%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM480+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 : n001.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 01:49:15 PM UTC 2026
% Result : Theorem 0.82s 0.70s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 91 ( 28 unt; 0 def)
% Number of atoms : 256 ( 119 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 272 ( 107 ~; 128 |; 23 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 34 !; 1 ?)
% 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(m__1524_04,hypothesis,
( doDivides0(xl,xm)
& xl != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524_04) ).
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(m__1524,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524) ).
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__1594,hypothesis,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1594) ).
fof(m__1553,hypothesis,
aNaturalNumber0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1553) ).
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__,conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_13,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_14,plain,
! [X67,X68,X69] :
( ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 = sdtsldt0(X68,X67)
| X68 != sdtasdt0(X67,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| X68 = sdtasdt0(X67,X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| aNaturalNumber0(X69) ) ),
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_13])])])])]) ).
fof(c_0_15,hypothesis,
( doDivides0(xl,xm)
& xl != sz00 ),
inference(fof_simplification,[status(thm)],[m__1524_04]) ).
cnf(c_0_16,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,hypothesis,
( doDivides0(xl,xm)
& xl != sz00 ),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X17,X18,X19] :
( sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19))
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_19,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,hypothesis,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1524]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1524]) ).
cnf(c_0_23,hypothesis,
xl != sz00,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,plain,
! [X63,X64,X66] :
( ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| doDivides0(X63,X64)
| X64 != sdtasdt0(X63,X66)
| ~ aNaturalNumber0(X66) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| X64 = sdtasdt0(X63,esk2_2(X63,X64)) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| aNaturalNumber0(esk2_2(X63,X64)) ) ),
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_25,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_26,hypothesis,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(split_conjunct,[status(thm)],[m__1594]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1553]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_30,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,hypothesis,
sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_21])]),c_0_29])]) ).
cnf(c_0_33,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_30]),c_0_31]) ).
cnf(c_0_34,hypothesis,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(rw,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_35,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xl,xn))
| aNaturalNumber0(sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_29])]) ).
fof(c_0_36,plain,
! [X15,X16] :
( sdtasdt0(X15,X16) = sdtasdt0(X16,X15)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2)
| X2 = sz00
| X1 = sdtasdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_38,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xl,xn))
| doDivides0(sdtasdt0(xl,xn),sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29])]) ).
cnf(c_0_39,hypothesis,
aNaturalNumber0(sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_31]),c_0_28]),c_0_21])]) ).
cnf(c_0_40,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,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_14]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_43,hypothesis,
doDivides0(sdtasdt0(xl,xn),sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_31]),c_0_28]),c_0_21])]) ).
cnf(c_0_44,hypothesis,
aNaturalNumber0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))),
inference(rw,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_45,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X2,X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_40]) ).
cnf(c_0_46,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_41]),c_0_31]),c_0_33]) ).
cnf(c_0_47,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xl,xn))
| sdtasdt0(xl,xn) = sz00
| sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xl,xn))) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_48,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xl,xn))
| aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xl,xn)))
| sdtasdt0(xl,xn) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_43]),c_0_44])]) ).
cnf(c_0_49,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xl,xn))
| doDivides0(sdtsldt0(xm,xl),sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_34]),c_0_29])]) ).
cnf(c_0_50,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X2 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X2) = X1 ),
inference(spm,[status(thm)],[c_0_46,c_0_40]) ).
cnf(c_0_51,hypothesis,
( sdtasdt0(xl,xn) = sz00
| sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xl,xn))) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_31]),c_0_28]),c_0_21])]) ).
cnf(c_0_52,hypothesis,
( aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xl,xn)))
| sdtasdt0(xl,xn) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_31]),c_0_28]),c_0_21])]) ).
cnf(c_0_53,hypothesis,
doDivides0(sdtsldt0(xm,xl),sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_31]),c_0_28]),c_0_21])]) ).
cnf(c_0_54,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xl,xn))
| sdtsldt0(xm,xl) = sz00
| sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtsldt0(xm,xl)) = sdtasdt0(xl,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_34]),c_0_29])]) ).
cnf(c_0_55,hypothesis,
( sdtasdt0(xl,xn) = sz00
| sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xl,xn)))) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_51]),c_0_28]),c_0_21])]),c_0_52]) ).
cnf(c_0_56,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xl,xn))
| sdtasdt0(xl,xn) = sz00
| sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xl,xn)) = sdtsldt0(xm,xl) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_34]),c_0_29])]) ).
cnf(c_0_57,hypothesis,
( sdtsldt0(xm,xl) = sz00
| sdtasdt0(sdtsldt0(xm,xl),sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtsldt0(xm,xl))) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_53]),c_0_29]),c_0_44])]) ).
cnf(c_0_58,hypothesis,
( sdtsldt0(xm,xl) = sz00
| sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtsldt0(xm,xl)) = sdtasdt0(xl,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_31]),c_0_28]),c_0_21])]) ).
