%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG062+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 02:05:41 PM UTC 2026
% Result : Theorem 1.67s 0.79s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 22
% Syntax : Number of formulae : 93 ( 36 unt; 0 def)
% Number of atoms : 246 ( 106 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 259 ( 106 ~; 91 |; 48 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 14 con; 0-2 aty)
% Number of variables : 68 ( 2 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',mDefSPN) ).
fof(m__1692,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1692) ).
fof(m__1726,hypothesis,
( xq = sziznziztdt0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xq,X1) = sdtlbdtrb0(xt,X1) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).
fof(m__1766,hypothesis,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1766) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).
fof(m__1678,hypothesis,
( aVector0(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).
fof(mScPr,axiom,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( aDimensionOf0(X1) = aDimensionOf0(X2)
=> aScalar0(sdtasasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).
fof(m__1800,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).
fof(m__1854,hypothesis,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1854) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',mArith) ).
fof(mMDNeg,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMDNeg) ).
fof(m__2144,hypothesis,
( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(xR,smndt0(xS)) = smndt0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2144) ).
fof(m__1930,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(m__1837,hypothesis,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
fof(m__,conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/benchmark/theBenchmark.p',mScZero) ).
fof(m__1892,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(m__2221,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2221) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
fof(c_0_22,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_23,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_simplification,[status(thm)],[m__1692]) ).
fof(c_0_24,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_22])])]) ).
fof(c_0_25,hypothesis,
! [X79] :
( xq = sziznziztdt0(xt)
& ( sdtlbdtrb0(xq,X79) = sdtlbdtrb0(xt,X79)
| ~ aNaturalNumber0(X79) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1726])])])]) ).
cnf(c_0_26,hypothesis,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_27,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
fof(c_0_28,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[c_0_23]) ).
cnf(c_0_29,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_24]) ).
cnf(c_0_30,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,hypothesis,
sdtlbdtrb0(xt,aDimensionOf0(xs)) = xB,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_33,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_34,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_35,hypothesis,
( ~ aVector0(X1)
| aDimensionOf0(X1) != aDimensionOf0(xs)
| sdtpldt0(sdtasasdt0(sziznziztdt0(X1),xq),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),xB)) = sdtasasdt0(X1,xt) ),
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_29,c_0_27]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_36,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_37,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
fof(c_0_38,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_39,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_40,plain,
( aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| aScalar0(sdtasasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,hypothesis,
sdtasasdt0(xt,xt) = sdtpldt0(xD,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_27]),c_0_30]),c_0_36]),c_0_31]),c_0_37]),c_0_32])]) ).
fof(c_0_42,plain,
! [X33,X34] :
( sdtasdt0(smndt0(X33),smndt0(X34)) = sdtasdt0(X33,X34)
| ~ aScalar0(X34)
| ~ aScalar0(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMDNeg])])]) ).
cnf(c_0_43,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,hypothesis,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_45,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,hypothesis,
aScalar0(sdtpldt0(xD,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_32])]) ).
cnf(c_0_47,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,hypothesis,
( ~ aScalar0(smndt0(xS))
| sdtasdt0(smndt0(xS),smndt0(smndt0(xS))) = smndt0(sdtasdt0(xS,xS)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_50,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_51,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_53,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_54,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_55,hypothesis,
( ~ aScalar0(smndt0(xS))
| smndt0(sdtasdt0(xS,xS)) = sdtasdt0(xS,smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
fof(c_0_56,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_57,hypothesis,
sdtasdt0(xD,xF) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53])]) ).
cnf(c_0_58,hypothesis,
( ~ aScalar0(smndt0(xS))
| sdtasdt0(smndt0(xS),xS) = sdtasdt0(xS,smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_49])]) ).
cnf(c_0_59,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_60,hypothesis,
sdtasdt0(xD,smndt0(xF)) = smndt0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_57]),c_0_52]),c_0_53])]) ).
fof(c_0_61,plain,
! [X19] :
( aScalar0(smndt0(X19))
| ~ aScalar0(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])])]) ).
fof(c_0_62,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_63,hypothesis,
( ~ aScalar0(smndt0(xS))
| smndt0(sdtasdt0(xS,smndt0(xS))) = sdtasdt0(xS,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_58]),c_0_44]),c_0_49])]) ).
