%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG092+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 02:05:48 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 12 unt; 0 def)
% Number of atoms : 295 ( 30 equ)
% Maximal formula atoms : 53 ( 5 avg)
% Number of connectives : 402 ( 157 ~; 166 |; 65 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 4 con; 0-4 aty)
% Number of variables : 78 ( 4 sgn 38 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ! [X1,X2,X3] :
( ( aElement0(X3)
& aElementOf0(X2,sdtpldt1(xI,xJ))
& aElementOf0(X1,sdtpldt1(xI,xJ)) )
=> ? [X4,X5] :
( ? [X6,X7] :
( aElementOf0(sdtasdt0(X3,X1),sdtpldt1(xI,xJ))
& aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ))
& sdtpldt0(X1,X2) = sdtpldt0(sdtpldt0(X4,X6),sdtpldt0(X5,X7))
& aElementOf0(sdtasdt0(X3,X5),xJ)
& aElementOf0(sdtasdt0(X3,X4),xI)
& aElementOf0(sdtpldt0(X5,X7),xJ)
& aElementOf0(sdtpldt0(X4,X6),xI)
& X2 = sdtpldt0(X6,X7)
& aElementOf0(X7,xJ)
& aElementOf0(X6,xI) )
& X1 = sdtpldt0(X4,X5)
& aElementOf0(X5,xJ)
& aElementOf0(X4,xI) ) )
=> aIdeal0(sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
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/sandbox/benchmark/theBenchmark.p',mDefSSum) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(m__870,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(c_0_8,negated_conjecture,
~ ( ! [X1,X2,X3] :
( ( aElement0(X3)
& aElementOf0(X2,sdtpldt1(xI,xJ))
& aElementOf0(X1,sdtpldt1(xI,xJ)) )
=> ? [X4,X5] :
( ? [X6,X7] :
( aElementOf0(sdtasdt0(X3,X1),sdtpldt1(xI,xJ))
& aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ))
& sdtpldt0(X1,X2) = sdtpldt0(sdtpldt0(X4,X6),sdtpldt0(X5,X7))
& aElementOf0(sdtasdt0(X3,X5),xJ)
& aElementOf0(sdtasdt0(X3,X4),xI)
& aElementOf0(sdtpldt0(X5,X7),xJ)
& aElementOf0(sdtpldt0(X4,X6),xI)
& X2 = sdtpldt0(X6,X7)
& aElementOf0(X7,xJ)
& aElementOf0(X6,xI) )
& X1 = sdtpldt0(X4,X5)
& aElementOf0(X5,xJ)
& aElementOf0(X4,xI) ) )
=> aIdeal0(sdtpldt1(xI,xJ)) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_9,negated_conjecture,
! [X71,X72,X73] :
( ~ aIdeal0(sdtpldt1(xI,xJ))
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| aElementOf0(sdtasdt0(X73,X71),sdtpldt1(xI,xJ)) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| aElementOf0(sdtpldt0(X71,X72),sdtpldt1(xI,xJ)) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| sdtpldt0(X71,X72) = sdtpldt0(sdtpldt0(esk12_3(X71,X72,X73),esk14_3(X71,X72,X73)),sdtpldt0(esk13_3(X71,X72,X73),esk15_3(X71,X72,X73))) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| aElementOf0(sdtasdt0(X73,esk13_3(X71,X72,X73)),xJ) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| aElementOf0(sdtasdt0(X73,esk12_3(X71,X72,X73)),xI) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| aElementOf0(sdtpldt0(esk13_3(X71,X72,X73),esk15_3(X71,X72,X73)),xJ) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| aElementOf0(sdtpldt0(esk12_3(X71,X72,X73),esk14_3(X71,X72,X73)),xI) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| X72 = sdtpldt0(esk14_3(X71,X72,X73),esk15_3(X71,X72,X73)) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| aElementOf0(esk15_3(X71,X72,X73),xJ) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| aElementOf0(esk14_3(X71,X72,X73),xI) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| X71 = sdtpldt0(esk12_3(X71,X72,X73),esk13_3(X71,X72,X73)) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| aElementOf0(esk13_3(X71,X72,X73),xJ) )
& ( ~ aElement0(X73)
| ~ aElementOf0(X72,sdtpldt1(xI,xJ))
| ~ aElementOf0(X71,sdtpldt1(xI,xJ))
| aElementOf0(esk12_3(X71,X72,X73),xI) ) ),
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_8])])])])])])]) ).
