%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG093+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 : 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 02:05:49 PM UTC 2026
% Result : Theorem 25.25s 4.48s
% Output : CNFRefutation 25.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 96 ( 28 unt; 0 def)
% Number of atoms : 343 ( 36 equ)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 429 ( 182 ~; 208 |; 26 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 128 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSInt,axiom,
! [X1,X2] :
( ( aSet0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtasasdt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElementOf0(X4,X2)
& aElementOf0(X4,X1) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSInt) ).
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(m__,conjecture,
aIdeal0(sdtasasdt0(xI,xJ)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1150,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1150) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
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/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(c_0_10,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( ~ aSet0(X56)
| ~ aSet0(X55)
| X60 = sdtasasdt0(X55,X56)
| ~ aSet0(X60)
| aElementOf0(esk8_3(X55,X56,X60),X60)
| aElementOf0(esk8_3(X55,X56,X60),X56) )
& ( ~ aSet0(X56)
| ~ aSet0(X55)
| X60 = sdtasasdt0(X55,X56)
| ~ aSet0(X60)
| aElementOf0(esk8_3(X55,X56,X60),X60)
| aElementOf0(esk8_3(X55,X56,X60),X55) )
& ( ~ aSet0(X56)
| ~ aSet0(X55)
| X60 = sdtasasdt0(X55,X56)
| ~ aSet0(X60)
| ~ aElementOf0(esk8_3(X55,X56,X60),X56)
| ~ aElementOf0(esk8_3(X55,X56,X60),X55)
| ~ aElementOf0(esk8_3(X55,X56,X60),X60) )
& ( ~ aSet0(X56)
| ~ aSet0(X55)
| X57 != sdtasasdt0(X55,X56)
| aElementOf0(X59,X57)
| ~ aElementOf0(X59,X56)
| ~ aElementOf0(X59,X55) )
& ( ~ aSet0(X56)
| ~ aSet0(X55)
| X57 != sdtasasdt0(X55,X56)
| ~ aElementOf0(X58,X57)
| aElementOf0(X58,X56) )
& ( ~ aSet0(X56)
| ~ aSet0(X55)
| X57 != sdtasasdt0(X55,X56)
| ~ aElementOf0(X58,X57)
| aElementOf0(X58,X55) )
& ( ~ aSet0(X56)
| ~ aSet0(X55)
| X57 != sdtasasdt0(X55,X56)
| aSet0(X57) ) ),
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)],[mDefSInt])])])])])])]) ).
fof(c_0_11,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])])])])])])]) ).
cnf(c_0_12,plain,
( ~ aSet0(X3)
| ~ aSet0(X2)
| X1 != sdtasasdt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,negated_conjecture,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_14,plain,
( ~ aSet0(X1)
| aIdeal0(X1)
| aElementOf0(esk9_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSet0(sdtasasdt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__1150]) ).
fof(c_0_18,negated_conjecture,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(esk9_1(sdtasasdt0(X1,X2)),sdtasasdt0(X1,X2))
| aIdeal0(sdtasasdt0(X1,X2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__1150]) ).
fof(c_0_22,negated_conjecture,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( ~ aSet0(X2)
| ~ aSet0(X4)
| X3 != sdtasasdt0(X4,X2)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,hypothesis,
( ~ aSet0(X1)
| aElementOf0(esk9_1(sdtasasdt0(X1,xJ)),sdtasasdt0(X1,xJ))
| aIdeal0(sdtasasdt0(X1,xJ)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ aSet0(X4)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,plain,
( ~ aSet0(X3)
| ~ aSet0(X2)
| X4 != sdtasasdt0(X2,X3)
| ~ aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_29,plain,
( ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aElementOf0(X1,sdtasasdt0(X3,X2))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_30,hypothesis,
aElementOf0(esk9_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_31,plain,
( ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aElementOf0(X1,sdtasasdt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
( ~ aSet0(X1)
| aIdeal0(X1)
| aElementOf0(esk10_1(X1),X1)
| aElement0(esk11_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_33,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_11]) ).
cnf(c_0_34,plain,
( ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,sdtasasdt0(X2,X3)) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( ~ aIdeal0(X3)
| ~ aElementOf0(X2,X3)
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_36,hypothesis,
aElementOf0(esk9_1(sdtasasdt0(xI,xJ)),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_25]),c_0_20])]) ).
