%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG106+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 02:05:52 PM UTC 2026
% Result : Theorem 0.25s 0.89s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 11 unt; 0 def)
% Number of atoms : 278 ( 44 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 357 ( 142 ~; 149 |; 49 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 87 ( 4 sgn 40 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ! [X1,X2,X3] :
( ( aElement0(X3)
& aElementOf0(X2,slsdtgt0(xc))
& aElementOf0(X1,slsdtgt0(xc)) )
=> ? [X4] :
( ? [X5] :
( aElementOf0(sdtasdt0(X3,X1),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X1,X2),slsdtgt0(xc))
& sdtasdt0(X3,X1) = sdtasdt0(xc,sdtasdt0(X4,X3))
& sdtpldt0(X1,X2) = sdtasdt0(xc,sdtpldt0(X4,X5))
& sdtasdt0(xc,X5) = X2
& aElement0(X5) )
& sdtasdt0(xc,X4) = X1
& aElement0(X4) ) )
=> aIdeal0(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(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
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(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(m__1905,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
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(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_11,negated_conjecture,
~ ( ! [X1,X2,X3] :
( ( aElement0(X3)
& aElementOf0(X2,slsdtgt0(xc))
& aElementOf0(X1,slsdtgt0(xc)) )
=> ? [X4] :
( ? [X5] :
( aElementOf0(sdtasdt0(X3,X1),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X1,X2),slsdtgt0(xc))
& sdtasdt0(X3,X1) = sdtasdt0(xc,sdtasdt0(X4,X3))
& sdtpldt0(X1,X2) = sdtasdt0(xc,sdtpldt0(X4,X5))
& sdtasdt0(xc,X5) = X2
& aElement0(X5) )
& sdtasdt0(xc,X4) = X1
& aElement0(X4) ) )
=> aIdeal0(slsdtgt0(xc)) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,negated_conjecture,
! [X115,X116,X117] :
( ~ aIdeal0(slsdtgt0(xc))
& ( ~ aElement0(X117)
| ~ aElementOf0(X116,slsdtgt0(xc))
| ~ aElementOf0(X115,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X117,X115),slsdtgt0(xc)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X116,slsdtgt0(xc))
| ~ aElementOf0(X115,slsdtgt0(xc))
| aElementOf0(sdtpldt0(X115,X116),slsdtgt0(xc)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X116,slsdtgt0(xc))
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(X117,X115) = sdtasdt0(xc,sdtasdt0(esk21_3(X115,X116,X117),X117)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X116,slsdtgt0(xc))
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtpldt0(X115,X116) = sdtasdt0(xc,sdtpldt0(esk21_3(X115,X116,X117),esk22_3(X115,X116,X117))) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X116,slsdtgt0(xc))
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,esk22_3(X115,X116,X117)) = X116 )
& ( ~ aElement0(X117)
| ~ aElementOf0(X116,slsdtgt0(xc))
| ~ aElementOf0(X115,slsdtgt0(xc))
| aElement0(esk22_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X116,slsdtgt0(xc))
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,esk21_3(X115,X116,X117)) = X115 )
& ( ~ aElement0(X117)
| ~ aElementOf0(X116,slsdtgt0(xc))
| ~ aElementOf0(X115,slsdtgt0(xc))
| aElement0(esk21_3(X115,X116,X117)) ) ),
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_11])])])])])])]) ).
fof(c_0_13,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_14,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_15,negated_conjecture,
( ~ aElement0(X1)
| ~ aElementOf0(X3,slsdtgt0(xc))
| ~ aElementOf0(X2,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(xc)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( ~ aSet0(X1)
| aIdeal0(X1)
| aElementOf0(esk9_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
~ aIdeal0(slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,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_19,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( ~ aElement0(X1)
| ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(X2,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(xc)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
( ~ aElement0(X2)
| X1 != slsdtgt0(X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( ~ aElement0(X2)
| X4 != slsdtgt0(X2)
| sdtasdt0(X2,X1) != X3
| ~ aElement0(X1)
| aElementOf0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,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])])])]) ).
cnf(c_0_24,negated_conjecture,
( ~ aElement0(X1)
| ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(X2,slsdtgt0(xc))
| aElement0(sdtasdt0(X1,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( ~ aElement0(X1)
| aSet0(slsdtgt0(X1)) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_26,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[m__1905]) ).
cnf(c_0_27,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_22])]) ).
cnf(c_0_28,plain,
( ~ aElement0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_30,negated_conjecture,
( ~ aElement0(X1)
| ~ aElementOf0(X2,slsdtgt0(xc))
| aElement0(sdtasdt0(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
( ~ aElement0(X1)
| aElementOf0(X1,slsdtgt0(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
fof(c_0_32,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_33,negated_conjecture,
( ~ aElement0(X1)
| aElement0(sdtasdt0(X1,xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_26])]) ).
