%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG062+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 : n011.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 2.44s 0.99s
% Output : CNFRefutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of formulae : 94 ( 37 unt; 0 def)
% Number of atoms : 251 ( 99 equ)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 270 ( 113 ~; 108 |; 32 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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; 13 con; 0-2 aty)
% Number of variables : 82 ( 4 sgn 40 !; 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(mElmSc,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aVector0(X1) )
=> aScalar0(sdtlbdtrb0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
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(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(m__1930,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
fof(m__1837,hypothesis,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m__1800,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
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/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
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/sandbox2/benchmark/theBenchmark.p',m__2144) ).
fof(m__1892,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__2221) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
fof(c_0_21,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_22,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_21])])])])])])]) ).
fof(c_0_23,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_simplification,[status(thm)],[m__1692]) ).
cnf(c_0_24,plain,
( ~ aVector0(X2)
| X1 != sziznziztdt0(X2)
| aDimensionOf0(X2) = sz00
| szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_25,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[c_0_23]) ).
fof(c_0_26,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_27,plain,
( ~ aVector0(X1)
| aDimensionOf0(X1) = sz00
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(X1))) = aDimensionOf0(X1) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_28,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_29,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
cnf(c_0_30,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_31,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( szszuzczcdt0(X1) != szszuzczcdt0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,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_27,c_0_28]),c_0_29]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_34,hypothesis,
xp = sziznziztdt0(xs),
inference(split_conjunct,[status(thm)],[m__1709]) ).
cnf(c_0_35,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_36,plain,
( ~ aVector0(X3)
| X2 != sziznziztdt0(X3)
| ~ aNaturalNumber0(X1)
| aDimensionOf0(X3) = sz00
| sdtlbdtrb0(X2,X1) = sdtlbdtrb0(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_37,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(aDimensionOf0(xq))
| szszuzczcdt0(X1) != aDimensionOf0(xs)
| aDimensionOf0(xq) = X1 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,hypothesis,
szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_34]),c_0_35])]),c_0_31]) ).
fof(c_0_39,plain,
! [X59] :
( aNaturalNumber0(aDimensionOf0(X59))
| ~ aVector0(X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDimNat])])]) ).
fof(c_0_40,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_41,plain,
( ~ aNaturalNumber0(X2)
| ~ aVector0(X1)
| aDimensionOf0(X1) = sz00
| sdtlbdtrb0(sziznziztdt0(X1),X2) = sdtlbdtrb0(X1,X2) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_42,hypothesis,
( ~ aNaturalNumber0(aDimensionOf0(xp))
| ~ aNaturalNumber0(aDimensionOf0(xq))
| aDimensionOf0(xp) = aDimensionOf0(xq) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( ~ aVector0(X1)
| aNaturalNumber0(aDimensionOf0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[m__1709]) ).
fof(c_0_45,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_46,plain,
( ~ aNaturalNumber0(X2)
| ~ aVector0(X1)
| aScalar0(sdtlbdtrb0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(xt,X1) = sdtlbdtrb0(xq,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_28]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_48,hypothesis,
( ~ aNaturalNumber0(aDimensionOf0(xq))
| aDimensionOf0(xp) = aDimensionOf0(xq) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_49,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_50,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,hypothesis,
( ~ aNaturalNumber0(X1)
| aScalar0(sdtlbdtrb0(xq,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_30])]) ).
cnf(c_0_52,hypothesis,
aDimensionOf0(xp) = aDimensionOf0(xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_43]),c_0_49])]) ).
cnf(c_0_53,hypothesis,
( ~ aNaturalNumber0(X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,hypothesis,
aNaturalNumber0(aDimensionOf0(xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_52]),c_0_44])]) ).
fof(c_0_55,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])])])]) ).
cnf(c_0_56,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_57,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_59,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
fof(c_0_60,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_61,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,hypothesis,
sdtasdt0(xD,xF) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59])]) ).