cnf(c_0_37,hypothesis,
aElementOf0(esk9_1(sdtasasdt0(xI,xJ)),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_30]),c_0_20]),c_0_25])]) ).
cnf(c_0_38,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElement0(esk11_1(sdtasasdt0(X1,X2)))
| aElementOf0(esk10_1(sdtasasdt0(X1,X2)),sdtasasdt0(X1,X2))
| aIdeal0(sdtasasdt0(X1,X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_15]) ).
cnf(c_0_39,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sdtasdt0(esk11_1(sdtasasdt0(X1,X2)),esk9_1(sdtasasdt0(X1,X2))),X1)
| ~ aElementOf0(sdtasdt0(esk11_1(sdtasasdt0(X1,X2)),esk9_1(sdtasasdt0(X1,X2))),X2)
| aElementOf0(esk10_1(sdtasasdt0(X1,X2)),sdtasasdt0(X1,X2))
| aIdeal0(sdtasasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_15]) ).
cnf(c_0_40,hypothesis,
( ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,esk9_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_17])]) ).
cnf(c_0_41,hypothesis,
( ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,esk9_1(sdtasasdt0(xI,xJ))),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_37]),c_0_21])]) ).
fof(c_0_42,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])])])]) ).
fof(c_0_43,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])])]) ).
fof(c_0_44,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])])]) ).
fof(c_0_45,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_46,hypothesis,
( ~ aSet0(X1)
| aElement0(esk11_1(sdtasasdt0(X1,xJ)))
| aElementOf0(esk10_1(sdtasasdt0(X1,xJ)),sdtasasdt0(X1,xJ))
| aIdeal0(sdtasasdt0(X1,xJ)) ),
inference(spm,[status(thm)],[c_0_38,c_0_20]) ).
cnf(c_0_47,hypothesis,
( ~ aElement0(esk11_1(sdtasasdt0(xI,xJ)))
| aElementOf0(esk10_1(sdtasasdt0(xI,xJ)),sdtasasdt0(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_39,c_0_40]),c_0_20]),c_0_25])]),c_0_26]),c_0_41]) ).
cnf(c_0_48,plain,
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X3)
| X3 = sdtasasdt0(X1,X2)
| aElementOf0(esk8_3(X1,X2,X3),X3)
| aElementOf0(esk8_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_49,plain,
( ~ aIdeal0(X2)
| ~ aElementOf0(X3,X2)
| ~ aElementOf0(X1,X2)
| aElementOf0(sdtpldt0(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_50,plain,
( ~ aElement0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_53,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,hypothesis,
aElementOf0(esk10_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_25]),c_0_26]),c_0_47]) ).
fof(c_0_56,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_57,hypothesis,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(esk8_3(X1,X2,xJ),X2)
| aElementOf0(esk8_3(X1,X2,xJ),xJ)
| xJ = sdtasasdt0(X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_20]) ).
cnf(c_0_58,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_11]) ).
cnf(c_0_59,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_11]) ).
cnf(c_0_60,hypothesis,
( ~ aElementOf0(X1,xJ)
| aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(xI,xJ)),X1),xJ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_36]),c_0_17])]) ).
cnf(c_0_61,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]),c_0_53]) ).
cnf(c_0_62,hypothesis,
aElement0(esk9_1(sdtasasdt0(xI,xJ))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_37]),c_0_25])]) ).
cnf(c_0_63,hypothesis,
aElementOf0(esk10_1(sdtasasdt0(xI,xJ)),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_55]),c_0_25]),c_0_20])]) ).
cnf(c_0_64,hypothesis,
aElementOf0(esk10_1(sdtasasdt0(xI,xJ)),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_55]),c_0_20]),c_0_25])]) ).
cnf(c_0_65,plain,
( ~ aElement0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,hypothesis,
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(xI,xJ)),X1),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_37]),c_0_21])]) ).
cnf(c_0_67,hypothesis,
( ~ aSet0(X1)
| aElementOf0(esk8_3(X1,xJ,xJ),xJ)
| sdtasasdt0(X1,xJ) = xJ ),
inference(spm,[status(thm)],[c_0_57,c_0_20]) ).
