%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG109+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 : n015.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 02:05:53 PM UTC 2026
% Result : Theorem 110.03s 16.83s
% Output : CNFRefutation 110.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 28
% Syntax : Number of formulae : 171 ( 53 unt; 0 def)
% Number of atoms : 612 ( 156 equ)
% Maximal formula atoms : 52 ( 3 avg)
% Number of connectives : 757 ( 316 ~; 323 |; 85 &)
% ( 8 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 6 con; 0-4 aty)
% Number of variables : 234 ( 0 sgn 100 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDivision,axiom,
! [X1,X2] :
( ( X2 != sz00
& aElement0(X2)
& aElement0(X1) )
=> ? [X3,X4] :
( ( X4 != sz00
=> iLess0(sbrdtbr0(X4),sbrdtbr0(X2)) )
& X1 = sdtpldt0(sdtasdt0(X3,X2),X4)
& aElement0(X4)
& aElement0(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivision) ).
fof(mUnNeZr,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mDefPrIdeal,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( X2 = slsdtgt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtasdt0(X1,X4) = X3
& aElement0(X4) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( sdtasdt0(X1,X3) = X2
& aElement0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__2203,hypothesis,
( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(m__2091,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(mDefGCD,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> ! [X3] :
( aGcdOfAnd0(X3,X1,X2)
<=> ( ! [X4] :
( ( aDivisorOf0(X4,X2)
& aDivisorOf0(X4,X1) )
=> doDivides0(X4,X3) )
& aDivisorOf0(X3,X2)
& aDivisorOf0(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefGCD) ).
fof(mDefDvs,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( doDivides0(X2,X1)
& aElement0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).
fof(m__2129,hypothesis,
aGcdOfAnd0(xc,xa,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2129) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ( sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mDefSSum,axiom,
! [X1,X2] :
( ( aSet0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtpldt1(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ? [X5,X6] :
( sdtpldt0(X5,X6) = X4
& aElementOf0(X6,X2)
& aElementOf0(X5,X1) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
fof(m__,conjecture,
? [X1] :
( X1 != sz00
& aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) )
& ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) ) ) )
& aSet0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(mAddInvr,axiom,
! [X1] :
( aElement0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
fof(mPrIdeal,axiom,
! [X1] :
( aElement0(X1)
=> aIdeal0(slsdtgt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrIdeal) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(m__2110,hypothesis,
( xb != sz00
| xa != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
fof(c_0_28,plain,
! [X1,X2] :
( ( X2 != sz00
& aElement0(X2)
& aElement0(X1) )
=> ? [X3,X4] :
( ( X4 != sz00
=> iLess0(sbrdtbr0(X4),sbrdtbr0(X2)) )
& X1 = sdtpldt0(sdtasdt0(X3,X2),X4)
& aElement0(X4)
& aElement0(X3) ) ),
inference(fof_simplification,[status(thm)],[mDivision]) ).
fof(c_0_29,plain,
sz10 != sz00,
inference(fof_simplification,[status(thm)],[mUnNeZr]) ).
fof(c_0_30,plain,
! [X87,X88] :
( ( X88 = sz00
| ~ aElement0(X88)
| ~ aElement0(X87)
| iLess0(sbrdtbr0(esk15_2(X87,X88)),sbrdtbr0(X88))
| esk15_2(X87,X88) = sz00 )
& ( X88 = sz00
| ~ aElement0(X88)
| ~ aElement0(X87)
| X87 = sdtpldt0(sdtasdt0(esk14_2(X87,X88),X88),esk15_2(X87,X88)) )
& ( X88 = sz00
| ~ aElement0(X88)
| ~ aElement0(X87)
| aElement0(esk15_2(X87,X88)) )
& ( X88 = sz00
| ~ aElement0(X88)
| ~ aElement0(X87)
| aElement0(esk14_2(X87,X88)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])]) ).
fof(c_0_31,plain,
! [X25] :
( ( ~ aElement0(X25)
| X25 = sdtasdt0(sz10,X25) )
& ( ~ aElement0(X25)
| sdtasdt0(X25,sz10) = X25 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])])]) ).
