%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG100+2 : 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 : n018.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 02:05:51 PM UTC 2026
% Result : Theorem 157.23s 23.46s
% Output : CNFRefutation 157.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 21
% Syntax : Number of formulae : 153 ( 40 unt; 0 def)
% Number of atoms : 525 ( 119 equ)
% Maximal formula atoms : 52 ( 3 avg)
% Number of connectives : 624 ( 252 ~; 271 |; 66 &)
% ( 7 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 6 con; 0-4 aty)
% Number of variables : 220 ( 0 sgn 94 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
<=> ? [X2] :
( sdtasdt0(xc,X2) = X1
& aElement0(X2) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc)) )
& ! [X2] :
( aElementOf0(X2,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X1,X2),slsdtgt0(xc)) ) ) ) ) ),
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(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(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(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
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(m__1905,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
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(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mMulMnOne,axiom,
! [X1] :
( aElement0(X1)
=> ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
& sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
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(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(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(c_0_21,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
<=> ? [X2] :
( sdtasdt0(xc,X2) = X1
& aElement0(X2) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc)) )
& ! [X2] :
( aElementOf0(X2,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X1,X2),slsdtgt0(xc)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_22,negated_conjecture,
! [X115,X117,X118] :
( ~ aIdeal0(slsdtgt0(xc))
& ( ~ aElementOf0(sdtpldt0(esk22_0,esk23_0),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(esk24_0,esk22_0),slsdtgt0(xc)) )
& ( ~ aElementOf0(sdtpldt0(esk22_0,esk23_0),slsdtgt0(xc))
| aElement0(esk24_0) )
& ( aElementOf0(esk23_0,slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(esk24_0,esk22_0),slsdtgt0(xc)) )
& ( aElementOf0(esk23_0,slsdtgt0(xc))
| aElement0(esk24_0) )
& aElementOf0(esk22_0,slsdtgt0(xc))
& ( aElementOf0(X117,slsdtgt0(xc))
| sdtasdt0(xc,X118) != X117
| ~ aElement0(X118) )
& ( ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,esk21_1(X115)) = X115 )
& ( ~ aElementOf0(X115,slsdtgt0(xc))
| aElement0(esk21_1(X115)) )
& aSet0(slsdtgt0(xc)) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])])])]) ).
fof(c_0_23,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_24,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_25,negated_conjecture,
( sdtasdt0(xc,X1) != X2
| ~ aElement0(X1)
| aElementOf0(X2,slsdtgt0(xc)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xc))
| sdtasdt0(xc,esk21_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ aSet0(X1)
| aIdeal0(X1)
| aElementOf0(esk9_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
aSet0(slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
~ aIdeal0(slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xc))
| aElement0(esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,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_24]) ).
cnf(c_0_32,negated_conjecture,
( ~ aElement0(X1)
| aElementOf0(sdtasdt0(xc,X1),slsdtgt0(xc)) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_33,negated_conjecture,
sdtasdt0(xc,esk21_1(esk9_1(slsdtgt0(xc)))) = esk9_1(slsdtgt0(xc)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
aElement0(esk21_1(esk9_1(slsdtgt0(xc)))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_27]),c_0_28])]),c_0_29]) ).
fof(c_0_35,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])])])])])])]) ).
cnf(c_0_36,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_31])]) ).
cnf(c_0_37,negated_conjecture,
aElementOf0(esk9_1(slsdtgt0(xc)),slsdtgt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_38,plain,
( ~ aElement0(X2)
| X4 != slsdtgt0(X2)
| sdtasdt0(X2,X1) != X3
| ~ aElement0(X1)
| aElementOf0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,plain,
( ~ aElement0(X2)
| X1 != slsdtgt0(X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_40,plain,
! [X34,X35] :
( aElement0(X35)
| ~ aElementOf0(X35,X34)
| ~ aSet0(X34) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_41,negated_conjecture,
( ~ aSet0(X2)
| ~ aElementOf0(X1,X2)
| aElementOf0(sdtpldt0(X1,esk9_1(slsdtgt0(xc))),sdtpldt1(X2,slsdtgt0(xc))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_28])]) ).
