%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG096+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 : n020.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 02:05:50 PM UTC 2026
% Result : Theorem 1.22s 0.64s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of formulae : 102 ( 37 unt; 0 def)
% Number of atoms : 282 ( 51 equ)
% Maximal formula atoms : 29 ( 2 avg)
% Number of connectives : 329 ( 149 ~; 135 |; 29 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__1205,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1205) ).
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__1294,hypothesis,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1294) ).
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(m__,conjecture,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1319) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__1217,hypothesis,
( aElement0(xy)
& aElement0(xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1217) ).
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(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ( sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(c_0_19,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_20,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_21,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__1205]) ).
cnf(c_0_23,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__1205]) ).
fof(c_0_24,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_25,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
aElementOf0(xb,xJ),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_27,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,hypothesis,
aElementOf0(xa,xI),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_29,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
fof(c_0_30,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])])])]) ).
fof(c_0_31,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_32,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_33,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,hypothesis,
sdtpldt0(xa,xb) = sz10,
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_35,hypothesis,
aElement0(xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_36,hypothesis,
aElement0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_28]),c_0_29])]) ).
fof(c_0_37,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_38,plain,
( ~ aElement0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
( ~ aElement0(X1)
| aElement0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_40,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_41,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_42,hypothesis,
( ~ aElement0(X1)
| sdtpldt0(xa,sdtpldt0(xb,X1)) = sdtpldt0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_43,plain,
( ~ aElement0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_45,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_46,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_38]),c_0_39]) ).
fof(c_0_47,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(fof_nnf,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
( ~ aElement0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_49,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,hypothesis,
sdtpldt0(sz10,sz00) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_34]),c_0_44]),c_0_35])]) ).
cnf(c_0_51,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_52,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,hypothesis,
sdtpldt0(smndt0(xa),sz10) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_54,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(split_conjunct,[status(thm)],[m__1319]) ).
fof(c_0_56,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])])]) ).
cnf(c_0_57,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_48]),c_0_39]) ).
cnf(c_0_58,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_44]),c_0_51])]) ).
cnf(c_0_59,hypothesis,
( ~ aElement0(smndt0(xa))
| aElement0(sdtpldt0(sz00,xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_51])]) ).
cnf(c_0_60,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_63,hypothesis,
sdtpldt0(xa,sdtpldt0(sz00,xb)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_53]),c_0_58]),c_0_51]),c_0_36])]) ).
cnf(c_0_64,hypothesis,
aElement0(sdtpldt0(sz00,xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_39]),c_0_36])]) ).
cnf(c_0_65,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xa,xy),sdtasdt0(xx,xb)),smndt0(xx)),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_36])]) ).
cnf(c_0_66,hypothesis,
sdtpldt0(sz00,sdtpldt0(sz00,xb)) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_63]),c_0_53]),c_0_64]),c_0_36])]) ).
cnf(c_0_67,plain,
( ~ aElement0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_68,negated_conjecture,
( ~ aElement0(smndt0(xx))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElementOf0(sdtpldt0(sdtasdt0(xa,xy),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),xI) ),
inference(spm,[status(thm)],[c_0_65,c_0_33]) ).
cnf(c_0_69,plain,
( ~ aIdeal0(X2)
| ~ aElementOf0(X3,X2)
| ~ aElementOf0(X1,X2)
| aElementOf0(sdtpldt0(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_70,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_71,hypothesis,
( ~ aElement0(smndt0(xa))
| sdtpldt0(sz10,smndt0(xa)) = sdtpldt0(sz00,xb) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_53]),c_0_51])]) ).
cnf(c_0_72,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_35])]) ).
cnf(c_0_73,negated_conjecture,
( ~ aElement0(smndt0(xx))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtpldt0(sdtasdt0(xx,xb),smndt0(xx)),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_23])]) ).
cnf(c_0_74,plain,
( ~ aElement0(X1)
| sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_75,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_76,hypothesis,
( ~ aElement0(smndt0(xa))
| sdtpldt0(sz10,smndt0(xa)) = xb ),
inference(rw,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(smndt0(sz10),xx))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtpldt0(sdtasdt0(xx,xb),sdtasdt0(smndt0(sz10),xx)),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_78,hypothesis,
( ~ aElement0(smndt0(xa))
| sdtpldt0(sz00,smndt0(xa)) = sdtpldt0(smndt0(sz10),xb) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_76]),c_0_51])]) ).