fof(c_0_32,plain,
sz10 != sz00,
inference(fof_nnf,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| X2 = sz00
| X1 = sdtpldt0(sdtasdt0(esk14_2(X1,X2),X2),esk15_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( ~ aElement0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_36,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_37,plain,
! [X15,X16,X17] :
( sdtpldt0(sdtpldt0(X15,X16),X17) = sdtpldt0(X15,sdtpldt0(X16,X17))
| ~ aElement0(X17)
| ~ aElement0(X16)
| ~ aElement0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_38,plain,
( ~ aElement0(X1)
| ~ aElement0(esk14_2(X1,sz10))
| sdtpldt0(esk14_2(X1,sz10),esk15_2(X1,sz10)) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_39,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| X2 = sz00
| aElement0(esk14_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,plain,
( ~ aElement0(X1)
| sdtpldt0(esk14_2(X1,sz10),esk15_2(X1,sz10)) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_35])]),c_0_36]) ).
cnf(c_0_42,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(esk14_2(X1,sz10))
| ~ aElement0(esk15_2(X1,sz10))
| sdtpldt0(esk14_2(X1,sz10),sdtpldt0(esk15_2(X1,sz10),X2)) = sdtpldt0(X1,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| X2 = sz00
| aElement0(esk15_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(esk14_2(X1,sz10))
| sdtpldt0(esk14_2(X1,sz10),sdtpldt0(esk15_2(X1,sz10),X2)) = sdtpldt0(X1,X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_35])]),c_0_36]) ).
fof(c_0_45,plain,
! [X18] :
( ( ~ aElement0(X18)
| X18 = sdtpldt0(sz00,X18) )
& ( ~ aElement0(X18)
| sdtpldt0(X18,sz00) = X18 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
cnf(c_0_46,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtpldt0(esk14_2(X1,sz10),sdtpldt0(esk15_2(X1,sz10),X2)) = sdtpldt0(X1,X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_39]),c_0_35])]),c_0_36]) ).
cnf(c_0_47,plain,
( ~ aElement0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_48,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_49,plain,
! [X105,X106,X107,X109,X110,X111,X113] :
( ( ~ aElement0(X105)
| X111 = slsdtgt0(X105)
| ~ aSet0(X111)
| aElementOf0(esk19_2(X105,X111),X111)
| sdtasdt0(X105,esk20_2(X105,X111)) = esk19_2(X105,X111) )
& ( ~ aElement0(X105)
| X111 = slsdtgt0(X105)
| ~ aSet0(X111)
| aElementOf0(esk19_2(X105,X111),X111)
| aElement0(esk20_2(X105,X111)) )
& ( ~ aElement0(X105)
| X111 = slsdtgt0(X105)
| ~ aSet0(X111)
| sdtasdt0(X105,X113) != esk19_2(X105,X111)
| ~ aElement0(X113)
| ~ aElementOf0(esk19_2(X105,X111),X111) )
& ( ~ aElement0(X105)
| X106 != slsdtgt0(X105)
| aElementOf0(X109,X106)
| sdtasdt0(X105,X110) != X109
| ~ aElement0(X110) )
& ( ~ aElement0(X105)
| X106 != slsdtgt0(X105)
| ~ aElementOf0(X107,X106)
| sdtasdt0(X105,esk18_3(X105,X106,X107)) = X107 )
& ( ~ aElement0(X105)
| X106 != slsdtgt0(X105)
| ~ aElementOf0(X107,X106)
| aElement0(esk18_3(X105,X106,X107)) )
& ( ~ aElement0(X105)
| X106 != slsdtgt0(X105)
| aSet0(X106) ) ),
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)],[mDefPrIdeal])])])])])])]) ).
fof(c_0_50,plain,
! [X13,X14] :
( sdtpldt0(X13,X14) = sdtpldt0(X14,X13)
| ~ aElement0(X14)
| ~ aElement0(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_51,plain,
( ~ aElement0(X1)
| ~ aElement0(esk15_2(X1,sz10))
| sdtpldt0(esk14_2(X1,sz10),esk15_2(X1,sz10)) = sdtpldt0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
fof(c_0_52,plain,
! [X91,X92,X94] :
( ( ~ aElement0(X92)
| ~ aElement0(X91)
| doDivides0(X91,X92)
| sdtasdt0(X91,X94) != X92
| ~ aElement0(X94) )
& ( ~ aElement0(X92)
| ~ aElement0(X91)
| ~ doDivides0(X91,X92)
| sdtasdt0(X91,esk16_2(X91,X92)) = X92 )
& ( ~ aElement0(X92)
| ~ aElement0(X91)
| ~ doDivides0(X91,X92)
| aElement0(esk16_2(X91,X92)) ) ),
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_53,plain,
! [X11,X12] :
( aElement0(sdtasdt0(X11,X12))
| ~ aElement0(X12)
| ~ aElement0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_54,plain,
( ~ aElement0(X1)
| X2 != slsdtgt0(X1)
| ~ aElementOf0(X3,X2)
| sdtasdt0(X1,esk18_3(X1,X2,X3)) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
( ~ aElement0(X1)
| X2 != slsdtgt0(X1)
| ~ aElementOf0(X3,X2)
| aElement0(esk18_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,plain,
( ~ aElement0(X1)
| sdtpldt0(esk14_2(X1,sz10),esk15_2(X1,sz10)) = sdtpldt0(X1,sz00) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_43]),c_0_35])]),c_0_36]) ).