cnf(c_0_42,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_38])]) ).
cnf(c_0_43,plain,
( ~ aElement0(X1)
| aSet0(slsdtgt0(X1)) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElementOf0(sdtpldt0(sdtasdt0(X1,X2),esk9_1(slsdtgt0(xc))),sdtpldt1(slsdtgt0(X1),slsdtgt0(xc))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_46,plain,
( ~ aSet0(X3)
| ~ aSet0(X2)
| X1 != sdtpldt1(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_47,negated_conjecture,
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aSet0(sdtpldt1(slsdtgt0(X1),slsdtgt0(xc)))
| aElement0(sdtpldt0(sdtasdt0(X1,X2),esk9_1(slsdtgt0(xc)))) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSet0(sdtpldt1(X1,X2)) ),
inference(er,[status(thm)],[c_0_46]) ).
fof(c_0_49,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_50,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_51,negated_conjecture,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(sdtasdt0(X1,X2),esk9_1(slsdtgt0(xc)))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_28])]),c_0_43]) ).
cnf(c_0_52,plain,
( ~ aElement0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_54,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_55,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_56,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[m__1905]) ).
fof(c_0_57,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_58,negated_conjecture,
( ~ aElement0(X1)
| aElement0(sdtpldt0(X1,esk9_1(slsdtgt0(xc)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
cnf(c_0_59,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_60,negated_conjecture,
aElement0(esk9_1(slsdtgt0(xc))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_33]),c_0_34]),c_0_56])]) ).
cnf(c_0_61,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_62,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_63,negated_conjecture,
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElement0(sdtpldt0(X1,sdtpldt0(X2,esk9_1(slsdtgt0(xc))))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]),c_0_61]) ).
cnf(c_0_64,plain,
( ~ aElement0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_65,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_66,negated_conjecture,
( ~ aElement0(X1)
| ~ aElement0(smndt0(esk9_1(slsdtgt0(xc))))
| aElement0(sdtpldt0(X1,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_60])]) ).
cnf(c_0_67,plain,
( ~ aElement0(X1)
| aElement0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
fof(c_0_68,plain,
! [X20,X21] :
( sdtasdt0(X20,X21) = sdtasdt0(X21,X20)
| ~ aElement0(X21)
| ~ aElement0(X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
fof(c_0_69,plain,
! [X29] :
( ( ~ aElement0(X29)
| smndt0(X29) = sdtasdt0(X29,smndt0(sz10)) )
& ( ~ aElement0(X29)
| sdtasdt0(smndt0(sz10),X29) = smndt0(X29) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])])]) ).
cnf(c_0_70,negated_conjecture,
( ~ aElement0(X1)
| aElement0(sdtpldt0(X1,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_60])]) ).
cnf(c_0_71,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_72,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_73,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_74,negated_conjecture,
aElementOf0(esk22_0,slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_75,plain,
( ~ aElement0(X1)
| smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,negated_conjecture,
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElement0(sdtpldt0(X1,sdtpldt0(X2,sz00))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_59]),c_0_71])]),c_0_61]) ).
cnf(c_0_77,plain,
( ~ aElement0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_78,plain,
( ~ aElement0(X1)
| X2 != slsdtgt0(X1)
| ~ aElementOf0(X3,X2)
| sdtasdt0(X1,esk18_3(X1,X2,X3)) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_79,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(X2)) ),
inference(spm,[status(thm)],[c_0_42,c_0_73]) ).
cnf(c_0_80,negated_conjecture,
sdtasdt0(xc,esk21_1(esk22_0)) = esk22_0,
inference(spm,[status(thm)],[c_0_26,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
aElement0(esk21_1(esk22_0)),
inference(spm,[status(thm)],[c_0_30,c_0_74]) ).
cnf(c_0_82,plain,
( ~ aElement0(X1)
| X2 != slsdtgt0(X1)
| ~ aElementOf0(X3,X2)
| aElement0(esk18_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_83,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])])])]) ).
fof(c_0_84,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])])]) ).
cnf(c_0_85,plain,
( ~ aElement0(X1)
| sdtpldt0(sdtasdt0(X1,smndt0(sz10)),X1) = sz00 ),
inference(spm,[status(thm)],[c_0_64,c_0_75]) ).