cnf(c_0_34,plain,
( ~ aElement0(X1)
| sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_35,plain,
! [X8] :
( aElement0(smndt0(X8))
| ~ aElement0(X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])])]) ).
fof(c_0_36,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_37,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| aElement0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_26])]) ).
cnf(c_0_38,plain,
( ~ aElement0(X1)
| aElement0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,plain,
( ~ aElement0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_41,negated_conjecture,
( ~ aElement0(X3)
| ~ aElementOf0(X2,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| aElementOf0(sdtpldt0(X1,X2),slsdtgt0(xc)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_42,negated_conjecture,
aElement0(smndt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_29])]) ).
cnf(c_0_43,negated_conjecture,
( ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| aElementOf0(sz00,slsdtgt0(xc)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_39]),c_0_40])]),c_0_19]) ).
cnf(c_0_44,plain,
( ~ aElement0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,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_13]) ).
cnf(c_0_46,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X2,slsdtgt0(xc))
| aElementOf0(sdtpldt0(X1,X2),slsdtgt0(xc)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xc))
| aElementOf0(sz00,slsdtgt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_25]),c_0_26])]) ).
cnf(c_0_48,plain,
( ~ aElement0(X1)
| aElementOf0(sz00,slsdtgt0(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_44]),c_0_40])]) ).
cnf(c_0_49,negated_conjecture,
( ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(esk9_1(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(esk10_1(slsdtgt0(xc)),slsdtgt0(xc))
| aElement0(esk11_1(slsdtgt0(xc))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_17]) ).
cnf(c_0_50,plain,
( ~ aSet0(X1)
| aIdeal0(X1)
| aElementOf0(esk10_1(X1),X1)
| aElement0(esk11_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_51,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_13]) ).
cnf(c_0_52,negated_conjecture,
aElementOf0(sz00,slsdtgt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_26])]) ).
cnf(c_0_53,negated_conjecture,
( ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(esk9_1(slsdtgt0(xc)),slsdtgt0(xc))
| aElement0(esk11_1(slsdtgt0(xc))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_17]) ).
cnf(c_0_54,negated_conjecture,
( ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(esk9_1(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(esk10_1(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(esk11_1(slsdtgt0(xc)),esk9_1(slsdtgt0(xc))),slsdtgt0(xc)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_46]),c_0_17]) ).
cnf(c_0_55,negated_conjecture,
( ~ aElement0(X1)
| ~ aElementOf0(X2,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(xc)) ),
inference(spm,[status(thm)],[c_0_15,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( ~ aSet0(slsdtgt0(xc))
| aElement0(esk11_1(slsdtgt0(xc))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_16]),c_0_17]) ).
cnf(c_0_57,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_13]) ).
cnf(c_0_58,negated_conjecture,
( ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(esk9_1(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(esk10_1(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( ~ aElement0(esk11_1(slsdtgt0(xc)))
| ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(esk9_1(slsdtgt0(xc)),slsdtgt0(xc))
| aElementOf0(esk10_1(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_55]),c_0_17]) ).
cnf(c_0_60,negated_conjecture,
( ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(esk9_1(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_56]) ).
cnf(c_0_61,negated_conjecture,
~ aSet0(slsdtgt0(xc)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_16]),c_0_17]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG106+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.66 % Computer : n017.cluster.edu
% 0.21/0.66 % Model : x86_64 x86_64
% 0.21/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.66 % Memory : 8046.5625MB
% 0.21/0.66 % OS : Linux 6.8.0-71-generic
% 0.21/0.66 % CPULimit : 300
% 0.21/0.66 % WCLimit : 300
% 0.21/0.66 % DateTime : Mon Sep 21 04:15:42 UTC 2026
% 0.21/0.66 % CPUTime :
% 0.21/0.66 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.73 Running first-order theorem proving
% 0.25/0.73 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.89 % Version: 3.5.1
% 0.25/0.89 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.89 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.89 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.89 % Starting sh5l with 300s (1) cores
% 0.25/0.89 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1406740 completed with status 0
% 0.25/0.89 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.25/0.89 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.89 % No SInE strategy applied
% 0.25/0.89 % Search class: FGUSF-FSMS32-MFFFFFNN
% 0.25/0.89 % partial match(1): FGUSF-FFMS32-MFFFFFNN
% 0.25/0.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.89 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.25/0.89 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.25/0.89 % Starting new_bool_3 with 136s (1) cores
% 0.25/0.89 % Starting new_bool_1 with 136s (1) cores
% 0.25/0.89 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 1406748 completed with status 0
% 0.25/0.89 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.25/0.89 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.89 % No SInE strategy applied
% 0.25/0.89 % Search class: FGUSF-FSMS32-MFFFFFNN
% 0.25/0.89 % partial match(1): FGUSF-FFMS32-MFFFFFNN
% 0.25/0.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.89 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.89 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.25/0.89 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.25/0.89 % Preprocessing time : 0.004 s
% 0.25/0.89 % Presaturation interreduction done
% 0.25/0.89
% 0.25/0.89 % Proof found!
