%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM527+3 : 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 : n026.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 01:49:26 PM UTC 2026
% Result : Theorem 10.90s 1.88s
% Output : CNFRefutation 10.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 101 ( 33 unt; 0 def)
% Number of atoms : 375 ( 131 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 438 ( 164 ~; 162 |; 87 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 58 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(m__3046,hypothesis,
( doDivides0(xp,xn)
& ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
fof(m__,conjecture,
( ( sdtlseqdt0(xn,xm)
& ? [X1] :
( sdtpldt0(xn,X1) = xm
& aNaturalNumber0(X1) ) )
=> ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ? [X1] :
( sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm)
& aNaturalNumber0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__3059,hypothesis,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_19,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_20,plain,
! [X65,X66,X68] :
( ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| doDivides0(X65,X66)
| X66 != sdtasdt0(X65,X68)
| ~ aNaturalNumber0(X68) )
& ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| ~ doDivides0(X65,X66)
| X66 = sdtasdt0(X65,esk2_2(X65,X66)) )
& ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| ~ doDivides0(X65,X66)
| aNaturalNumber0(esk2_2(X65,X66)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])])]) ).
fof(c_0_21,plain,
! [X9,X10] :
( aNaturalNumber0(sdtasdt0(X9,X10))
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_22,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_simplification,[status(thm)],[m__2987]) ).
fof(c_0_23,plain,
! [X69,X70,X71] :
( ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 = sdtsldt0(X70,X69)
| X70 != sdtasdt0(X69,X71)
| ~ aNaturalNumber0(X71) )
& ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 != sdtsldt0(X70,X69)
| X70 = sdtasdt0(X69,X71) )
& ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 != sdtsldt0(X70,X69)
| aNaturalNumber0(X71) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])]) ).
cnf(c_0_24,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_26,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| X3 = sz00
| X1 = sdtsldt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25]) ).
fof(c_0_29,hypothesis,
( doDivides0(xp,xn)
& xn = sdtasdt0(xp,esk8_0)
& aNaturalNumber0(esk8_0)
& doDivides0(xp,sdtasdt0(xn,xn))
& sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0)
& aNaturalNumber0(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__3046])]) ).
cnf(c_0_30,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,negated_conjecture,
~ ( ( sdtlseqdt0(xn,xm)
& ? [X1] :
( sdtpldt0(xn,X1) = xm
& aNaturalNumber0(X1) ) )
=> ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ? [X1] :
( sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm)
& aNaturalNumber0(X1) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_33,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_25]),c_0_28]) ).
cnf(c_0_34,hypothesis,
sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,hypothesis,
aNaturalNumber0(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_30]),c_0_31])]) ).
cnf(c_0_38,hypothesis,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
fof(c_0_39,negated_conjecture,
! [X104] :
( ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
& ( sdtpldt0(sdtasdt0(xn,xn),X104) != sdtasdt0(xm,xm)
| ~ aNaturalNumber0(X104) )
& sdtlseqdt0(xn,xm)
& sdtpldt0(xn,esk9_0) = xm
& aNaturalNumber0(esk9_0) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])])]) ).
cnf(c_0_40,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_41,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xp) = esk7_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_31]),c_0_35])]),c_0_36]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_25]),c_0_38])]) ).
fof(c_0_43,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_44,plain,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
inference(fof_simplification,[status(thm)],[mMonMul]) ).
cnf(c_0_45,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,hypothesis,
sdtasdt0(xm,xm) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_31])]),c_0_36]),c_0_41]),c_0_42])]) ).
fof(c_0_47,plain,
! [X50,X51] :
( ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| sdtlseqdt0(X50,X51)
| sdtlseqdt0(X51,X50) )
& ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| sdtlseqdt0(X50,X51)
| X51 != X50 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])]) ).