fof(c_0_59,negated_conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_60,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xl,xn))))
| sdtasdt0(xl,xn) = sz00
| sdtasdt0(xn,sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xl,xn))) = sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),xl) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_55]),c_0_21])]),c_0_23]) ).
cnf(c_0_61,hypothesis,
( sdtasdt0(xl,xn) = sz00
| sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xl,xn)) = sdtsldt0(xm,xl) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_31]),c_0_28]),c_0_21])]) ).
cnf(c_0_62,hypothesis,
( sdtsldt0(xm,xl) = sz00
| sdtasdt0(sdtsldt0(xm,xl),sdtasdt0(xl,xn)) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_27]),c_0_31]) ).
fof(c_0_64,negated_conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
cnf(c_0_65,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,sdtsldt0(xm,xl)))
| sdtasdt0(xl,xn) = sz00
| sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),xl) = sdtasdt0(xn,sdtsldt0(xm,xl)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,hypothesis,
( sdtsldt0(xm,xl) = sz00
| sdtasdt0(xn,sdtasdt0(sdtsldt0(xm,xl),xl)) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_28]),c_0_21]),c_0_29])]) ).
cnf(c_0_67,hypothesis,
sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
fof(c_0_68,negated_conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(fof_nnf,[status(thm)],[c_0_64]) ).
cnf(c_0_69,hypothesis,
( sdtasdt0(xl,xn) = sz00
| sdtsldt0(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),xl) = sdtasdt0(xn,sdtsldt0(xm,xl)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_31]),c_0_29]),c_0_28])]) ).
cnf(c_0_70,hypothesis,
( sdtsldt0(xm,xl) = sz00
| sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) = sdtasdt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_40]),c_0_67]),c_0_21]),c_0_29])]) ).
cnf(c_0_71,negated_conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
fof(c_0_72,plain,
! [X33,X34] :
( X34 = sz00
| X33 = sz00
| sdtasdt0(X33,X34) != sz00
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
cnf(c_0_73,hypothesis,
( sdtasdt0(xl,xn) = sz00
| sdtsldt0(xm,xl) = sz00 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
fof(c_0_74,plain,
! [X21] :
( ( ~ aNaturalNumber0(X21)
| sz00 = sdtasdt0(sz00,X21) )
& ( ~ aNaturalNumber0(X21)
| sdtasdt0(X21,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
cnf(c_0_75,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_76,hypothesis,
( sdtasdt0(xl,sz00) = xm
| sdtasdt0(xl,xn) = sz00 ),
inference(spm,[status(thm)],[c_0_67,c_0_73]) ).
cnf(c_0_77,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_78,hypothesis,
( xn = sz00
| sdtasdt0(xl,sz00) = xm ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_28]),c_0_21])]),c_0_23]) ).
cnf(c_0_79,hypothesis,
( xm = sz00
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_21])]) ).
cnf(c_0_80,negated_conjecture,
( sdtsldt0(sdtasdt0(sz00,xm),xl) != sdtasdt0(sz00,sdtsldt0(xm,xl))
| xm = sz00 ),
inference(spm,[status(thm)],[c_0_71,c_0_79]) ).
cnf(c_0_81,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_82,negated_conjecture,
( sdtasdt0(sz00,sdtsldt0(xm,xl)) != sdtsldt0(sz00,xl)
| xm = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_22])]) ).
cnf(c_0_83,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_84,negated_conjecture,
( sdtsldt0(sz00,xl) != sz00
| xm = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_81]),c_0_29])]) ).
cnf(c_0_85,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(sz00,X1) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_77]),c_0_83])]) ).
cnf(c_0_86,negated_conjecture,
xm = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_21])]),c_0_23]) ).
cnf(c_0_87,negated_conjecture,
sdtsldt0(sdtasdt0(xn,sz00),xl) != sdtasdt0(xn,sdtsldt0(sz00,xl)),
inference(spm,[status(thm)],[c_0_71,c_0_86]) ).
cnf(c_0_88,negated_conjecture,
sdtasdt0(xn,sdtsldt0(sz00,xl)) != sdtsldt0(sz00,xl),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_77]),c_0_28])]) ).
cnf(c_0_89,negated_conjecture,
sdtasdt0(xn,sz00) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_85]),c_0_21])]),c_0_23]) ).
cnf(c_0_90,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_77]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM480+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 : n001.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 02:39:14 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.52 Running first-order theorem proving
% 0.27/0.52 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
% 0.82/0.70 % Version: 3.5.1
% 0.82/0.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.82/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.82/0.70 % Starting new_bool_3 with 300s (1) cores
% 0.82/0.70 % Starting new_bool_1 with 300s (1) cores
% 0.82/0.70 % Starting sh5l with 300s (1) cores
% 0.82/0.70 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2007940 completed with status 0
% 0.82/0.70 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.82/0.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.82/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.82/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.82/0.70 % No SInE strategy applied
% 0.82/0.70 % Search class: FGUSF-FFMM22-MFFFFFNN
% 0.82/0.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.82/0.70 % Starting SubtermCWHack with 136s (1) cores
% 0.82/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.82/0.70 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.82/0.70 % Starting new_bool_3 with 136s (1) cores
% 0.82/0.70 % Starting new_bool_1 with 136s (1) cores
% 0.82/0.70 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2007946 completed with status 0
% 0.82/0.70 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.82/0.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.82/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.82/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.82/0.70 % No SInE strategy applied
% 0.82/0.70 % Search class: FGUSF-FFMM22-MFFFFFNN
% 0.82/0.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.82/0.70 % Starting SubtermCWHack with 136s (1) cores
% 0.82/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.82/0.70 % Preprocessing time : 0.003 s
% 0.82/0.70 % Presaturation interreduction done
% 0.82/0.70
% 0.82/0.70 % Proof found!