cnf(c_0_86,negated_conjecture,
( ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,sdtpldt0(X2,sdtpldt0(X3,sz00)))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_59]),c_0_71])]),c_0_61]) ).
fof(c_0_87,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_88,plain,
( ~ aElement0(smndt0(sz00))
| smndt0(sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_64]),c_0_71])]) ).
cnf(c_0_89,plain,
( ~ aElement0(X1)
| ~ aElementOf0(X2,slsdtgt0(X1))
| sdtasdt0(X1,esk18_3(X1,slsdtgt0(X1),X2)) = X2 ),
inference(er,[status(thm)],[c_0_78]) ).
cnf(c_0_90,negated_conjecture,
aElementOf0(esk22_0,slsdtgt0(esk21_1(esk22_0))),
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_56])]) ).
cnf(c_0_91,plain,
( ~ aElement0(X1)
| ~ aElementOf0(X2,slsdtgt0(X1))
| aElement0(esk18_3(X1,slsdtgt0(X1),X2)) ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_92,plain,
( ~ aElement0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_93,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_94,plain,
( ~ aElement0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_95,plain,
( ~ aElement0(smndt0(sz10))
| sdtpldt0(smndt0(sz10),sz10) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_52]),c_0_53])]) ).
cnf(c_0_96,negated_conjecture,
( ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,sdtpldt0(X2,X3))) ),
inference(spm,[status(thm)],[c_0_86,c_0_77]) ).
cnf(c_0_97,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_98,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_67]),c_0_71])]) ).
cnf(c_0_99,negated_conjecture,
sdtasdt0(esk21_1(esk22_0),esk18_3(esk21_1(esk22_0),slsdtgt0(esk21_1(esk22_0)),esk22_0)) = esk22_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_81])]) ).
cnf(c_0_100,negated_conjecture,
aElement0(esk18_3(esk21_1(esk22_0),slsdtgt0(esk21_1(esk22_0)),esk22_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_90]),c_0_81])]) ).
cnf(c_0_101,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_71])]),c_0_55]) ).
cnf(c_0_102,negated_conjecture,
( ~ aElement0(X1)
| sdtasdt0(xc,sdtasdt0(esk21_1(esk22_0),X1)) = sdtasdt0(esk22_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_80]),c_0_81]),c_0_56])]) ).
cnf(c_0_103,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_94]),c_0_67]) ).
cnf(c_0_104,plain,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_67]),c_0_53])]) ).
cnf(c_0_105,negated_conjecture,
( ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,sdtasdt0(X2,sdtpldt0(X3,X4)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_55]),c_0_55]) ).
cnf(c_0_106,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_98]),c_0_71])]) ).
cnf(c_0_107,plain,
( ~ aElement0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_108,negated_conjecture,
( ~ aElement0(X1)
| sdtasdt0(esk21_1(esk22_0),sdtasdt0(esk18_3(esk21_1(esk22_0),slsdtgt0(esk21_1(esk22_0)),esk22_0),X1)) = sdtasdt0(esk22_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_99]),c_0_100]),c_0_81])]) ).
cnf(c_0_109,negated_conjecture,
sdtasdt0(esk22_0,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_81]),c_0_56]),c_0_71])]) ).
cnf(c_0_110,plain,
sdtpldt0(sz10,sz00) = sdtpldt0(sz00,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_53])]) ).
cnf(c_0_111,negated_conjecture,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,sdtasdt0(X2,sz00))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_71])]) ).
cnf(c_0_112,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_107]),c_0_53])]) ).
cnf(c_0_113,negated_conjecture,
sdtasdt0(esk21_1(esk22_0),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_92]),c_0_109]),c_0_71]),c_0_100])]) ).
cnf(c_0_114,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_110]),c_0_53])]) ).
cnf(c_0_115,negated_conjecture,
( aElementOf0(esk23_0,slsdtgt0(xc))
| aElement0(esk24_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_116,negated_conjecture,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,sdtasdt0(sz00,X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_73]),c_0_71])]) ).
cnf(c_0_117,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_87]) ).