fof(c_0_48,plain,
! [X55,X56,X57] :
( ( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X55)
| ~ sdtlseqdt0(X56,X57)
| X56 = X57
| X55 = sz00
| sdtlseqdt0(sdtasdt0(X56,X55),sdtasdt0(X57,X55)) )
& ( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X55)
| ~ sdtlseqdt0(X56,X57)
| X56 = X57
| X55 = sz00
| sdtasdt0(X56,X55) != sdtasdt0(X57,X55) )
& ( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X55)
| ~ sdtlseqdt0(X56,X57)
| X56 = X57
| X55 = sz00
| sdtlseqdt0(sdtasdt0(X55,X56),sdtasdt0(X55,X57)) )
& ( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X55)
| ~ sdtlseqdt0(X56,X57)
| X56 = X57
| X55 = sz00
| sdtasdt0(X55,X56) != sdtasdt0(X55,X57) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
fof(c_0_49,plain,
! [X47,X48,X49] :
( sdtlseqdt0(X47,X49)
| ~ sdtlseqdt0(X48,X49)
| ~ sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| ~ aNaturalNumber0(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).
cnf(c_0_50,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xn,xn),esk7_0),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_34]),c_0_35]),c_0_31])]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| X2 = X3
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,negated_conjecture,
sdtlseqdt0(xn,xm),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_55,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_56,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_57,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_58,negated_conjecture,
sdtlseqdt0(esk7_0,sdtasdt0(xn,xn)),
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_35])]) ).
cnf(c_0_59,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xm))
| X1 = sz00
| xm = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_56])]) ).
cnf(c_0_60,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_61,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
cnf(c_0_62,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,esk7_0)
| sdtlseqdt0(X1,sdtasdt0(xn,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_52]),c_0_35])]) ).
cnf(c_0_63,hypothesis,
( sdtlseqdt0(sdtasdt0(xm,xn),esk7_0)
| xm = xn ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_46]),c_0_55])]),c_0_60]) ).
fof(c_0_64,plain,
! [X22] :
( ( ~ aNaturalNumber0(X22)
| X22 = sdtasdt0(sz10,X22) )
& ( ~ aNaturalNumber0(X22)
| sdtasdt0(X22,sz10) = X22 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_65,plain,
! [X19,X20,X21] :
( sdtasdt0(sdtasdt0(X19,X20),X21) = sdtasdt0(X19,sdtasdt0(X20,X21))
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X20)
| ~ aNaturalNumber0(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_66,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_61]) ).
fof(c_0_67,plain,
! [X45,X46] :
( X45 = X46
| ~ sdtlseqdt0(X46,X45)
| ~ sdtlseqdt0(X45,X46)
| ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
cnf(c_0_68,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xn))
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| xm = xn ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_70,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_71,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_72,hypothesis,
xn = sdtasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_73,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_74,hypothesis,
( sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| xm = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_25]),c_0_56]),c_0_55])]) ).
cnf(c_0_75,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_76,plain,
! [X17,X18] :
( sdtasdt0(X17,X18) = sdtasdt0(X18,X17)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_77,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]),c_0_25]) ).
cnf(c_0_78,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_72]),c_0_38]),c_0_31])]) ).
cnf(c_0_79,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn))
| xm = xn
| sdtasdt0(xm,xn) = sdtasdt0(xn,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_52])]) ).
cnf(c_0_80,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X3)
| X1 = X3
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_81,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_75]),c_0_71])]) ).
cnf(c_0_82,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_83,hypothesis,
sdtasdt0(xn,sz10) = 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_77,c_0_78]),c_0_72]),c_0_38]),c_0_31]),c_0_71])]) ).
fof(c_0_84,plain,
! [X16] :
( ( ~ aNaturalNumber0(X16)
| X16 = sdtpldt0(sz00,X16) )
& ( ~ aNaturalNumber0(X16)
| sdtpldt0(X16,sz00) = X16 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
cnf(c_0_85,hypothesis,
( ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn))
| xm = xn
| sdtasdt0(xm,xn) = sdtasdt0(xn,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_25]),c_0_56]),c_0_55])]) ).