fof(c_0_63,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_64,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,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_61,c_0_62]),c_0_58]),c_0_59])]) ).
fof(c_0_66,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_67,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_63]) ).
cnf(c_0_68,hypothesis,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_69,hypothesis,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_70,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_71,hypothesis,
( ~ aScalar0(smndt0(xF))
| aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_59])]) ).
cnf(c_0_72,plain,
( ~ aScalar0(X1)
| aScalar0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_73,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_67]) ).
cnf(c_0_74,hypothesis,
( ~ aScalar0(smndt0(xS))
| aScalar0(sdtasdt0(xS,xS)) ),
inference(spm,[status(thm)],[c_0_64,c_0_68]) ).
cnf(c_0_75,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_76,hypothesis,
( ~ aScalar0(smndt0(xS))
| aScalar0(smndt0(xN)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_69]),c_0_70])]) ).
cnf(c_0_77,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_58])]) ).
cnf(c_0_78,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_73]) ).
cnf(c_0_79,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_80,hypothesis,
aScalar0(sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_72]),c_0_75])]) ).
cnf(c_0_81,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_82,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_83,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)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]),c_0_81])]) ).
cnf(c_0_84,hypothesis,
( ~ aNaturalNumber0(X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_51]) ).
cnf(c_0_85,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_83,c_0_79]),c_0_81])]) ).
cnf(c_0_86,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_54]) ).
cnf(c_0_87,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_88,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_85,c_0_86]),c_0_81])]) ).
fof(c_0_89,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_90,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_87,c_0_79]),c_0_81])]),c_0_88]) ).
cnf(c_0_91,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_92,hypothesis,
~ aScalar0(sdtasdt0(xR,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_81]),c_0_80])]) ).
cnf(c_0_93,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_64]),c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG062+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n011.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 04:16:55 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.51 Running first-order theorem proving
% 0.28/0.51 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
% 2.44/0.99 % Version: 3.5.1
% 2.44/0.99 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.44/0.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.44/0.99 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.44/0.99 % Starting new_bool_3 with 300s (1) cores
% 2.44/0.99 % Starting new_bool_1 with 300s (1) cores
% 2.44/0.99 % Starting sh5l with 300s (1) cores
% 2.44/0.99 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 952571 completed with status 0
% 2.44/0.99 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 2.44/0.99 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.44/0.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.44/0.99 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.44/0.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.44/0.99 % No SInE strategy applied
% 2.44/0.99 % Search class: FGHSF-FFMM21-MFFFFFNN
% 2.44/0.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.44/0.99 % Starting SubtermCWHack with 136s (1) cores
% 2.44/0.99 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.44/0.99 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 2.44/0.99 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 2.44/0.99 % Starting new_bool_3 with 136s (1) cores
% 2.44/0.99 % SAT001_MinMin_p005000_rr_RG with pid 952577 completed with status 0
% 2.44/0.99 % Result found by SAT001_MinMin_p005000_rr_RG
% 2.44/0.99 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.44/0.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.44/0.99 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.44/0.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.44/0.99 % No SInE strategy applied
% 2.44/0.99 % Search class: FGHSF-FFMM21-MFFFFFNN
% 2.44/0.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.44/0.99 % Starting SubtermCWHack with 136s (1) cores
% 2.44/0.99 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.44/0.99 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 2.44/0.99 % Preprocessing time : 0.004 s
% 2.44/0.99 % Presaturation interreduction done
% 2.44/0.99
% 2.44/0.99 % Proof found!