cnf(c_0_68,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(X1,X2)),esk10_1(sdtasasdt0(X1,X2))),X1)
| ~ aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(X1,X2)),esk10_1(sdtasasdt0(X1,X2))),X2)
| aElement0(esk11_1(sdtasasdt0(X1,X2)))
| aIdeal0(sdtasasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_34]),c_0_15]) ).
cnf(c_0_69,hypothesis,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(esk8_3(X1,X2,xI),X2)
| aElementOf0(esk8_3(X1,X2,xI),xI)
| xI = sdtasasdt0(X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
cnf(c_0_70,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(X1,X2)),esk10_1(sdtasasdt0(X1,X2))),X1)
| ~ aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(X1,X2)),esk10_1(sdtasasdt0(X1,X2))),X2)
| ~ aElementOf0(sdtasdt0(esk11_1(sdtasasdt0(X1,X2)),esk9_1(sdtasasdt0(X1,X2))),sdtasasdt0(X1,X2))
| aIdeal0(sdtasasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_34]),c_0_15]) ).
cnf(c_0_71,hypothesis,
( ~ aElement0(X1)
| ~ aElementOf0(sdtpldt0(X1,sz00),xJ)
| aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(xI,xJ)),X1),xJ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_72,hypothesis,
( ~ aElementOf0(X1,xJ)
| aElementOf0(sdtpldt0(esk10_1(sdtasasdt0(xI,xJ)),X1),xJ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_63]),c_0_17])]) ).
cnf(c_0_73,hypothesis,
aElement0(esk10_1(sdtasasdt0(xI,xJ))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_64]),c_0_25])]) ).
cnf(c_0_74,hypothesis,
aElementOf0(sz00,xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_65]),c_0_52]),c_0_62])]) ).
cnf(c_0_75,hypothesis,
( ~ aElement0(X1)
| ~ aElementOf0(sdtpldt0(X1,sz00),xI)
| aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(xI,xJ)),X1),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_61]),c_0_62])]) ).
cnf(c_0_76,hypothesis,
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(esk10_1(sdtasasdt0(xI,xJ)),X1),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_64]),c_0_21])]) ).
cnf(c_0_77,hypothesis,
aElementOf0(sz00,xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_65]),c_0_52]),c_0_62])]) ).
cnf(c_0_78,plain,
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X3)
| ~ aElementOf0(esk8_3(X1,X2,X3),X2)
| ~ aElementOf0(esk8_3(X1,X2,X3),X1)
| ~ aElementOf0(esk8_3(X1,X2,X3),X3)
| X3 = sdtasasdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_79,hypothesis,
( aElementOf0(esk8_3(xJ,xJ,xJ),xJ)
| sdtasasdt0(xJ,xJ) = xJ ),
inference(spm,[status(thm)],[c_0_67,c_0_20]) ).
cnf(c_0_80,hypothesis,
( ~ aElementOf0(esk10_1(sdtasasdt0(xI,xJ)),xJ)
| ~ aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(xI,xJ)),esk10_1(sdtasasdt0(xI,xJ))),xI)
| aElement0(esk11_1(sdtasasdt0(xI,xJ))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_60]),c_0_20]),c_0_25])]),c_0_26]) ).
cnf(c_0_81,hypothesis,
( ~ aSet0(X1)
| aElementOf0(esk8_3(X1,xI,xI),xI)
| sdtasasdt0(X1,xI) = xI ),
inference(spm,[status(thm)],[c_0_69,c_0_25]) ).
cnf(c_0_82,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sdtasdt0(esk11_1(sdtasasdt0(X1,X2)),esk9_1(sdtasasdt0(X1,X2))),X1)
| ~ aElementOf0(sdtasdt0(esk11_1(sdtasasdt0(X1,X2)),esk9_1(sdtasasdt0(X1,X2))),X2)
| ~ aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(X1,X2)),esk10_1(sdtasasdt0(X1,X2))),X1)
| ~ aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(X1,X2)),esk10_1(sdtasasdt0(X1,X2))),X2)
| aIdeal0(sdtasasdt0(X1,X2)) ),
inference(spm,[status(thm)],[c_0_70,c_0_34]) ).
cnf(c_0_83,hypothesis,
aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(xI,xJ)),esk10_1(sdtasasdt0(xI,xJ))),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_84,hypothesis,
aElementOf0(sdtpldt0(esk9_1(sdtasasdt0(xI,xJ)),esk10_1(sdtasasdt0(xI,xJ))),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_73]),c_0_77])]) ).