cnf(c_0_79,negated_conjecture,
( ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(smndt0(sz10),xx))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtpldt0(sdtasdt0(smndt0(sz10),xx),sdtasdt0(xx,xb)),xI) ),
inference(spm,[status(thm)],[c_0_77,c_0_49]) ).
fof(c_0_80,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_81,hypothesis,
( ~ aElement0(smndt0(xa))
| smndt0(xa) = sdtpldt0(smndt0(sz10),xb) ),
inference(spm,[status(thm)],[c_0_67,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xb,xx))
| ~ aElement0(sdtasdt0(smndt0(sz10),xx))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtpldt0(sdtasdt0(smndt0(sz10),xx),sdtasdt0(xb,xx)),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_61]),c_0_35]),c_0_75])]) ).
cnf(c_0_83,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_80]) ).
cnf(c_0_84,plain,
( ~ aElement0(X1)
| smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_85,hypothesis,
smndt0(xa) = sdtpldt0(smndt0(sz10),xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_39]),c_0_36])]) ).
cnf(c_0_86,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xb,xx))
| ~ aElement0(sdtasdt0(smndt0(sz10),xx))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtasdt0(sdtpldt0(smndt0(sz10),xb),xx),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_75]),c_0_35])]) ).
cnf(c_0_87,hypothesis,
sdtpldt0(smndt0(sz10),xb) = sdtasdt0(xa,smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_36])]) ).
cnf(c_0_88,plain,
( ~ aIdeal0(X3)
| ~ aElementOf0(X2,X3)
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_89,hypothesis,
aElement0(sdtpldt0(smndt0(sz10),xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_85]),c_0_36])]) ).
cnf(c_0_90,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xb,xx))
| ~ aElement0(sdtasdt0(smndt0(sz10),xx))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtasdt0(sdtasdt0(xa,smndt0(sz10)),xx),xI) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X1,X3)
| ~ aIdeal0(X3)
| aElementOf0(sdtasdt0(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_88,c_0_61]) ).
cnf(c_0_92,hypothesis,
aElement0(sdtasdt0(xa,smndt0(sz10))),
inference(rw,[status(thm)],[c_0_89,c_0_87]) ).
fof(c_0_93,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_94,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xb,xx))
| ~ aElement0(sdtasdt0(smndt0(sz10),xx))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtasdt0(xa,smndt0(sz10)),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_23]),c_0_75]),c_0_92])]) ).
cnf(c_0_95,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_96,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xb,xx))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtasdt0(xa,smndt0(sz10)),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_75])]) ).
cnf(c_0_97,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtasdt0(xa,smndt0(sz10)),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_95]),c_0_75]),c_0_35])]) ).
cnf(c_0_98,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElementOf0(sdtasdt0(xa,xy),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_91]),c_0_23]),c_0_28]),c_0_36])]) ).
cnf(c_0_99,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_91]),c_0_23]),c_0_28]),c_0_62]),c_0_36])]) ).
cnf(c_0_100,negated_conjecture,
~ aElement0(sdtasdt0(xa,xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_39]),c_0_51])]) ).
cnf(c_0_101,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_95]),c_0_62]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG096+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 04:20:18 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 1.22/0.64 % Version: 3.5.1
% 1.22/0.64 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.22/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.22/0.64 % Starting new_bool_3 with 300s (1) cores
% 1.22/0.64 % Starting new_bool_1 with 300s (1) cores
% 1.22/0.64 % Starting sh5l with 300s (1) cores
% 1.22/0.64 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1987397 completed with status 0
% 1.22/0.64 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 1.22/0.64 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.22/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.22/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.22/0.64 % No SInE strategy applied
% 1.22/0.64 % Search class: FGUSF-FFMM32-SFFFFFNN
% 1.22/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.22/0.64 % Starting SubtermCWHack with 136s (1) cores
% 1.22/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 1.22/0.64 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.22/0.64 % Starting new_bool_3 with 136s (1) cores
% 1.22/0.64 % Starting new_bool_1 with 136s (1) cores
% 1.22/0.64 % G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1987405 completed with status 0
% 1.22/0.64 % Result found by G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 1.22/0.64 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.22/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.22/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.22/0.64 % No SInE strategy applied
% 1.22/0.64 % Search class: FGUSF-FFMM32-SFFFFFNN
% 1.22/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.22/0.64 % Starting SubtermCWHack with 136s (1) cores
% 1.22/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 1.22/0.64 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.22/0.64 % Preprocessing time : 0.002 s
% 1.22/0.64 % Presaturation interreduction done
% 1.22/0.64
% 1.22/0.64 % Proof found!