% 0.25/0.89 % SZS status Theorem
% 0.25/0.89 % SZS output start CNFRefutation
% See solution above
% 0.25/0.89 % Parsed axioms : 39
% 0.25/0.89 % Removed by relevancy pruning/SinE : 0
% 0.25/0.89 % Initial clauses : 102
% 0.25/0.89 % Removed in clause preprocessing : 4
% 0.25/0.89 % Initial clauses in saturation : 98
% 0.25/0.89 % Processed clauses : 845
% 0.25/0.89 % ...of these trivial : 4
% 0.25/0.89 % ...subsumed : 377
% 0.25/0.89 % ...remaining for further processing : 464
% 0.25/0.89 % Other redundant clauses eliminated : 20
% 0.25/0.89 % Clauses deleted for lack of memory : 0
% 0.25/0.89 % Backward-subsumed : 67
% 0.25/0.89 % Backward-rewritten : 13
% 0.25/0.89 % Generated clauses : 2358
% 0.25/0.89 % ...of the previous two non-redundant : 2003
% 0.25/0.89 % ...aggressively subsumed : 0
% 0.25/0.89 % Contextual simplify-reflections : 19
% 0.25/0.89 % Paramodulations : 2340
% 0.25/0.89 % Factorizations : 0
% 0.25/0.89 % NegExts : 0
% 0.25/0.89 % Equation resolutions : 20
% 0.25/0.89 % Disequality decompositions : 0
% 0.25/0.89 % Total rewrite steps : 1346
% 0.25/0.89 % ...of those cached : 1326
% 0.25/0.89 % Propositional unsat checks : 0
% 0.25/0.89 % Propositional check models : 0
% 0.25/0.89 % Propositional check unsatisfiable : 0
% 0.25/0.89 % Propositional clauses : 0
% 0.25/0.89 % Propositional clauses after purity: 0
% 0.25/0.89 % Propositional unsat core size : 0
% 0.25/0.89 % Propositional preprocessing time : 0.000
% 0.25/0.89 % Propositional encoding time : 0.000
% 0.25/0.89 % Propositional solver time : 0.000
% 0.25/0.89 % Success case prop preproc time : 0.000
% 0.25/0.89 % Success case prop encoding time : 0.000
% 0.25/0.89 % Success case prop solver time : 0.000
% 0.25/0.89 % Current number of processed clauses : 272
% 0.25/0.89 % Positive orientable unit clauses : 21
% 0.25/0.89 % Positive unorientable unit clauses: 0
% 0.25/0.89 % Negative unit clauses : 3
% 0.25/0.89 % Non-unit-clauses : 248
% 0.25/0.89 % Current number of unprocessed clauses: 946
% 0.25/0.89 % ...number of literals in the above : 4996
% 0.25/0.89 % Current number of archived formulas : 0
% 0.25/0.89 % Current number of archived clauses : 178
% 0.25/0.89 % Clause-clause subsumption calls (NU) : 21943
% 0.25/0.89 % Rec. Clause-clause subsumption calls : 14641
% 0.25/0.89 % Non-unit clause-clause subsumptions : 434
% 0.25/0.89 % Unit Clause-clause subsumption calls : 214
% 0.25/0.89 % Rewrite failures with RHS unbound : 0
% 0.25/0.89 % BW rewrite match attempts : 11
% 0.25/0.89 % BW rewrite match successes : 11
% 0.25/0.89 % Condensation attempts : 0
% 0.25/0.89 % Condensation successes : 0
% 0.25/0.89 % Termbank termtop insertions : 44541
% 0.25/0.89 % Search garbage collected termcells : 2031
% 0.25/0.89
% 0.25/0.89 % -------------------------------------------------
% 0.25/0.89 % User time : 0.080 s
% 0.25/0.89 % System time : 0.008 s
% 0.25/0.89 % Total time : 0.088 s
% 0.25/0.89 % Maximum resident set size: 3688 pages
% 0.25/0.89
% 0.25/0.89 % -------------------------------------------------
% 0.25/0.89 % User time : 0.248 s
% 0.25/0.89 % System time : 0.037 s
% 0.25/0.89 % Total time : 0.284 s
% 0.25/0.89 % Maximum resident set size: 4864 pages
% 0.25/0.89 % E exiting
%------------------------------------------------------------------------------