% 2.44/0.99 % SZS status Theorem
% 2.44/0.99 % SZS output start CNFRefutation
% See solution above
% 2.44/0.99 % Parsed axioms : 61
% 2.44/0.99 % Removed by relevancy pruning/SinE : 0
% 2.44/0.99 % Initial clauses : 97
% 2.44/0.99 % Removed in clause preprocessing : 5
% 2.44/0.99 % Initial clauses in saturation : 92
% 2.44/0.99 % Processed clauses : 1196
% 2.44/0.99 % ...of these trivial : 113
% 2.44/0.99 % ...subsumed : 355
% 2.44/0.99 % ...remaining for further processing : 728
% 2.44/0.99 % Other redundant clauses eliminated : 7
% 2.44/0.99 % Clauses deleted for lack of memory : 0
% 2.44/0.99 % Backward-subsumed : 29
% 2.44/0.99 % Backward-rewritten : 87
% 2.44/0.99 % Generated clauses : 9078
% 2.44/0.99 % ...of the previous two non-redundant : 7829
% 2.44/0.99 % ...aggressively subsumed : 0
% 2.44/0.99 % Contextual simplify-reflections : 27
% 2.44/0.99 % Paramodulations : 9068
% 2.44/0.99 % Factorizations : 0
% 2.44/0.99 % NegExts : 0
% 2.44/0.99 % Equation resolutions : 10
% 2.44/0.99 % Disequality decompositions : 0
% 2.44/0.99 % Total rewrite steps : 9120
% 2.44/0.99 % ...of those cached : 8886
% 2.44/0.99 % Propositional unsat checks : 0
% 2.44/0.99 % Propositional check models : 0
% 2.44/0.99 % Propositional check unsatisfiable : 0
% 2.44/0.99 % Propositional clauses : 0
% 2.44/0.99 % Propositional clauses after purity: 0
% 2.44/0.99 % Propositional unsat core size : 0
% 2.44/0.99 % Propositional preprocessing time : 0.000
% 2.44/0.99 % Propositional encoding time : 0.000
% 2.44/0.99 % Propositional solver time : 0.000
% 2.44/0.99 % Success case prop preproc time : 0.000
% 2.44/0.99 % Success case prop encoding time : 0.000
% 2.44/0.99 % Success case prop solver time : 0.000
% 2.44/0.99 % Current number of processed clauses : 517
% 2.44/0.99 % Positive orientable unit clauses : 286
% 2.44/0.99 % Positive unorientable unit clauses: 0
% 2.44/0.99 % Negative unit clauses : 3
% 2.44/0.99 % Non-unit-clauses : 228
% 2.44/0.99 % Current number of unprocessed clauses: 6597
% 2.44/0.99 % ...number of literals in the above : 21859
% 2.44/0.99 % Current number of archived formulas : 0
% 2.44/0.99 % Current number of archived clauses : 208
% 2.44/0.99 % Clause-clause subsumption calls (NU) : 15685
% 2.44/0.99 % Rec. Clause-clause subsumption calls : 10225
% 2.44/0.99 % Non-unit clause-clause subsumptions : 387
% 2.44/0.99 % Unit Clause-clause subsumption calls : 1942
% 2.44/0.99 % Rewrite failures with RHS unbound : 0
% 2.44/0.99 % BW rewrite match attempts : 573
% 2.44/0.99 % BW rewrite match successes : 27
% 2.44/0.99 % Condensation attempts : 0
% 2.44/0.99 % Condensation successes : 0
% 2.44/0.99 % Termbank termtop insertions : 168879
% 2.44/0.99 % Search garbage collected termcells : 883
% 2.44/0.99
% 2.44/0.99 % -------------------------------------------------
% 2.44/0.99 % User time : 0.277 s
% 2.44/0.99 % System time : 0.023 s
% 2.44/0.99 % Total time : 0.300 s
% 2.44/0.99 % Maximum resident set size: 3704 pages
% 2.44/0.99
% 2.44/0.99 % -------------------------------------------------
% 2.44/0.99 % User time : 1.566 s
% 2.44/0.99 % System time : 0.105 s
% 2.44/0.99 % Total time : 1.672 s
% 2.44/0.99 % Maximum resident set size: 4608 pages
% 2.44/0.99 % E exiting
%------------------------------------------------------------------------------