% 1.22/0.64 % SZS status Theorem
% 1.22/0.64 % SZS output start CNFRefutation
% See solution above
% 1.22/0.64 % Parsed axioms : 33
% 1.22/0.64 % Removed by relevancy pruning/SinE : 0
% 1.22/0.64 % Initial clauses : 68
% 1.22/0.64 % Removed in clause preprocessing : 2
% 1.22/0.64 % Initial clauses in saturation : 66
% 1.22/0.64 % Processed clauses : 1619
% 1.22/0.64 % ...of these trivial : 46
% 1.22/0.64 % ...subsumed : 814
% 1.22/0.64 % ...remaining for further processing : 759
% 1.22/0.64 % Other redundant clauses eliminated : 10
% 1.22/0.64 % Clauses deleted for lack of memory : 0
% 1.22/0.64 % Backward-subsumed : 156
% 1.22/0.64 % Backward-rewritten : 53
% 1.22/0.64 % Generated clauses : 6909
% 1.22/0.64 % ...of the previous two non-redundant : 5497
% 1.22/0.64 % ...aggressively subsumed : 0
% 1.22/0.64 % Contextual simplify-reflections : 41
% 1.22/0.64 % Paramodulations : 6900
% 1.22/0.64 % Factorizations : 0
% 1.22/0.64 % NegExts : 0
% 1.22/0.64 % Equation resolutions : 10
% 1.22/0.64 % Disequality decompositions : 0
% 1.22/0.64 % Total rewrite steps : 9189
% 1.22/0.64 % ...of those cached : 9080
% 1.22/0.64 % Propositional unsat checks : 0
% 1.22/0.64 % Propositional check models : 0
% 1.22/0.64 % Propositional check unsatisfiable : 0
% 1.22/0.64 % Propositional clauses : 0
% 1.22/0.64 % Propositional clauses after purity: 0
% 1.22/0.64 % Propositional unsat core size : 0
% 1.22/0.64 % Propositional preprocessing time : 0.000
% 1.22/0.64 % Propositional encoding time : 0.000
% 1.22/0.64 % Propositional solver time : 0.000
% 1.22/0.64 % Success case prop preproc time : 0.000
% 1.22/0.64 % Success case prop encoding time : 0.000
% 1.22/0.64 % Success case prop solver time : 0.000
% 1.22/0.64 % Current number of processed clauses : 475
% 1.22/0.64 % Positive orientable unit clauses : 95
% 1.22/0.64 % Positive unorientable unit clauses: 0
% 1.22/0.64 % Negative unit clauses : 17
% 1.22/0.64 % Non-unit-clauses : 363
% 1.22/0.64 % Current number of unprocessed clauses: 3833
% 1.22/0.64 % ...number of literals in the above : 16810
% 1.22/0.64 % Current number of archived formulas : 0
% 1.22/0.64 % Current number of archived clauses : 275
% 1.22/0.64 % Clause-clause subsumption calls (NU) : 71158
% 1.22/0.64 % Rec. Clause-clause subsumption calls : 9174
% 1.22/0.64 % Non-unit clause-clause subsumptions : 867
% 1.22/0.64 % Unit Clause-clause subsumption calls : 2540
% 1.22/0.64 % Rewrite failures with RHS unbound : 0
% 1.22/0.64 % BW rewrite match attempts : 302
% 1.22/0.64 % BW rewrite match successes : 21
% 1.22/0.64 % Condensation attempts : 0
% 1.22/0.64 % Condensation successes : 0
% 1.22/0.64 % Termbank termtop insertions : 125678
% 1.22/0.64 % Search garbage collected termcells : 1100
% 1.22/0.64
% 1.22/0.64 % -------------------------------------------------
% 1.22/0.64 % User time : 0.176 s
% 1.22/0.64 % System time : 0.019 s
% 1.22/0.64 % Total time : 0.195 s
% 1.22/0.64 % Maximum resident set size: 3672 pages
% 1.22/0.64
% 1.22/0.64 % -------------------------------------------------
% 1.22/0.64 % User time : 0.812 s
% 1.22/0.64 % System time : 0.068 s
% 1.22/0.64 % Total time : 0.879 s
% 1.22/0.64 % Maximum resident set size: 4608 pages
% 1.22/0.64 % E exiting
%------------------------------------------------------------------------------