cnf(c_0_86,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(xn,X1),sdtasdt0(xm,X1))
| X1 = sz00
| xm = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_54]),c_0_55]),c_0_56])]) ).
cnf(c_0_87,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_88,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,X2) = sz00
| sdtsldt0(sdtasdt0(X1,sdtasdt0(X2,X3)),sdtasdt0(X1,X2)) = X3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_70]),c_0_25]) ).
cnf(c_0_89,hypothesis,
sdtasdt0(sz10,sdtasdt0(xn,xn)) = sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_34]),c_0_35]),c_0_31])]) ).
cnf(c_0_90,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_71]),c_0_56])]) ).
cnf(c_0_91,negated_conjecture,
( sdtpldt0(sdtasdt0(xn,xn),X1) != sdtasdt0(xm,xm)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_92,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_93,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_94,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X2 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X2) = X1 ),
inference(spm,[status(thm)],[c_0_33,c_0_82]) ).
cnf(c_0_95,negated_conjecture,
( xm = xn
| sdtasdt0(xm,xn) = sdtasdt0(xn,xn) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_56])]),c_0_87]) ).
cnf(c_0_96,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xn) = xn,
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_88,c_0_89]),c_0_90]),c_0_90]),c_0_56]),c_0_71])]),c_0_87]) ).
cnf(c_0_97,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93])]),c_0_52])]) ).
cnf(c_0_98,negated_conjecture,
xm = xn,
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_94,c_0_95]),c_0_96]),c_0_56]),c_0_55])]),c_0_87]) ).
cnf(c_0_99,negated_conjecture,
sdtasdt0(xn,xn) != esk7_0,
inference(rw,[status(thm)],[c_0_97,c_0_46]) ).
cnf(c_0_100,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_98]),c_0_98]),c_0_99]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM527+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 02:40:51 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 10.90/1.88 % Version: 3.5.1
% 10.90/1.88 % Preprocessing class: FSLSSMSSSSSNFFN.
% 10.90/1.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.90/1.88 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 10.90/1.88 % Starting new_bool_3 with 300s (1) cores
% 10.90/1.88 % Starting new_bool_1 with 300s (1) cores
% 10.90/1.88 % Starting sh5l with 300s (1) cores
% 10.90/1.88 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1189092 completed with status 0
% 10.90/1.88 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 10.90/1.88 % Preprocessing class: FSLSSMSSSSSNFFN.
% 10.90/1.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.90/1.88 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 10.90/1.88 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.90/1.88 % No SInE strategy applied
% 10.90/1.88 % Search class: FGHSF-FSMM32-SFFFFFNN
% 10.90/1.88 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 10.90/1.88 % Starting SubtermCWHack with 136s (1) cores
% 10.90/1.88 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 10.90/1.88 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 10.90/1.88 % Starting new_bool_3 with 136s (1) cores
% 10.90/1.88 % Starting new_bool_1 with 136s (1) cores
% 10.90/1.88 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1189098 completed with status 0
% 10.90/1.88 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 10.90/1.88 % Preprocessing class: FSLSSMSSSSSNFFN.
% 10.90/1.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.90/1.88 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 10.90/1.88 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.90/1.88 % No SInE strategy applied
% 10.90/1.88 % Search class: FGHSF-FSMM32-SFFFFFNN
% 10.90/1.88 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 10.90/1.88 % Starting SubtermCWHack with 136s (1) cores
% 10.90/1.88 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 10.90/1.88 % Preprocessing time : 0.003 s
% 10.90/1.88 % Presaturation interreduction done
% 10.90/1.88
% 10.90/1.88 % Proof found!