fof(c_0_10,plain,
! [X63,X64,X65,X66,X67] :
( ( aIdeal0(X67)
| ~ aSet0(X67)
| ~ aElementOf0(sdtpldt0(esk9_1(X67),esk10_1(X67)),X67)
| ~ aElementOf0(sdtasdt0(esk11_1(X67),esk9_1(X67)),X67) )
& ( aIdeal0(X67)
| ~ aSet0(X67)
| ~ aElementOf0(sdtpldt0(esk9_1(X67),esk10_1(X67)),X67)
| aElement0(esk11_1(X67)) )
& ( aIdeal0(X67)
| ~ aSet0(X67)
| aElementOf0(esk10_1(X67),X67)
| ~ aElementOf0(sdtasdt0(esk11_1(X67),esk9_1(X67)),X67) )
& ( aIdeal0(X67)
| ~ aSet0(X67)
| aElementOf0(esk10_1(X67),X67)
| aElement0(esk11_1(X67)) )
& ( aIdeal0(X67)
| ~ aSet0(X67)
| aElementOf0(esk9_1(X67),X67) )
& ( ~ aIdeal0(X63)
| ~ aElementOf0(X64,X63)
| aElementOf0(sdtasdt0(X66,X64),X63)
| ~ aElement0(X66) )
& ( ~ aIdeal0(X63)
| ~ aElementOf0(X64,X63)
| aElementOf0(sdtpldt0(X64,X65),X63)
| ~ aElementOf0(X65,X63) )
& ( ~ aIdeal0(X63)
| aSet0(X63) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefIdeal])])])])])])]) ).
cnf(c_0_11,negated_conjecture,
( ~ aElement0(X1)
| ~ aElementOf0(X3,sdtpldt1(xI,xJ))
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| aElementOf0(sdtasdt0(X1,X2),sdtpldt1(xI,xJ)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( ~ aSet0(X1)
| aIdeal0(X1)
| aElementOf0(esk9_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
~ aIdeal0(sdtpldt1(xI,xJ)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X31] :
( ( ~ aElement0(X31)
| sz00 = sdtasdt0(sz00,X31) )
& ( ~ aElement0(X31)
| sdtasdt0(X31,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_15,plain,
! [X35,X36] :
( aElement0(X36)
| ~ aElementOf0(X36,X35)
| ~ aSet0(X35) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_16,plain,
! [X41,X42,X43,X44,X47,X48,X49,X50,X52,X53] :
( ( ~ aSet0(X42)
| ~ aSet0(X41)
| X50 = sdtpldt1(X41,X42)
| ~ aSet0(X50)
| aElementOf0(esk5_3(X41,X42,X50),X50)
| sdtpldt0(esk6_3(X41,X42,X50),esk7_3(X41,X42,X50)) = esk5_3(X41,X42,X50) )
& ( ~ aSet0(X42)
| ~ aSet0(X41)
| X50 = sdtpldt1(X41,X42)
| ~ aSet0(X50)
| aElementOf0(esk5_3(X41,X42,X50),X50)
| aElementOf0(esk7_3(X41,X42,X50),X42) )
& ( ~ aSet0(X42)
| ~ aSet0(X41)
| X50 = sdtpldt1(X41,X42)
| ~ aSet0(X50)
| aElementOf0(esk5_3(X41,X42,X50),X50)
| aElementOf0(esk6_3(X41,X42,X50),X41) )
& ( ~ aSet0(X42)
| ~ aSet0(X41)
| X50 = sdtpldt1(X41,X42)
| ~ aSet0(X50)
| sdtpldt0(X52,X53) != esk5_3(X41,X42,X50)
| ~ aElementOf0(X53,X42)
| ~ aElementOf0(X52,X41)
| ~ aElementOf0(esk5_3(X41,X42,X50),X50) )
& ( ~ aSet0(X42)
| ~ aSet0(X41)
| X43 != sdtpldt1(X41,X42)
| aElementOf0(X47,X43)
| sdtpldt0(X48,X49) != X47
| ~ aElementOf0(X49,X42)
| ~ aElementOf0(X48,X41) )
& ( ~ aSet0(X42)
| ~ aSet0(X41)
| X43 != sdtpldt1(X41,X42)
| ~ aElementOf0(X44,X43)
| sdtpldt0(esk3_4(X41,X42,X43,X44),esk4_4(X41,X42,X43,X44)) = X44 )
& ( ~ aSet0(X42)
| ~ aSet0(X41)
| X43 != sdtpldt1(X41,X42)
| ~ aElementOf0(X44,X43)
| aElementOf0(esk4_4(X41,X42,X43,X44),X42) )
& ( ~ aSet0(X42)
| ~ aSet0(X41)
| X43 != sdtpldt1(X41,X42)
| ~ aElementOf0(X44,X43)
| aElementOf0(esk3_4(X41,X42,X43,X44),X41) )
& ( ~ aSet0(X42)
| ~ aSet0(X41)
| X43 != sdtpldt1(X41,X42)
| aSet0(X43) ) ),
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_17,negated_conjecture,
( ~ aElement0(X1)
| ~ aSet0(sdtpldt1(xI,xJ))
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| aElementOf0(sdtasdt0(X1,X2),sdtpldt1(xI,xJ)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_18,plain,
( ~ aElement0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_20,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( ~ aSet0(X3)
| ~ aSet0(X2)
| X1 != sdtpldt1(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
cnf(c_0_24,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
cnf(c_0_25,negated_conjecture,
( ~ aSet0(sdtpldt1(xI,xJ))
| ~ aElementOf0(X1,sdtpldt1(xI,xJ))
| aElementOf0(sz00,sdtpldt1(xI,xJ)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_26,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSet0(sdtpldt1(X1,X2)) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_27,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( ~ aElementOf0(X1,sdtpldt1(xI,xJ))
| aElementOf0(sz00,sdtpldt1(xI,xJ)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_30,negated_conjecture,
( ~ aSet0(sdtpldt1(xI,xJ))
| aElementOf0(sz00,sdtpldt1(xI,xJ)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_12]),c_0_13]) ).