fof(c_0_118,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_119,plain,
( ~ aElement0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_120,negated_conjecture,
sdtpldt0(sz00,esk21_1(esk22_0)) = sdtasdt0(esk21_1(esk22_0),sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]),c_0_71]),c_0_81])]) ).
cnf(c_0_121,negated_conjecture,
( ~ aElement0(X1)
| sdtpldt0(sdtasdt0(xc,X1),esk22_0) = sdtasdt0(xc,sdtpldt0(X1,esk21_1(esk22_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_80]),c_0_81]),c_0_56])]) ).
cnf(c_0_122,negated_conjecture,
( aElement0(esk24_0)
| sdtasdt0(xc,esk21_1(esk23_0)) = esk23_0 ),
inference(spm,[status(thm)],[c_0_26,c_0_115]) ).
cnf(c_0_123,negated_conjecture,
( aElement0(esk24_0)
| aElement0(esk21_1(esk23_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_115]) ).
cnf(c_0_124,negated_conjecture,
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElement0(sdtasdt0(sdtpldt0(X1,sz00),X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_71])]),c_0_55]) ).
cnf(c_0_125,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_126,negated_conjecture,
sdtasdt0(esk21_1(esk22_0),sz10) = esk21_1(esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_81])]) ).
cnf(c_0_127,negated_conjecture,
( aElement0(esk24_0)
| sdtasdt0(xc,sdtpldt0(esk21_1(esk23_0),esk21_1(esk22_0))) = sdtpldt0(esk23_0,esk22_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123]) ).
cnf(c_0_128,negated_conjecture,
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElement0(sdtasdt0(sdtpldt0(sz00,X1),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_71])]) ).
cnf(c_0_129,negated_conjecture,
sdtpldt0(sz00,esk21_1(esk22_0)) = esk21_1(esk22_0),
inference(rw,[status(thm)],[c_0_120,c_0_126]) ).
cnf(c_0_130,negated_conjecture,
( ~ aElement0(sdtpldt0(esk21_1(esk23_0),esk21_1(esk22_0)))
| aElement0(esk24_0)
| aElementOf0(sdtpldt0(esk23_0,esk22_0),slsdtgt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_127]),c_0_56])]) ).
cnf(c_0_131,negated_conjecture,
( ~ aElementOf0(sdtasdt0(esk24_0,esk22_0),slsdtgt0(xc))
| aElementOf0(esk23_0,slsdtgt0(xc)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_132,negated_conjecture,
aElement0(esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_74]),c_0_28])]) ).
cnf(c_0_133,negated_conjecture,
( ~ aElement0(X1)
| aElement0(sdtasdt0(esk21_1(esk22_0),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_81])]) ).
cnf(c_0_134,negated_conjecture,
( aElement0(esk24_0)
| aElementOf0(sdtpldt0(esk23_0,esk22_0),slsdtgt0(xc)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_61]),c_0_81])]),c_0_123]) ).
cnf(c_0_135,negated_conjecture,
( aElement0(esk23_0)
| aElement0(esk24_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_115]),c_0_28])]) ).
cnf(c_0_136,negated_conjecture,
( ~ aElementOf0(sdtpldt0(esk22_0,esk23_0),slsdtgt0(xc))
| aElement0(esk24_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_137,negated_conjecture,
( ~ aElementOf0(sdtasdt0(esk22_0,esk24_0),slsdtgt0(xc))
| aElementOf0(esk23_0,slsdtgt0(xc)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_73]),c_0_132])]),c_0_115]) ).
cnf(c_0_138,negated_conjecture,
( ~ aElement0(X1)
| aElementOf0(sdtasdt0(esk22_0,X1),slsdtgt0(xc)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_102]),c_0_56])]),c_0_133]) ).
cnf(c_0_139,negated_conjecture,
aElement0(esk24_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_125]),c_0_132])]),c_0_135]),c_0_136]) ).
cnf(c_0_140,negated_conjecture,
aElementOf0(esk23_0,slsdtgt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139])]) ).
cnf(c_0_141,negated_conjecture,
sdtasdt0(xc,esk21_1(esk23_0)) = esk23_0,
inference(spm,[status(thm)],[c_0_26,c_0_140]) ).