cnf(c_0_58,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| sdtasdt0(X2,X1) != X3
| ~ aElement0(X1)
| doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
( ~ aElement0(X1)
| ~ aElementOf0(X2,slsdtgt0(X1))
| sdtasdt0(X1,esk18_3(X1,slsdtgt0(X1),X2)) = X2 ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_61,hypothesis,
aElementOf0(xa,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[m__2203]) ).
cnf(c_0_62,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_63,plain,
( ~ aElement0(X1)
| ~ aElementOf0(X2,slsdtgt0(X1))
| aElement0(esk18_3(X1,slsdtgt0(X1),X2)) ),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_64,plain,
( ~ aElement0(X1)
| ~ aElement0(esk14_2(X1,sz10))
| ~ aElement0(esk15_2(X1,sz10))
| sdtpldt0(esk15_2(X1,sz10),esk14_2(X1,sz10)) = sdtpldt0(X1,sz00) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_65,plain,
! [X22,X23,X24] :
( sdtasdt0(sdtasdt0(X22,X23),X24) = sdtasdt0(X22,sdtasdt0(X23,X24))
| ~ aElement0(X24)
| ~ aElement0(X23)
| ~ aElement0(X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_66,plain,
! [X30] :
( ( ~ aElement0(X30)
| sz00 = sdtasdt0(sz00,X30) )
& ( ~ aElement0(X30)
| sdtasdt0(X30,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])])]) ).
cnf(c_0_67,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_58]),c_0_59]) ).
cnf(c_0_68,hypothesis,
sdtasdt0(xa,esk18_3(xa,slsdtgt0(xa),xa)) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_69,hypothesis,
aElement0(esk18_3(xa,slsdtgt0(xa),xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_61]),c_0_62])]) ).
fof(c_0_70,plain,
! [X97,X98,X99,X100,X101] :
( ( ~ aElement0(X98)
| ~ aElement0(X97)
| aGcdOfAnd0(X101,X97,X98)
| ~ aDivisorOf0(X101,X98)
| ~ aDivisorOf0(X101,X97)
| ~ doDivides0(esk17_3(X97,X98,X101),X101) )
& ( ~ aElement0(X98)
| ~ aElement0(X97)
| aGcdOfAnd0(X101,X97,X98)
| ~ aDivisorOf0(X101,X98)
| ~ aDivisorOf0(X101,X97)
| aDivisorOf0(esk17_3(X97,X98,X101),X98) )
& ( ~ aElement0(X98)
| ~ aElement0(X97)
| aGcdOfAnd0(X101,X97,X98)
| ~ aDivisorOf0(X101,X98)
| ~ aDivisorOf0(X101,X97)
| aDivisorOf0(esk17_3(X97,X98,X101),X97) )
& ( ~ aElement0(X98)
| ~ aElement0(X97)
| ~ aGcdOfAnd0(X99,X97,X98)
| doDivides0(X100,X99)
| ~ aDivisorOf0(X100,X98)
| ~ aDivisorOf0(X100,X97) )
& ( ~ aElement0(X98)
| ~ aElement0(X97)
| ~ aGcdOfAnd0(X99,X97,X98)
| aDivisorOf0(X99,X98) )
& ( ~ aElement0(X98)
| ~ aElement0(X97)
| ~ aGcdOfAnd0(X99,X97,X98)
| aDivisorOf0(X99,X97) ) ),
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)],[mDefGCD])])])])])])]) ).
cnf(c_0_71,plain,
( ~ aElement0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_72,plain,
( ~ aElement0(X1)
| ~ aElement0(esk14_2(X1,sz10))
| sdtpldt0(esk15_2(X1,sz10),esk14_2(X1,sz10)) = sdtpldt0(X1,sz00) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_43]),c_0_35])]),c_0_36]) ).
cnf(c_0_73,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,plain,
( ~ aElement0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ doDivides0(X1,X2)
| sdtasdt0(X1,esk16_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_76,hypothesis,
doDivides0(xa,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_62]),c_0_69])]) ).