cnf(c_0_64,hypothesis,
( ~ aScalar0(smndt0(xF))
| aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_53])]) ).
cnf(c_0_65,plain,
( ~ aScalar0(X1)
| aScalar0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_66,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
cnf(c_0_67,hypothesis,
( ~ aScalar0(smndt0(xS))
| sdtasdt0(xS,smndt0(smndt0(xS))) = sdtasdt0(xS,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_63]),c_0_49])]) ).
cnf(c_0_68,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_52])]) ).
fof(c_0_69,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(fof_nnf,[status(thm)],[c_0_66]) ).
cnf(c_0_70,hypothesis,
sdtasdt0(xS,smndt0(smndt0(xS))) = sdtasdt0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
fof(c_0_71,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])])])]) ).
cnf(c_0_72,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_73,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_74,hypothesis,
( ~ aScalar0(smndt0(smndt0(xS)))
| aScalar0(sdtasdt0(xS,xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_70]),c_0_49])]) ).
cnf(c_0_75,plain,
( ~ aScalar0(X1)
| smndt0(smndt0(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( ~ aScalar0(smndt0(xN))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(sdtasdt0(xS,xS))
| sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),smndt0(xN)) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,hypothesis,
aScalar0(sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_49])]) ).
cnf(c_0_78,hypothesis,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_79,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_80,negated_conjecture,
( ~ aScalar0(smndt0(xN))
| ~ aScalar0(sdtasdt0(xR,xR))
| sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),smndt0(xN)) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_81,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_78]),c_0_79])]),c_0_68])]) ).
cnf(c_0_82,negated_conjecture,
( ~ aScalar0(sdtasdt0(xR,xR))
| sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),smndt0(xN)) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).
cnf(c_0_83,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_84,negated_conjecture,
( ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)))
| sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),smndt0(xN))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_73]),c_0_81])]) ).
cnf(c_0_85,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_46]) ).
cnf(c_0_86,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(split_conjunct,[status(thm)],[m__2221]) ).
cnf(c_0_87,hypothesis,
( ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)))
| sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(smndt0(xN),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_81])]) ).
fof(c_0_88,plain,
! [X15,X16] :
( aScalar0(sdtpldt0(X15,X16))
| ~ aScalar0(X16)
| ~ aScalar0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])])]) ).
cnf(c_0_89,hypothesis,
( ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_73]),c_0_81])]),c_0_87]) ).
cnf(c_0_90,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_91,hypothesis,
~ aScalar0(sdtasdt0(xR,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_81]),c_0_77])]) ).
cnf(c_0_92,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_59]),c_0_79])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG062+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:19:31 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.44 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 1.67/0.79 % Version: 3.5.1
% 1.67/0.79 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.67/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.67/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.67/0.79 % Starting new_bool_3 with 300s (1) cores
% 1.67/0.79 % Starting new_bool_1 with 300s (1) cores
% 1.67/0.79 % Starting sh5l with 300s (1) cores
% 1.67/0.79 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2410915 completed with status 0
% 1.67/0.79 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.67/0.79 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.67/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.67/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.67/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.67/0.79 % No SInE strategy applied
% 1.67/0.79 % Search class: FGHSF-FFMM21-MFFFFFNN
% 1.67/0.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.67/0.79 % Starting SubtermCWHack with 136s (1) cores
% 1.67/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.67/0.79 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 1.67/0.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 1.67/0.79 % Starting new_bool_3 with 136s (1) cores
% 1.67/0.79 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 2410923 completed with status 0
% 1.67/0.79 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 1.67/0.79 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.67/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.67/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.67/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.67/0.79 % No SInE strategy applied
% 1.67/0.79 % Search class: FGHSF-FFMM21-MFFFFFNN
% 1.67/0.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.67/0.79 % Starting SubtermCWHack with 136s (1) cores
% 1.67/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.67/0.79 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 1.67/0.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 1.67/0.79 % Preprocessing time : 0.004 s
% 1.67/0.79 % Presaturation interreduction done
% 1.67/0.79
% 1.67/0.79 % Proof found!