cnf(c_0_142,negated_conjecture,
aElement0(esk21_1(esk23_0)),
inference(spm,[status(thm)],[c_0_30,c_0_140]) ).
cnf(c_0_143,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_97]),c_0_55]),c_0_55]) ).
cnf(c_0_144,negated_conjecture,
sdtasdt0(xc,sdtpldt0(esk21_1(esk23_0),esk21_1(esk22_0))) = sdtpldt0(esk23_0,esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_141]),c_0_142])]) ).
cnf(c_0_145,negated_conjecture,
sdtpldt0(esk23_0,esk22_0) = sdtpldt0(esk22_0,esk23_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_80]),c_0_141]),c_0_81]),c_0_142]),c_0_56])]) ).
cnf(c_0_146,negated_conjecture,
sdtasdt0(xc,sdtpldt0(esk21_1(esk23_0),esk21_1(esk22_0))) = sdtpldt0(esk22_0,esk23_0),
inference(rw,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_147,negated_conjecture,
( ~ aElement0(sdtpldt0(esk21_1(esk23_0),esk21_1(esk22_0)))
| aElementOf0(sdtpldt0(esk22_0,esk23_0),slsdtgt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_146]),c_0_56])]) ).
cnf(c_0_148,negated_conjecture,
( ~ aElementOf0(sdtpldt0(esk22_0,esk23_0),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(esk24_0,esk22_0),slsdtgt0(xc)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_149,negated_conjecture,
aElementOf0(sdtpldt0(esk22_0,esk23_0),slsdtgt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_61]),c_0_81]),c_0_142])]) ).
cnf(c_0_150,negated_conjecture,
~ aElementOf0(sdtasdt0(esk24_0,esk22_0),slsdtgt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_149])]) ).
cnf(c_0_151,negated_conjecture,
~ aElementOf0(sdtasdt0(esk22_0,esk24_0),slsdtgt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_73]),c_0_132]),c_0_139])]) ).
cnf(c_0_152,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_138]),c_0_139])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG100+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 04:21:44 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 157.23/23.46 % Version: 3.5.1
% 157.23/23.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 157.23/23.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 157.23/23.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 157.23/23.46 % Starting new_bool_3 with 300s (1) cores
% 157.23/23.46 % Starting new_bool_1 with 300s (1) cores
% 157.23/23.46 % Starting sh5l with 300s (1) cores
% 157.23/23.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 954540 completed with status 0
% 157.23/23.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 157.23/23.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 157.23/23.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 157.23/23.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 157.23/23.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 157.23/23.46 % No SInE strategy applied
% 157.23/23.46 % Search class: FGHSF-FFMM32-MFFFFFNN
% 157.23/23.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 157.23/23.46 % Starting SubtermCWHack with 136s (1) cores
% 157.23/23.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 157.23/23.46 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S2q with 136s (1) cores
% 157.23/23.46 % Starting new_bool_3 with 136s (1) cores
% 157.23/23.46 % Starting new_bool_1 with 136s (1) cores
% 157.23/23.46 % G-E--_208_B07_F1_SE_CS_SP_PS_S2q with pid 954548 completed with status 0
% 157.23/23.46 % Result found by G-E--_208_B07_F1_SE_CS_SP_PS_S2q
% 157.23/23.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 157.23/23.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 157.23/23.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 157.23/23.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 157.23/23.46 % No SInE strategy applied
% 157.23/23.46 % Search class: FGHSF-FFMM32-MFFFFFNN
% 157.23/23.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 157.23/23.46 % Starting SubtermCWHack with 136s (1) cores
% 157.23/23.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 157.23/23.46 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S2q with 136s (1) cores
% 157.23/23.46 % Preprocessing time : 0.002 s
% 157.23/23.46 % Presaturation interreduction done
% 157.23/23.46
% 157.23/23.46 % Proof found!