cnf(c_0_77,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ doDivides0(X1,X2)
| aElement0(esk16_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_78,plain,
! [X95,X96] :
( ( ~ aElement0(X95)
| aDivisorOf0(X96,X95)
| ~ doDivides0(X96,X95)
| ~ aElement0(X96) )
& ( ~ aElement0(X95)
| ~ aDivisorOf0(X96,X95)
| doDivides0(X96,X95) )
& ( ~ aElement0(X95)
| ~ aDivisorOf0(X96,X95)
| aElement0(X96) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDvs])])])])]) ).
cnf(c_0_79,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aGcdOfAnd0(X1,X2,X3)
| aDivisorOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,hypothesis,
aGcdOfAnd0(xc,xa,xb),
inference(split_conjunct,[status(thm)],[m__2129]) ).
cnf(c_0_81,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_82,plain,
( ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aGcdOfAnd0(X1,X3,X2)
| aDivisorOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_83,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_71]),c_0_48])]) ).
cnf(c_0_84,plain,
( ~ aElement0(X1)
| sdtpldt0(esk15_2(X1,sz10),esk14_2(X1,sz10)) = sdtpldt0(X1,sz00) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_39]),c_0_35])]),c_0_36]) ).
fof(c_0_85,plain,
! [X26,X27,X28] :
( ( ~ aElement0(X28)
| ~ aElement0(X27)
| ~ aElement0(X26)
| sdtasdt0(sdtpldt0(X27,X28),X26) = sdtpldt0(sdtasdt0(X27,X26),sdtasdt0(X28,X26)) )
& ( ~ aElement0(X28)
| ~ aElement0(X27)
| ~ aElement0(X26)
| sdtasdt0(X26,sdtpldt0(X27,X28)) = sdtpldt0(sdtasdt0(X26,X27),sdtasdt0(X26,X28)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])])]) ).
cnf(c_0_86,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_48])]) ).
cnf(c_0_87,hypothesis,
sdtasdt0(xa,esk16_2(xa,xa)) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_62])]) ).
cnf(c_0_88,hypothesis,
aElement0(esk16_2(xa,xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_76]),c_0_62])]) ).
cnf(c_0_89,plain,
( ~ aElement0(X2)
| ~ aDivisorOf0(X1,X2)
| doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_90,hypothesis,
aDivisorOf0(xc,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_62])]) ).
cnf(c_0_91,plain,
( ~ aElement0(X2)
| ~ aDivisorOf0(X1,X2)
| aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_92,hypothesis,
aDivisorOf0(xc,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_80]),c_0_62]),c_0_81])]) ).
fof(c_0_93,plain,
! [X9,X10] :
( aElement0(sdtpldt0(X9,X10))
| ~ aElement0(X10)
| ~ aElement0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
cnf(c_0_94,plain,
( ~ aElement0(X1)
| ~ aElement0(esk15_2(X1,sz10))
| ~ aElement0(esk14_2(X1,sz10))
| sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_95,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X3)
| sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_96,plain,
( ~ aElement0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_97,hypothesis,
sdtasdt0(sz00,esk16_2(xa,xa)) = sdtasdt0(sz00,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]),c_0_62])]) ).
cnf(c_0_98,hypothesis,
doDivides0(xc,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_62])]) ).
cnf(c_0_99,hypothesis,
aElement0(xc),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_81])]) ).
fof(c_0_100,plain,
! [X40,X41,X42,X43,X46,X47,X48,X49,X51,X52] :
( ( ~ aSet0(X41)
| ~ aSet0(X40)
| X49 = sdtpldt1(X40,X41)
| ~ aSet0(X49)
| aElementOf0(esk5_3(X40,X41,X49),X49)
| sdtpldt0(esk6_3(X40,X41,X49),esk7_3(X40,X41,X49)) = esk5_3(X40,X41,X49) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X49 = sdtpldt1(X40,X41)
| ~ aSet0(X49)
| aElementOf0(esk5_3(X40,X41,X49),X49)
| aElementOf0(esk7_3(X40,X41,X49),X41) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X49 = sdtpldt1(X40,X41)
| ~ aSet0(X49)
| aElementOf0(esk5_3(X40,X41,X49),X49)
| aElementOf0(esk6_3(X40,X41,X49),X40) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X49 = sdtpldt1(X40,X41)
| ~ aSet0(X49)
| sdtpldt0(X51,X52) != esk5_3(X40,X41,X49)
| ~ aElementOf0(X52,X41)
| ~ aElementOf0(X51,X40)
| ~ aElementOf0(esk5_3(X40,X41,X49),X49) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X42 != sdtpldt1(X40,X41)
| aElementOf0(X46,X42)
| sdtpldt0(X47,X48) != X46
| ~ aElementOf0(X48,X41)
| ~ aElementOf0(X47,X40) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X42 != sdtpldt1(X40,X41)
| ~ aElementOf0(X43,X42)
| sdtpldt0(esk3_4(X40,X41,X42,X43),esk4_4(X40,X41,X42,X43)) = X43 )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X42 != sdtpldt1(X40,X41)
| ~ aElementOf0(X43,X42)
| aElementOf0(esk4_4(X40,X41,X42,X43),X41) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X42 != sdtpldt1(X40,X41)
| ~ aElementOf0(X43,X42)
| aElementOf0(esk3_4(X40,X41,X42,X43),X40) )
& ( ~ aSet0(X41)
| ~ aSet0(X40)
| X42 != sdtpldt1(X40,X41)
| aSet0(X42) ) ),
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)],[mDefSSum])])])])])])]) ).