cnf(c_0_31,negated_conjecture,
aElementOf0(sz00,sdtpldt1(xI,xJ)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
( ~ aElement0(X3)
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| ~ aElementOf0(X1,sdtpldt1(xI,xJ))
| aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_33,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_34,plain,
( ~ aSet0(X1)
| ~ aElementOf0(sdtpldt0(esk9_1(X1),esk10_1(X1)),X1)
| ~ aElementOf0(sdtasdt0(esk11_1(X1),esk9_1(X1)),X1)
| aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_35,negated_conjecture,
( ~ aElement0(X1)
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| aElementOf0(sdtasdt0(X1,X2),sdtpldt1(xI,xJ)) ),
inference(spm,[status(thm)],[c_0_11,c_0_31]) ).
cnf(c_0_36,plain,
( ~ aSet0(X1)
| ~ aElementOf0(sdtpldt0(esk9_1(X1),esk10_1(X1)),X1)
| aIdeal0(X1)
| aElement0(esk11_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_37,negated_conjecture,
( ~ aElementOf0(X1,sdtpldt1(xI,xJ))
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( ~ aElement0(esk11_1(sdtpldt1(xI,xJ)))
| ~ aSet0(sdtpldt1(xI,xJ))
| ~ aElementOf0(esk9_1(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(esk9_1(sdtpldt1(xI,xJ)),esk10_1(sdtpldt1(xI,xJ))),sdtpldt1(xI,xJ)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_13]) ).
cnf(c_0_39,negated_conjecture,
( ~ aSet0(sdtpldt1(xI,xJ))
| ~ aElementOf0(esk9_1(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| ~ aElementOf0(esk10_1(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| aElement0(esk11_1(sdtpldt1(xI,xJ))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_13]) ).
cnf(c_0_40,plain,
( ~ aSet0(X1)
| ~ aElementOf0(sdtasdt0(esk11_1(X1),esk9_1(X1)),X1)
| aIdeal0(X1)
| aElementOf0(esk10_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_41,negated_conjecture,
( ~ aSet0(sdtpldt1(xI,xJ))
| ~ aElementOf0(esk10_1(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| ~ aElementOf0(esk9_1(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( ~ aElement0(esk11_1(sdtpldt1(xI,xJ)))
| ~ aSet0(sdtpldt1(xI,xJ))
| ~ aElementOf0(esk9_1(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))
| aElementOf0(esk10_1(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_35]),c_0_13]) ).
cnf(c_0_43,plain,
( ~ aSet0(X1)
| aIdeal0(X1)
| aElementOf0(esk10_1(X1),X1)
| aElement0(esk11_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_44,negated_conjecture,
( ~ aElement0(esk11_1(sdtpldt1(xI,xJ)))
| ~ aSet0(sdtpldt1(xI,xJ))
| ~ aElementOf0(esk9_1(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElement0(esk11_1(sdtpldt1(X1,X2)))
| aElementOf0(esk10_1(sdtpldt1(X1,X2)),sdtpldt1(X1,X2))
| aIdeal0(sdtpldt1(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_26]) ).
cnf(c_0_46,negated_conjecture,
( ~ aElement0(esk11_1(sdtpldt1(xI,xJ)))
| ~ aSet0(sdtpldt1(xI,xJ)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_12]),c_0_13]) ).
cnf(c_0_47,negated_conjecture,
( ~ aSet0(sdtpldt1(xI,xJ))
| ~ aElementOf0(esk9_1(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_45]),c_0_27]),c_0_28])]),c_0_13]),c_0_46]) ).
cnf(c_0_48,negated_conjecture,
~ aSet0(sdtpldt1(xI,xJ)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_12]),c_0_13]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_26]),c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG092+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.35 % Computer : n004.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 04:18:50 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.13/0.45 % Version: 3.5.1
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.45 % Starting sh5l with 300s (1) cores
% 0.13/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2226314 completed with status 0
% 0.13/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.45 % No SInE strategy applied
% 0.13/0.45 % Search class: FGUSF-FFMS32-MFFFFFNN
% 0.13/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.45 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 2226323 completed with status 0
% 0.13/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.45 % No SInE strategy applied
% 0.13/0.45 % Search class: FGUSF-FFMS32-MFFFFFNN
% 0.13/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.45 % Preprocessing time : 0.001 s
% 0.13/0.45 % Presaturation interreduction done
% 0.13/0.45
% 0.13/0.45 % Proof found!