% 157.23/23.46 % SZS status Theorem
% 157.23/23.46 % SZS output start CNFRefutation
% See solution above
% 157.23/23.46 % Parsed axioms : 39
% 157.23/23.46 % Removed by relevancy pruning/SinE : 0
% 157.23/23.46 % Initial clauses : 103
% 157.23/23.46 % Removed in clause preprocessing : 4
% 157.23/23.46 % Initial clauses in saturation : 99
% 157.23/23.46 % Processed clauses : 37397
% 157.23/23.46 % ...of these trivial : 8696
% 157.23/23.46 % ...subsumed : 17136
% 157.23/23.46 % ...remaining for further processing : 11565
% 157.23/23.46 % Other redundant clauses eliminated : 41
% 157.23/23.46 % Clauses deleted for lack of memory : 0
% 157.23/23.46 % Backward-subsumed : 175
% 157.23/23.46 % Backward-rewritten : 1974
% 157.23/23.46 % Generated clauses : 1720177
% 157.23/23.46 % ...of the previous two non-redundant : 1568108
% 157.23/23.46 % ...aggressively subsumed : 0
% 157.23/23.46 % Contextual simplify-reflections : 1465
% 157.23/23.46 % Paramodulations : 1720116
% 157.23/23.46 % Factorizations : 22
% 157.23/23.46 % NegExts : 0
% 157.23/23.46 % Equation resolutions : 41
% 157.23/23.46 % Disequality decompositions : 0
% 157.23/23.46 % Total rewrite steps : 2231973
% 157.23/23.46 % ...of those cached : 2225735
% 157.23/23.46 % Propositional unsat checks : 0
% 157.23/23.46 % Propositional check models : 0
% 157.23/23.46 % Propositional check unsatisfiable : 0
% 157.23/23.46 % Propositional clauses : 0
% 157.23/23.46 % Propositional clauses after purity: 0
% 157.23/23.46 % Propositional unsat core size : 0
% 157.23/23.46 % Propositional preprocessing time : 0.000
% 157.23/23.46 % Propositional encoding time : 0.000
% 157.23/23.46 % Propositional solver time : 0.000
% 157.23/23.46 % Success case prop preproc time : 0.000
% 157.23/23.46 % Success case prop encoding time : 0.000
% 157.23/23.46 % Success case prop solver time : 0.000
% 157.23/23.46 % Current number of processed clauses : 9302
% 157.23/23.46 % Positive orientable unit clauses : 5838
% 157.23/23.46 % Positive unorientable unit clauses: 0
% 157.23/23.46 % Negative unit clauses : 4
% 157.23/23.46 % Non-unit-clauses : 3460
% 157.23/23.46 % Current number of unprocessed clauses: 1525556
% 157.23/23.46 % ...number of literals in the above : 7114599
% 157.23/23.46 % Current number of archived formulas : 0
% 157.23/23.46 % Current number of archived clauses : 2248
% 157.23/23.46 % Clause-clause subsumption calls (NU) : 1392965
% 157.23/23.46 % Rec. Clause-clause subsumption calls : 812674
% 157.23/23.46 % Non-unit clause-clause subsumptions : 18551
% 157.23/23.46 % Unit Clause-clause subsumption calls : 153118
% 157.23/23.46 % Rewrite failures with RHS unbound : 0
% 157.23/23.46 % BW rewrite match attempts : 568265
% 157.23/23.46 % BW rewrite match successes : 1185
% 157.23/23.46 % Condensation attempts : 0
% 157.23/23.46 % Condensation successes : 0
% 157.23/23.46 % Termbank termtop insertions : 45550618
% 157.23/23.46 % Search garbage collected termcells : 2017
% 157.23/23.46
% 157.23/23.46 % -------------------------------------------------
% 157.23/23.46 % User time : 21.396 s
% 157.23/23.46 % System time : 0.923 s
% 157.23/23.46 % Total time : 22.320 s
% 157.23/23.46 % Maximum resident set size: 3892 pages
% 157.23/23.46
% 157.23/23.46 % -------------------------------------------------
% 157.23/23.46 % User time : 107.801 s
% 157.23/23.46 % System time : 4.093 s
% 157.23/23.46 % Total time : 111.894 s
% 157.23/23.46 % Maximum resident set size: 4608 pages
% 157.23/23.46 % E exiting
%------------------------------------------------------------------------------