cnf(c_0_101,plain,
( ~ aElement0(X2)
| X4 != slsdtgt0(X2)
| sdtasdt0(X2,X1) != X3
| ~ aElement0(X1)
| aElementOf0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_102,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_103,plain,
( ~ aElement0(X1)
| ~ aElement0(esk15_2(X1,sz10))
| sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_39]),c_0_35])]),c_0_36]) ).
cnf(c_0_104,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_35])]) ).
cnf(c_0_105,hypothesis,
sdtasdt0(sz00,xa) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_97]),c_0_88])]) ).
cnf(c_0_106,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_96]),c_0_35])]) ).
cnf(c_0_107,hypothesis,
sdtasdt0(xc,esk16_2(xc,xa)) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_98]),c_0_62]),c_0_99])]) ).
cnf(c_0_108,hypothesis,
aElement0(esk16_2(xc,xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_98]),c_0_62]),c_0_99])]) ).
cnf(c_0_109,hypothesis,
aElementOf0(xb,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2203]) ).
cnf(c_0_110,plain,
( ~ aSet0(X4)
| ~ aSet0(X2)
| X6 != sdtpldt1(X2,X4)
| sdtpldt0(X1,X3) != X5
| ~ aElementOf0(X3,X4)
| ~ aElementOf0(X1,X2)
| aElementOf0(X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_111,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_101])]) ).
cnf(c_0_112,plain,
( ~ aElement0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_113,plain,
( ~ aElement0(X2)
| X1 != slsdtgt0(X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_114,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_40]),c_0_102]) ).
cnf(c_0_115,plain,
( ~ aElement0(X1)
| sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_43]),c_0_35])]),c_0_36]) ).
cnf(c_0_116,hypothesis,
sdtasdt0(sdtpldt0(sz00,sz10),xa) = sdtpldt0(sz00,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_62]),c_0_48])]) ).
cnf(c_0_117,hypothesis,
sdtasdt0(sz10,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_99])]) ).
cnf(c_0_118,hypothesis,
sdtasdt0(xb,esk18_3(xb,slsdtgt0(xb),xb)) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_109]),c_0_81])]) ).
cnf(c_0_119,hypothesis,
aElement0(esk18_3(xb,slsdtgt0(xb),xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_109]),c_0_81])]) ).
fof(c_0_120,negated_conjecture,
~ ? [X1] :
( X1 != sz00
& aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_121,plain,
( ~ aSet0(X3)
| ~ aSet0(X4)
| ~ aElementOf0(X1,X3)
| ~ aElementOf0(X2,X4)
| aElementOf0(sdtpldt0(X1,X2),sdtpldt1(X3,X4)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_110])]) ).
cnf(c_0_122,plain,
( ~ aElement0(X1)
| aElementOf0(sz00,slsdtgt0(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_48])]) ).
cnf(c_0_123,plain,
( ~ aElement0(X1)
| aSet0(slsdtgt0(X1)) ),
inference(er,[status(thm)],[c_0_113]) ).
cnf(c_0_124,plain,
( ~ aElement0(X1)
| sdtpldt0(sz00,sdtpldt0(sz00,X1)) = sdtpldt0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_48])]) ).
cnf(c_0_125,hypothesis,
sdtpldt0(sz00,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_71]),c_0_117]),c_0_35])]) ).
cnf(c_0_126,hypothesis,
doDivides0(xb,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_118]),c_0_81]),c_0_119])]) ).