cnf(c_0_85,plain,
( ~ aElement0(X1)
| ~ aSet0(X3)
| ~ aSet0(X4)
| ~ aElementOf0(X2,X3)
| ~ aElementOf0(X2,X4)
| ~ aIdeal0(sdtasasdt0(X3,X4))
| aElementOf0(sdtasdt0(X1,X2),sdtasasdt0(X3,X4)) ),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_86,hypothesis,
sdtasasdt0(xJ,xJ) = xJ,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_20])]),c_0_79]) ).
cnf(c_0_87,hypothesis,
( ~ aElementOf0(esk10_1(sdtasasdt0(xI,xJ)),xI)
| ~ aElementOf0(esk10_1(sdtasasdt0(xI,xJ)),xJ)
| aElement0(esk11_1(sdtasasdt0(xI,xJ))) ),
inference(spm,[status(thm)],[c_0_80,c_0_66]) ).
cnf(c_0_88,hypothesis,
( aElementOf0(esk8_3(xI,xI,xI),xI)
| sdtasasdt0(xI,xI) = xI ),
inference(spm,[status(thm)],[c_0_81,c_0_25]) ).
cnf(c_0_89,hypothesis,
( ~ aElementOf0(sdtasdt0(esk11_1(sdtasasdt0(xI,xJ)),esk9_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk11_1(sdtasasdt0(xI,xJ)),esk9_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_20]),c_0_25])]),c_0_26]) ).
cnf(c_0_90,hypothesis,
( ~ aElement0(X1)
| ~ aElementOf0(X2,xJ)
| aElementOf0(sdtasdt0(X1,X2),xJ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_17]),c_0_20])]) ).
cnf(c_0_91,hypothesis,
aElement0(esk11_1(sdtasasdt0(xI,xJ))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_64])]),c_0_63])]) ).
cnf(c_0_92,hypothesis,
sdtasasdt0(xI,xI) = xI,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_88]),c_0_25])]),c_0_88]) ).
cnf(c_0_93,hypothesis,
~ aElementOf0(sdtasdt0(esk11_1(sdtasasdt0(xI,xJ)),esk9_1(sdtasasdt0(xI,xJ))),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_36]),c_0_91])]) ).
cnf(c_0_94,hypothesis,
( ~ aElement0(X1)
| ~ aElementOf0(X2,xI)
| aElementOf0(sdtasdt0(X1,X2),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_92]),c_0_21]),c_0_25])]) ).
cnf(c_0_95,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_37]),c_0_91])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG093+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % 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 04:22:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 25.25/4.48 % Version: 3.5.1
% 25.25/4.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 25.25/4.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.25/4.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 25.25/4.48 % Starting new_bool_3 with 300s (1) cores
% 25.25/4.48 % Starting new_bool_1 with 300s (1) cores
% 25.25/4.48 % Starting sh5l with 300s (1) cores
% 25.25/4.48 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 544312 completed with status 0
% 25.25/4.48 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 25.25/4.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 25.25/4.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.25/4.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 25.25/4.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 25.25/4.48 % No SInE strategy applied
% 25.25/4.48 % Search class: FGUSF-FFMS32-SFFFFFNN
% 25.25/4.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 25.25/4.48 % Starting SubtermCWHack with 136s (1) cores
% 25.25/4.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 25.25/4.48 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 25.25/4.48 % Starting new_bool_3 with 136s (1) cores
% 25.25/4.48 % Starting new_bool_1 with 136s (1) cores
% 25.25/4.48 % G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 544321 completed with status 0
% 25.25/4.48 % Result found by G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 25.25/4.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 25.25/4.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.25/4.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 25.25/4.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 25.25/4.48 % No SInE strategy applied
% 25.25/4.48 % Search class: FGUSF-FFMS32-SFFFFFNN
% 25.25/4.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 25.25/4.48 % Starting SubtermCWHack with 136s (1) cores
% 25.25/4.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 25.25/4.48 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 25.25/4.48 % Preprocessing time : 0.001 s
% 25.25/4.48 % Presaturation interreduction done
% 25.25/4.48
% 25.25/4.48 % Proof found!
