%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG096+2 : 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 : n005.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 2.67s 1.35s
% Output : CNFRefutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 106 ( 36 unt; 0 def)
% Number of atoms : 332 ( 50 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 395 ( 169 ~; 157 |; 45 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__1205,hypothesis,
( aIdeal0(xJ)
& ! [X1] :
( aElementOf0(X1,xJ)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xJ) )
& ! [X2] :
( aElementOf0(X2,xJ)
=> aElementOf0(sdtpldt0(X1,X2),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) )
& ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(m__1294,hypothesis,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).
fof(mAddInvr,axiom,
! [X1] :
( aElement0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddInvr) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1319) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(m__1217,hypothesis,
( aElement0(xy)
& aElement0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
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(mMulMnOne,axiom,
! [X1] :
( aElement0(X1)
=> ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
& sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDefMod,axiom,
! [X1,X2,X3] :
( ( aIdeal0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aElementOf0(sdtpldt0(X1,smndt0(X2)),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMod) ).
fof(c_0_20,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_21,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])])])]) ).
fof(c_0_22,hypothesis,
! [X77,X78,X79,X80,X81,X82] :
( aIdeal0(xJ)
& ( ~ aElementOf0(X80,xJ)
| aElementOf0(sdtasdt0(X82,X80),xJ)
| ~ aElement0(X82) )
& ( ~ aElementOf0(X80,xJ)
| aElementOf0(sdtpldt0(X80,X81),xJ)
| ~ aElementOf0(X81,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ( ~ aElementOf0(X77,xI)
| aElementOf0(sdtasdt0(X79,X77),xI)
| ~ aElement0(X79) )
& ( ~ aElementOf0(X77,xI)
| aElementOf0(sdtpldt0(X77,X78),xI)
| ~ aElementOf0(X78,xI) )
& aSet0(xI) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1205])])])])]) ).
fof(c_0_23,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
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_21]) ).
cnf(c_0_26,hypothesis,
aElementOf0(xb,xJ),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_27,hypothesis,
aSet0(xJ),
inference(split_conjunct,[status(thm)],[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(split_conjunct,[status(thm)],[c_0_22]) ).
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(fof_nnf,[status(thm)],[c_0_23]) ).
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]) ).
cnf(c_0_40,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(split_conjunct,[status(thm)],[m__1319]) ).
fof(c_0_42,plain,
! [X20,X21] :
( sdtasdt0(X20,X21) = sdtasdt0(X21,X20)
| ~ aElement0(X21)
| ~ aElement0(X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
fof(c_0_43,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_44,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_45,plain,
( ~ aElement0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_47,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_48,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]) ).
cnf(c_0_49,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_52,plain,
( ~ aElement0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_53,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_54,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_44,c_0_45]),c_0_34]),c_0_46]),c_0_35])]) ).
cnf(c_0_55,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_56,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,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_48,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_58,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_49,c_0_50]),c_0_51]),c_0_36])]) ).
fof(c_0_59,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_60,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_52]),c_0_39]) ).
cnf(c_0_61,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_46]),c_0_55])]) ).
cnf(c_0_62,hypothesis,
( ~ aElement0(smndt0(xa))
| aElement0(sdtpldt0(sz00,xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_55])]) ).
cnf(c_0_63,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_58,c_0_33]) ).
cnf(c_0_64,plain,
( ~ aIdeal0(X2)
| ~ aElementOf0(X3,X2)
| ~ aElementOf0(X1,X2)
| aElementOf0(sdtpldt0(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_65,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_66,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_67,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_60,c_0_57]),c_0_61]),c_0_55]),c_0_36])]) ).
cnf(c_0_68,hypothesis,
aElement0(sdtpldt0(sz00,xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_39]),c_0_36])]) ).
cnf(c_0_69,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_63,c_0_64]),c_0_65])]) ).
cnf(c_0_70,plain,
( ~ aElement0(X1)
| smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_71,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__1217]) ).
fof(c_0_72,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_73,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_48,c_0_67]),c_0_57]),c_0_68]),c_0_36])]) ).