% 0.13/0.45 % SZS status Theorem
% 0.13/0.45 % SZS output start CNFRefutation
% See solution above
% 0.13/0.45 % Parsed axioms : 26
% 0.13/0.45 % Removed by relevancy pruning/SinE : 0
% 0.13/0.45 % Initial clauses : 70
% 0.13/0.45 % Removed in clause preprocessing : 2
% 0.13/0.45 % Initial clauses in saturation : 68
% 0.13/0.45 % Processed clauses : 575
% 0.13/0.45 % ...of these trivial : 3
% 0.13/0.45 % ...subsumed : 296
% 0.13/0.45 % ...remaining for further processing : 276
% 0.13/0.45 % Other redundant clauses eliminated : 10
% 0.13/0.45 % Clauses deleted for lack of memory : 0
% 0.13/0.45 % Backward-subsumed : 50
% 0.13/0.45 % Backward-rewritten : 10
% 0.13/0.45 % Generated clauses : 1518
% 0.13/0.45 % ...of the previous two non-redundant : 1193
% 0.13/0.45 % ...aggressively subsumed : 0
% 0.13/0.45 % Contextual simplify-reflections : 13
% 0.13/0.45 % Paramodulations : 1509
% 0.13/0.45 % Factorizations : 0
% 0.13/0.45 % NegExts : 0
% 0.13/0.45 % Equation resolutions : 10
% 0.13/0.45 % Disequality decompositions : 0
% 0.13/0.45 % Total rewrite steps : 999
% 0.13/0.45 % ...of those cached : 987
% 0.13/0.45 % Propositional unsat checks : 0
% 0.13/0.45 % Propositional check models : 0
% 0.13/0.45 % Propositional check unsatisfiable : 0
% 0.13/0.45 % Propositional clauses : 0
% 0.13/0.45 % Propositional clauses after purity: 0
% 0.13/0.45 % Propositional unsat core size : 0
% 0.13/0.45 % Propositional preprocessing time : 0.000
% 0.13/0.45 % Propositional encoding time : 0.000
% 0.13/0.45 % Propositional solver time : 0.000
% 0.13/0.45 % Success case prop preproc time : 0.000
% 0.13/0.45 % Success case prop encoding time : 0.000
% 0.13/0.45 % Success case prop solver time : 0.000
% 0.13/0.45 % Current number of processed clauses : 139
% 0.13/0.45 % Positive orientable unit clauses : 12
% 0.13/0.45 % Positive unorientable unit clauses: 0
% 0.13/0.45 % Negative unit clauses : 3
% 0.13/0.45 % Non-unit-clauses : 124
% 0.13/0.45 % Current number of unprocessed clauses: 582
% 0.13/0.45 % ...number of literals in the above : 3226
% 0.13/0.45 % Current number of archived formulas : 0
% 0.13/0.45 % Current number of archived clauses : 128
% 0.13/0.45 % Clause-clause subsumption calls (NU) : 5271
% 0.13/0.45 % Rec. Clause-clause subsumption calls : 2193
% 0.13/0.45 % Non-unit clause-clause subsumptions : 344
% 0.13/0.45 % Unit Clause-clause subsumption calls : 23
% 0.13/0.45 % Rewrite failures with RHS unbound : 0
% 0.13/0.45 % BW rewrite match attempts : 5
% 0.13/0.45 % BW rewrite match successes : 5
% 0.13/0.45 % Condensation attempts : 0
% 0.13/0.45 % Condensation successes : 0
% 0.13/0.45 % Termbank termtop insertions : 31885
% 0.13/0.45 % Search garbage collected termcells : 1302
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.032 s
% 0.13/0.45 % System time : 0.004 s
% 0.13/0.45 % Total time : 0.036 s
% 0.13/0.45 % Maximum resident set size: 3668 pages
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.130 s
% 0.13/0.45 % System time : 0.021 s
% 0.13/0.45 % Total time : 0.151 s
% 0.13/0.45 % Maximum resident set size: 4864 pages
% 0.13/0.45 % E exiting
%------------------------------------------------------------------------------