% 1.67/0.79 % SZS status Theorem
% 1.67/0.79 % SZS output start CNFRefutation
% See solution above
% 1.67/0.79 % Parsed axioms : 61
% 1.67/0.79 % Removed by relevancy pruning/SinE : 0
% 1.67/0.79 % Initial clauses : 101
% 1.67/0.79 % Removed in clause preprocessing : 5
% 1.67/0.79 % Initial clauses in saturation : 96
% 1.67/0.79 % Processed clauses : 1218
% 1.67/0.79 % ...of these trivial : 133
% 1.67/0.79 % ...subsumed : 355
% 1.67/0.79 % ...remaining for further processing : 730
% 1.67/0.79 % Other redundant clauses eliminated : 6
% 1.67/0.79 % Clauses deleted for lack of memory : 0
% 1.67/0.79 % Backward-subsumed : 26
% 1.67/0.79 % Backward-rewritten : 74
% 1.67/0.79 % Generated clauses : 9174
% 1.67/0.79 % ...of the previous two non-redundant : 7929
% 1.67/0.79 % ...aggressively subsumed : 0
% 1.67/0.79 % Contextual simplify-reflections : 26
% 1.67/0.79 % Paramodulations : 9165
% 1.67/0.79 % Factorizations : 0
% 1.67/0.79 % NegExts : 0
% 1.67/0.79 % Equation resolutions : 9
% 1.67/0.79 % Disequality decompositions : 0
% 1.67/0.79 % Total rewrite steps : 8808
% 1.67/0.79 % ...of those cached : 8564
% 1.67/0.79 % Propositional unsat checks : 0
% 1.67/0.79 % Propositional check models : 0
% 1.67/0.79 % Propositional check unsatisfiable : 0
% 1.67/0.79 % Propositional clauses : 0
% 1.67/0.79 % Propositional clauses after purity: 0
% 1.67/0.79 % Propositional unsat core size : 0
% 1.67/0.79 % Propositional preprocessing time : 0.000
% 1.67/0.79 % Propositional encoding time : 0.000
% 1.67/0.79 % Propositional solver time : 0.000
% 1.67/0.79 % Success case prop preproc time : 0.000
% 1.67/0.79 % Success case prop encoding time : 0.000
% 1.67/0.79 % Success case prop solver time : 0.000
% 1.67/0.79 % Current number of processed clauses : 531
% 1.67/0.79 % Positive orientable unit clauses : 305
% 1.67/0.79 % Positive unorientable unit clauses: 0
% 1.67/0.79 % Negative unit clauses : 3
% 1.67/0.79 % Non-unit-clauses : 223
% 1.67/0.79 % Current number of unprocessed clauses: 6704
% 1.67/0.79 % ...number of literals in the above : 22115
% 1.67/0.79 % Current number of archived formulas : 0
% 1.67/0.79 % Current number of archived clauses : 196
% 1.67/0.79 % Clause-clause subsumption calls (NU) : 14616
% 1.67/0.79 % Rec. Clause-clause subsumption calls : 9145
% 1.67/0.79 % Non-unit clause-clause subsumptions : 383
% 1.67/0.79 % Unit Clause-clause subsumption calls : 2215
% 1.67/0.79 % Rewrite failures with RHS unbound : 0
% 1.67/0.79 % BW rewrite match attempts : 856
% 1.67/0.79 % BW rewrite match successes : 21
% 1.67/0.79 % Condensation attempts : 0
% 1.67/0.79 % Condensation successes : 0
% 1.67/0.79 % Termbank termtop insertions : 169085
% 1.67/0.79 % Search garbage collected termcells : 888
% 1.67/0.79
% 1.67/0.79 % -------------------------------------------------
% 1.67/0.79 % User time : 0.282 s
% 1.67/0.79 % System time : 0.018 s
% 1.67/0.79 % Total time : 0.300 s
% 1.67/0.79 % Maximum resident set size: 3708 pages
% 1.67/0.79
% 1.67/0.79 % -------------------------------------------------
% 1.67/0.79 % User time : 1.120 s
% 1.67/0.79 % System time : 0.069 s
% 1.67/0.79 % Total time : 1.190 s
% 1.67/0.79 % Maximum resident set size: 4608 pages
% 1.67/0.79 % E exiting
%------------------------------------------------------------------------------