fof(c_0_127,plain,
! [X62,X63,X64,X65,X66] :
( ( aIdeal0(X66)
| ~ aSet0(X66)
| ~ aElementOf0(sdtpldt0(esk9_1(X66),esk10_1(X66)),X66)
| ~ aElementOf0(sdtasdt0(esk11_1(X66),esk9_1(X66)),X66) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| ~ aElementOf0(sdtpldt0(esk9_1(X66),esk10_1(X66)),X66)
| aElement0(esk11_1(X66)) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk10_1(X66),X66)
| ~ aElementOf0(sdtasdt0(esk11_1(X66),esk9_1(X66)),X66) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk10_1(X66),X66)
| aElement0(esk11_1(X66)) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk9_1(X66),X66) )
& ( ~ aIdeal0(X62)
| ~ aElementOf0(X63,X62)
| aElementOf0(sdtasdt0(X65,X63),X62)
| ~ aElement0(X65) )
& ( ~ aIdeal0(X62)
| ~ aElementOf0(X63,X62)
| aElementOf0(sdtpldt0(X63,X64),X62)
| ~ aElementOf0(X64,X62) )
& ( ~ aIdeal0(X62)
| aSet0(X62) ) ),
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)],[mDefIdeal])])])])])])]) ).
fof(c_0_128,negated_conjecture,
~ ? [X1] :
( X1 != sz00
& aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
cnf(c_0_129,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| ~ aElementOf0(X1,X2)
| aElementOf0(sdtpldt0(X1,sz00),sdtpldt1(X2,slsdtgt0(X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123]) ).
cnf(c_0_130,hypothesis,
sdtpldt0(xa,sz00) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_125]),c_0_62])]) ).
fof(c_0_131,plain,
! [X19] :
( ( ~ aElement0(X19)
| sz00 = sdtpldt0(smndt0(X19),X19) )
& ( ~ aElement0(X19)
| sdtpldt0(X19,smndt0(X19)) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])])]) ).
cnf(c_0_132,hypothesis,
sdtasdt0(xb,esk16_2(xb,xb)) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_126]),c_0_81])]) ).
cnf(c_0_133,hypothesis,
aElement0(esk16_2(xb,xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_126]),c_0_81])]) ).
cnf(c_0_134,plain,
( ~ aIdeal0(X2)
| ~ aElementOf0(X3,X2)
| ~ aElementOf0(X1,X2)
| aElementOf0(sdtpldt0(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
fof(c_0_135,plain,
! [X115] :
( aIdeal0(slsdtgt0(X115))
| ~ aElement0(X115) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrIdeal])])]) ).
fof(c_0_136,negated_conjecture,
! [X116] :
( X116 = sz00
| ~ aElementOf0(X116,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_128])])]) ).
cnf(c_0_137,hypothesis,
( ~ aElement0(X1)
| ~ aSet0(slsdtgt0(xa))
| aElementOf0(xa,sdtpldt1(slsdtgt0(xa),slsdtgt0(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_61]),c_0_130]) ).
cnf(c_0_138,plain,
( ~ aElement0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
fof(c_0_139,plain,
! [X8] :
( aElement0(smndt0(X8))
| ~ aElement0(X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])])]) ).
cnf(c_0_140,hypothesis,
sdtasdt0(sz00,esk16_2(xb,xb)) = sdtasdt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_132]),c_0_133]),c_0_81])]) ).
cnf(c_0_141,hypothesis,
doDivides0(xc,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_92]),c_0_81])]) ).
cnf(c_0_142,hypothesis,
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aIdeal0(slsdtgt0(xa))
| aElementOf0(sdtpldt0(xa,X1),slsdtgt0(xa)) ),
inference(spm,[status(thm)],[c_0_134,c_0_61]) ).
cnf(c_0_143,plain,
( ~ aElement0(X1)
| aIdeal0(slsdtgt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_144,negated_conjecture,
( ~ aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_145,hypothesis,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2174]) ).
cnf(c_0_146,hypothesis,
( ~ aElement0(X1)
| aElementOf0(xa,sdtpldt1(slsdtgt0(xa),slsdtgt0(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_123]),c_0_62])]) ).
cnf(c_0_147,plain,
( ~ aElement0(smndt0(sz00))
| smndt0(sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_138]),c_0_48])]) ).
cnf(c_0_148,plain,
( ~ aElement0(X1)
| aElement0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_149,hypothesis,
sdtasdt0(sz00,xb) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_140]),c_0_133])]) ).
cnf(c_0_150,hypothesis,
sdtasdt0(xc,esk16_2(xc,xb)) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_141]),c_0_81]),c_0_99])]) ).
