/1.08 % Success case prop solver time : 0.000
% 2.61/1.08 % Current number of processed clauses : 814
% 2.61/1.08 % Positive orientable unit clauses : 592
% 2.61/1.08 % Positive unorientable unit clauses: 0
% 2.61/1.08 % Negative unit clauses : 3
% 2.61/1.08 % Non-unit-clauses : 219
% 2.61/1.08 % Current number of unprocessed clauses: 13223
% 2.61/1.08 % ...number of literals in the above : 34983
% 2.61/1.08 % Current number of archived formulas : 0
% 2.61/1.08 % Current number of archived clauses : 273
% 2.61/1.08 % Clause-clause subsumption calls (NU) : 18107
% 2.61/1.08 % Rec. Clause-clause subsumption calls : 10449
% 2.61/1.08 % Non-unit clause-clause subsumptions : 473
% 2.61/1.08 % Unit Clause-clause subsumption calls : 3153
% 2.61/1.08 % Rewrite failures with RHS unbound : 0
% 2.61/1.08 % BW rewrite match attempts : 636
% 2.61/1.08 % BW rewrite match successes : 128
% 2.61/1.08 % Condensation attempts : 0
% 2.61/1.08 % Condensation successes : 0
% 2.61/1.08 % Termbank termtop insertions : 393722
% 2.61/1.08 % Search garbage collected termcells : 883
% 2.61/1.08
% 2.61/1.08 % -------------------------------------------------
% 2.61/1.08 % User time : 0.496 s
% 2.61/1.08 % System time : 0.024 s
% 2.61/1.08 % Total time : 0.520 s
% 2.61/1.08 % Maximum resident set size: 3956 pages
% 2.61/1.08
% 2.61/1.08 % -------------------------------------------------
% 2.61/1.08 % User time : 2.432 s
% 2.61/1.08 % System time : 0.126 s
% 2.61/1.08 % Total time : 2.558 s
% 2.61/1.08 % Maximum resident set size: 4864 pages
% 2.61/1.08 % E exiting
%------------------------------------------------------------------------------