% 25.25/4.48 % SZS status Theorem
% 25.25/4.48 % SZS output start CNFRefutation
% See solution above
% 25.25/4.48 % Parsed axioms : 27
% 25.25/4.48 % Removed by relevancy pruning/SinE : 0
% 25.25/4.48 % Initial clauses : 58
% 25.25/4.48 % Removed in clause preprocessing : 2
% 25.25/4.48 % Initial clauses in saturation : 56
% 25.25/4.48 % Processed clauses : 8321
% 25.25/4.48 % ...of these trivial : 477
% 25.25/4.48 % ...subsumed : 5296
% 25.25/4.48 % ...remaining for further processing : 2548
% 25.25/4.48 % Other redundant clauses eliminated : 24
% 25.25/4.48 % Clauses deleted for lack of memory : 0
% 25.25/4.48 % Backward-subsumed : 132
% 25.25/4.48 % Backward-rewritten : 180
% 25.25/4.48 % Generated clauses : 256721
% 25.25/4.48 % ...of the previous two non-redundant : 247230
% 25.25/4.48 % ...aggressively subsumed : 0
% 25.25/4.48 % Contextual simplify-reflections : 342
% 25.25/4.48 % Paramodulations : 256698
% 25.25/4.48 % Factorizations : 0
% 25.25/4.48 % NegExts : 0
% 25.25/4.48 % Equation resolutions : 24
% 25.25/4.48 % Disequality decompositions : 0
% 25.25/4.48 % Total rewrite steps : 62628
% 25.25/4.48 % ...of those cached : 62426
% 25.25/4.48 % Propositional unsat checks : 0
% 25.25/4.48 % Propositional check models : 0
% 25.25/4.48 % Propositional check unsatisfiable : 0
% 25.25/4.48 % Propositional clauses : 0
% 25.25/4.48 % Propositional clauses after purity: 0
% 25.25/4.48 % Propositional unsat core size : 0
% 25.25/4.48 % Propositional preprocessing time : 0.000
% 25.25/4.48 % Propositional encoding time : 0.000
% 25.25/4.48 % Propositional solver time : 0.000
% 25.25/4.48 % Success case prop preproc time : 0.000
% 25.25/4.48 % Success case prop encoding time : 0.000
% 25.25/4.48 % Success case prop solver time : 0.000
% 25.25/4.48 % Current number of processed clauses : 2171
% 25.25/4.48 % Positive orientable unit clauses : 205
% 25.25/4.48 % Positive unorientable unit clauses: 0
% 25.25/4.48 % Negative unit clauses : 7
% 25.25/4.48 % Non-unit-clauses : 1959
% 25.25/4.48 % Current number of unprocessed clauses: 237987
% 25.25/4.48 % ...number of literals in the above : 809513
% 25.25/4.48 % Current number of archived formulas : 0
% 25.25/4.48 % Current number of archived clauses : 368
% 25.25/4.48 % Clause-clause subsumption calls (NU) : 260727
% 25.25/4.48 % Rec. Clause-clause subsumption calls : 173445
% 25.25/4.48 % Non-unit clause-clause subsumptions : 5640
% 25.25/4.48 % Unit Clause-clause subsumption calls : 6141
% 25.25/4.48 % Rewrite failures with RHS unbound : 0
% 25.25/4.48 % BW rewrite match attempts : 782
% 25.25/4.48 % BW rewrite match successes : 22
% 25.25/4.48 % Condensation attempts : 0
% 25.25/4.48 % Condensation successes : 0
% 25.25/4.48 % Termbank termtop insertions : 6155102
% 25.25/4.48 % Search garbage collected termcells : 1030
% 25.25/4.48
% 25.25/4.48 % -------------------------------------------------
% 25.25/4.48 % User time : 3.721 s
% 25.25/4.48 % System time : 0.193 s
% 25.25/4.48 % Total time : 3.915 s
% 25.25/4.48 % Maximum resident set size: 3608 pages
% 25.25/4.48
% 25.25/4.48 % -------------------------------------------------
% 25.25/4.48 % User time : 18.045 s
% 25.25/4.48 % System time : 0.742 s
% 25.25/4.48 % Total time : 18.787 s
% 25.25/4.48 % Maximum resident set size: 4864 pages
% 25.25/4.48 % E exiting
%------------------------------------------------------------------------------