cnf(c_0_151,hypothesis,
aElement0(esk16_2(xc,xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_141]),c_0_81]),c_0_99])]) ).
cnf(c_0_152,hypothesis,
( ~ aSet0(X2)
| ~ aSet0(slsdtgt0(xb))
| ~ aElementOf0(X1,X2)
| aElementOf0(sdtpldt0(X1,xb),sdtpldt1(X2,slsdtgt0(xb))) ),
inference(spm,[status(thm)],[c_0_121,c_0_109]) ).
cnf(c_0_153,hypothesis,
( ~ aElementOf0(X1,slsdtgt0(xa))
| aElementOf0(sdtpldt0(xa,X1),slsdtgt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_62])]) ).
cnf(c_0_154,negated_conjecture,
( ~ aElementOf0(X1,xI)
| X1 = sz00 ),
inference(rw,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_155,hypothesis,
aElementOf0(xa,xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_145]),c_0_81])]) ).
cnf(c_0_156,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_48])]) ).
cnf(c_0_157,hypothesis,
sdtasdt0(sdtpldt0(sz00,sz10),xb) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_149]),c_0_81]),c_0_48])]) ).
cnf(c_0_158,hypothesis,
sdtasdt0(sz10,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_150]),c_0_151]),c_0_99])]) ).
fof(c_0_159,hypothesis,
( xb != sz00
| xa != sz00 ),
inference(fof_simplification,[status(thm)],[m__2110]) ).
cnf(c_0_160,hypothesis,
( ~ aSet0(X2)
| ~ aElementOf0(X1,X2)
| aElementOf0(sdtpldt0(X1,xb),sdtpldt1(X2,slsdtgt0(xb))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_123]),c_0_81])]) ).
cnf(c_0_161,hypothesis,
aElementOf0(sdtpldt0(xa,xa),slsdtgt0(xa)),
inference(spm,[status(thm)],[c_0_153,c_0_61]) ).
cnf(c_0_162,negated_conjecture,
xa = sz00,
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_163,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_156]),c_0_48])]) ).
cnf(c_0_164,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_71]),c_0_158]),c_0_35])]) ).
fof(c_0_165,hypothesis,
( xb != sz00
| xa != sz00 ),
inference(fof_nnf,[status(thm)],[c_0_159]) ).
cnf(c_0_166,hypothesis,
( ~ aSet0(slsdtgt0(sz00))
| aElementOf0(xb,xI) ),
inference(rw,[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_160,c_0_161]),c_0_162]),c_0_162]),c_0_163]),c_0_164]),c_0_145]),c_0_162]) ).
cnf(c_0_167,hypothesis,
( xb != sz00
| xa != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_165]) ).
cnf(c_0_168,hypothesis,
aElementOf0(xb,xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_123]),c_0_48])]) ).
cnf(c_0_169,hypothesis,
xb != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_162])]) ).
cnf(c_0_170,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_168]),c_0_169]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG109+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:23:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 110.03/16.83 % Version: 3.5.1
% 110.03/16.83 % Preprocessing class: FSLSSMSSSSSNFFN.
% 110.03/16.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.03/16.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 110.03/16.83 % Starting new_bool_3 with 300s (1) cores
% 110.03/16.83 % Starting new_bool_1 with 300s (1) cores
% 110.03/16.83 % Starting sh5l with 300s (1) cores
% 110.03/16.83 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 546716 completed with status 0
% 110.03/16.83 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 110.03/16.83 % Preprocessing class: FSLSSMSSSSSNFFN.
% 110.03/16.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.03/16.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 110.03/16.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 110.03/16.83 % No SInE strategy applied
% 110.03/16.83 % Search class: FGHSF-FFMM32-MFFFFFNN
% 110.03/16.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 110.03/16.83 % Starting SubtermCWHack with 136s (1) cores
% 110.03/16.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 110.03/16.83 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S2q with 136s (1) cores
% 110.03/16.83 % Starting new_bool_3 with 136s (1) cores
% 110.03/16.83 % Starting new_bool_1 with 136s (1) cores
% 110.03/16.83 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 546723 completed with status 0
% 110.03/16.83 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 110.03/16.83 % Preprocessing class: FSLSSMSSSSSNFFN.
% 110.03/16.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.03/16.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 110.03/16.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 110.03/16.83 % No SInE strategy applied
% 110.03/16.83 % Search class: FGHSF-FFMM32-MFFFFFNN
% 110.03/16.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 110.03/16.83 % Starting SubtermCWHack with 136s (1) cores
% 110.03/16.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 110.03/16.83 % Preprocessing time : 0.002 s
% 110.03/16.83 % Presaturation interreduction done
% 110.03/16.83
% 110.03/16.83 % Proof found!