% 10.90/1.88 % SZS status Theorem
% 10.90/1.88 % SZS output start CNFRefutation
% See solution above
% 10.90/1.88 % Parsed axioms : 47
% 10.90/1.88 % Removed by relevancy pruning/SinE : 0
% 10.90/1.88 % Initial clauses : 104
% 10.90/1.88 % Removed in clause preprocessing : 3
% 10.90/1.88 % Initial clauses in saturation : 101
% 10.90/1.88 % Processed clauses : 4805
% 10.90/1.88 % ...of these trivial : 226
% 10.90/1.88 % ...subsumed : 2557
% 10.90/1.88 % ...remaining for further processing : 2022
% 10.90/1.88 % Other redundant clauses eliminated : 114
% 10.90/1.88 % Clauses deleted for lack of memory : 0
% 10.90/1.88 % Backward-subsumed : 68
% 10.90/1.88 % Backward-rewritten : 618
% 10.90/1.88 % Generated clauses : 38450
% 10.90/1.88 % ...of the previous two non-redundant : 34196
% 10.90/1.88 % ...aggressively subsumed : 0
% 10.90/1.88 % Contextual simplify-reflections : 143
% 10.90/1.88 % Paramodulations : 38321
% 10.90/1.88 % Factorizations : 5
% 10.90/1.88 % NegExts : 0
% 10.90/1.88 % Equation resolutions : 122
% 10.90/1.88 % Disequality decompositions : 0
% 10.90/1.88 % Total rewrite steps : 51421
% 10.90/1.88 % ...of those cached : 50850
% 10.90/1.88 % Propositional unsat checks : 0
% 10.90/1.88 % Propositional check models : 0
% 10.90/1.88 % Propositional check unsatisfiable : 0
% 10.90/1.88 % Propositional clauses : 0
% 10.90/1.88 % Propositional clauses after purity: 0
% 10.90/1.88 % Propositional unsat core size : 0
% 10.90/1.88 % Propositional preprocessing time : 0.000
% 10.90/1.88 % Propositional encoding time : 0.000
% 10.90/1.88 % Propositional solver time : 0.000
% 10.90/1.88 % Success case prop preproc time : 0.000
% 10.90/1.88 % Success case prop encoding time : 0.000
% 10.90/1.88 % Success case prop solver time : 0.000
% 10.90/1.88 % Current number of processed clauses : 1227
% 10.90/1.88 % Positive orientable unit clauses : 416
% 10.90/1.88 % Positive unorientable unit clauses: 0
% 10.90/1.88 % Negative unit clauses : 226
% 10.90/1.88 % Non-unit-clauses : 585
% 10.90/1.88 % Current number of unprocessed clauses: 28929
% 10.90/1.88 % ...number of literals in the above : 124128
% 10.90/1.88 % Current number of archived formulas : 0
% 10.90/1.88 % Current number of archived clauses : 784
% 10.90/1.88 % Clause-clause subsumption calls (NU) : 67938
% 10.90/1.88 % Rec. Clause-clause subsumption calls : 26893
% 10.90/1.88 % Non-unit clause-clause subsumptions : 1329
% 10.90/1.88 % Unit Clause-clause subsumption calls : 14549
% 10.90/1.88 % Rewrite failures with RHS unbound : 0
% 10.90/1.88 % BW rewrite match attempts : 167
% 10.90/1.88 % BW rewrite match successes : 108
% 10.90/1.88 % Condensation attempts : 0
% 10.90/1.88 % Condensation successes : 0
% 10.90/1.88 % Termbank termtop insertions : 729002
% 10.90/1.88 % Search garbage collected termcells : 1695
% 10.90/1.88
% 10.90/1.88 % -------------------------------------------------
% 10.90/1.88 % User time : 1.337 s
% 10.90/1.88 % System time : 0.059 s
% 10.90/1.88 % Total time : 1.396 s
% 10.90/1.88 % Maximum resident set size: 3948 pages
% 10.90/1.88
% 10.90/1.88 % -------------------------------------------------
% 10.90/1.88 % User time : 6.564 s
% 10.90/1.88 % System time : 0.270 s
% 10.90/1.88 % Total time : 6.835 s
% 10.90/1.88 % Maximum resident set size: 4864 pages
% 10.90/1.88 % E exiting
%------------------------------------------------------------------------------