% 0.82/0.70 % SZS status Theorem
% 0.82/0.70 % SZS output start CNFRefutation
% See solution above
% 0.82/0.70 % Parsed axioms : 40
% 0.82/0.70 % Removed by relevancy pruning/SinE : 0
% 0.82/0.70 % Initial clauses : 66
% 0.82/0.70 % Removed in clause preprocessing : 3
% 0.82/0.70 % Initial clauses in saturation : 63
% 0.82/0.70 % Processed clauses : 1082
% 0.82/0.70 % ...of these trivial : 48
% 0.82/0.70 % ...subsumed : 449
% 0.82/0.70 % ...remaining for further processing : 585
% 0.82/0.70 % Other redundant clauses eliminated : 25
% 0.82/0.70 % Clauses deleted for lack of memory : 0
% 0.82/0.70 % Backward-subsumed : 48
% 0.82/0.70 % Backward-rewritten : 255
% 0.82/0.70 % Generated clauses : 5033
% 0.82/0.70 % ...of the previous two non-redundant : 4398
% 0.82/0.70 % ...aggressively subsumed : 0
% 0.82/0.70 % Contextual simplify-reflections : 68
% 0.82/0.70 % Paramodulations : 5001
% 0.82/0.70 % Factorizations : 2
% 0.82/0.70 % NegExts : 0
% 0.82/0.70 % Equation resolutions : 30
% 0.82/0.70 % Disequality decompositions : 0
% 0.82/0.70 % Total rewrite steps : 6129
% 0.82/0.70 % ...of those cached : 6037
% 0.82/0.70 % Propositional unsat checks : 0
% 0.82/0.70 % Propositional check models : 0
% 0.82/0.70 % Propositional check unsatisfiable : 0
% 0.82/0.70 % Propositional clauses : 0
% 0.82/0.70 % Propositional clauses after purity: 0
% 0.82/0.70 % Propositional unsat core size : 0
% 0.82/0.70 % Propositional preprocessing time : 0.000
% 0.82/0.70 % Propositional encoding time : 0.000
% 0.82/0.70 % Propositional solver time : 0.000
% 0.82/0.70 % Success case prop preproc time : 0.000
% 0.82/0.70 % Success case prop encoding time : 0.000
% 0.82/0.70 % Success case prop solver time : 0.000
% 0.82/0.70 % Current number of processed clauses : 215
% 0.82/0.70 % Positive orientable unit clauses : 50
% 0.82/0.70 % Positive unorientable unit clauses: 0
% 0.82/0.70 % Negative unit clauses : 8
% 0.82/0.70 % Non-unit-clauses : 157
% 0.82/0.70 % Current number of unprocessed clauses: 3322
% 0.82/0.70 % ...number of literals in the above : 13468
% 0.82/0.70 % Current number of archived formulas : 0
% 0.82/0.70 % Current number of archived clauses : 361
% 0.82/0.70 % Clause-clause subsumption calls (NU) : 11623
% 0.82/0.70 % Rec. Clause-clause subsumption calls : 7175
% 0.82/0.70 % Non-unit clause-clause subsumptions : 537
% 0.82/0.70 % Unit Clause-clause subsumption calls : 1362
% 0.82/0.70 % Rewrite failures with RHS unbound : 0
% 0.82/0.70 % BW rewrite match attempts : 40
% 0.82/0.70 % BW rewrite match successes : 39
% 0.82/0.70 % Condensation attempts : 0
% 0.82/0.70 % Condensation successes : 0
% 0.82/0.70 % Termbank termtop insertions : 105464
% 0.82/0.70 % Search garbage collected termcells : 1099
% 0.82/0.70
% 0.82/0.70 % -------------------------------------------------
% 0.82/0.70 % User time : 0.114 s
% 0.82/0.70 % System time : 0.010 s
% 0.82/0.70 % Total time : 0.124 s
% 0.82/0.70 % Maximum resident set size: 3676 pages
% 0.82/0.70
% 0.82/0.70 % -------------------------------------------------
% 0.82/0.70 % User time : 0.361 s
% 0.82/0.70 % System time : 0.040 s
% 0.82/0.70 % Total time : 0.401 s
% 0.82/0.70 % Maximum resident set size: 4608 pages
% 0.82/0.70 % E exiting
%------------------------------------------------------------------------------