% 110.03/16.83 % SZS status Theorem
% 110.03/16.83 % SZS output start CNFRefutation
% See solution above
% 110.03/16.83 % Parsed axioms : 44
% 110.03/16.83 % Removed by relevancy pruning/SinE : 0
% 110.03/16.83 % Initial clauses : 104
% 110.03/16.83 % Removed in clause preprocessing : 4
% 110.03/16.83 % Initial clauses in saturation : 100
% 110.03/16.83 % Processed clauses : 35935
% 110.03/16.83 % ...of these trivial : 4000
% 110.03/16.83 % ...subsumed : 22699
% 110.03/16.83 % ...remaining for further processing : 9236
% 110.03/16.83 % Other redundant clauses eliminated : 66
% 110.03/16.83 % Clauses deleted for lack of memory : 0
% 110.03/16.83 % Backward-subsumed : 361
% 110.03/16.83 % Backward-rewritten : 2103
% 110.03/16.83 % Generated clauses : 1259740
% 110.03/16.83 % ...of the previous two non-redundant : 1131126
% 110.03/16.83 % ...aggressively subsumed : 0
% 110.03/16.83 % Contextual simplify-reflections : 1267
% 110.03/16.83 % Paramodulations : 1259646
% 110.03/16.83 % Factorizations : 22
% 110.03/16.83 % NegExts : 0
% 110.03/16.83 % Equation resolutions : 66
% 110.03/16.83 % Disequality decompositions : 0
% 110.03/16.83 % Total rewrite steps : 1629191
% 110.03/16.83 % ...of those cached : 1625331
% 110.03/16.83 % Propositional unsat checks : 1
% 110.03/16.83 % Propositional check models : 0
% 110.03/16.83 % Propositional check unsatisfiable : 0
% 110.03/16.83 % Propositional clauses : 0
% 110.03/16.83 % Propositional clauses after purity: 0
% 110.03/16.83 % Propositional unsat core size : 0
% 110.03/16.83 % Propositional preprocessing time : 0.000
% 110.03/16.83 % Propositional encoding time : 0.247
% 110.03/16.83 % Propositional solver time : 0.184
% 110.03/16.83 % Success case prop preproc time : 0.000
% 110.03/16.83 % Success case prop encoding time : 0.000
% 110.03/16.83 % Success case prop solver time : 0.000
% 110.03/16.83 % Current number of processed clauses : 6650
% 110.03/16.83 % Positive orientable unit clauses : 3520
% 110.03/16.83 % Positive unorientable unit clauses: 0
% 110.03/16.83 % Negative unit clauses : 6
% 110.03/16.83 % Non-unit-clauses : 3124
% 110.03/16.83 % Current number of unprocessed clauses: 1093571
% 110.03/16.83 % ...number of literals in the above : 5475031
% 110.03/16.83 % Current number of archived formulas : 0
% 110.03/16.83 % Current number of archived clauses : 2572
% 110.03/16.83 % Clause-clause subsumption calls (NU) : 1433174
% 110.03/16.83 % Rec. Clause-clause subsumption calls : 892206
% 110.03/16.83 % Non-unit clause-clause subsumptions : 23860
% 110.03/16.83 % Unit Clause-clause subsumption calls : 55489
% 110.03/16.83 % Rewrite failures with RHS unbound : 0
% 110.03/16.83 % BW rewrite match attempts : 49500
% 110.03/16.83 % BW rewrite match successes : 1284
% 110.03/16.83 % Condensation attempts : 0
% 110.03/16.83 % Condensation successes : 0
% 110.03/16.83 % Termbank termtop insertions : 31946915
% 110.03/16.83 % Search garbage collected termcells : 1862
% 110.03/16.83
% 110.03/16.83 % -------------------------------------------------
% 110.03/16.83 % User time : 15.216 s
% 110.03/16.83 % System time : 0.694 s
% 110.03/16.83 % Total time : 15.910 s
% 110.03/16.83 % Maximum resident set size: 3948 pages
% 110.03/16.83
% 110.03/16.83 % -------------------------------------------------
% 110.03/16.83 % User time : 75.356 s
% 110.03/16.83 % System time : 2.815 s
% 110.03/16.83 % Total time : 78.171 s
% 110.03/16.83 % Maximum resident set size: 4608 pages
% 110.03/16.83 % E exiting
%------------------------------------------------------------------------------