cnf(c_0_74,plain,
( ~ aElement0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_75,negated_conjecture,
( ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xx,smndt0(sz10)))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtpldt0(sdtasdt0(xx,xb),sdtasdt0(xx,smndt0(sz10))),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).
cnf(c_0_76,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_77,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_35])]) ).
cnf(c_0_78,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xx,smndt0(sz10)))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),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_35]),c_0_71])]) ).
cnf(c_0_79,plain,
( ~ aIdeal0(X3)
| ~ aElementOf0(X2,X3)
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_80,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_81,hypothesis,
sdtpldt0(smndt0(xa),sz10) = xb,
inference(rw,[status(thm)],[c_0_57,c_0_77]) ).
cnf(c_0_82,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xx,smndt0(sz10)))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_65]),c_0_71])]) ).
cnf(c_0_83,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_84,hypothesis,
( ~ aElement0(smndt0(xa))
| sdtpldt0(sz10,smndt0(xa)) = xb ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_81]),c_0_55])]) ).
cnf(c_0_85,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_71])]) ).
fof(c_0_86,plain,
! [X74,X75,X76] :
( ( ~ aIdeal0(X76)
| ~ aElement0(X75)
| ~ aElement0(X74)
| sdteqdtlpzmzozddtrp0(X74,X75,X76)
| ~ aElementOf0(sdtpldt0(X74,smndt0(X75)),X76) )
& ( ~ aIdeal0(X76)
| ~ aElement0(X75)
| ~ aElement0(X74)
| aElementOf0(sdtpldt0(X74,smndt0(X75)),X76)
| ~ sdteqdtlpzmzozddtrp0(X74,X75,X76) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefMod])])])]) ).
cnf(c_0_87,hypothesis,
( ~ aElementOf0(X2,xI)
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,X2),xI) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_88,plain,
( ~ aElement0(X1)
| sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_89,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_48,c_0_84]),c_0_55])]) ).
cnf(c_0_90,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_83]),c_0_35]),c_0_71])]) ).
cnf(c_0_91,plain,
( ~ aIdeal0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| aElementOf0(sdtpldt0(X1,smndt0(X2)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_92,hypothesis,
( ~ aElement0(X1)
| ~ aElement0(smndt0(sz10))
| ~ aElementOf0(X1,xI)
| aElementOf0(smndt0(X1),xI) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_93,hypothesis,
( ~ aElement0(smndt0(xa))
| smndt0(xa) = sdtpldt0(smndt0(sz10),xb) ),
inference(spm,[status(thm)],[c_0_74,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ sdteqdtlpzmzozddtrp0(xb,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_65]),c_0_55]),c_0_35])]) ).
cnf(c_0_95,plain,
( ~ aIdeal0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_96,hypothesis,
( ~ aElement0(X1)
| ~ aElementOf0(X1,xI)
| aElementOf0(smndt0(X1),xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_39]),c_0_55])]) ).
cnf(c_0_97,hypothesis,
smndt0(xa) = sdtpldt0(smndt0(sz10),xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_39]),c_0_36])]) ).
cnf(c_0_98,negated_conjecture,
( ~ aElement0(sdtasdt0(xa,xy))
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ sdteqdtlpzmzozddtrp0(xb,sz10,xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_39]),c_0_55])]) ).
cnf(c_0_99,hypothesis,
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X1,xI)
| aElementOf0(sdtasdt0(X1,X2),xI) ),
inference(spm,[status(thm)],[c_0_87,c_0_50]) ).
cnf(c_0_100,plain,
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(sdtpldt0(smndt0(X2),X1),X3)
| ~ aIdeal0(X3)
| sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_53]),c_0_39]) ).
cnf(c_0_101,hypothesis,
aElementOf0(sdtpldt0(smndt0(sz10),xb),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_28]),c_0_36])]) ).
cnf(c_0_102,negated_conjecture,
( ~ aElement0(sdtasdt0(xa,xy))
| ~ sdteqdtlpzmzozddtrp0(xb,sz10,xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_28]),c_0_51]),c_0_36])]) ).
cnf(c_0_103,hypothesis,
sdteqdtlpzmzozddtrp0(xb,sz10,xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_65]),c_0_55]),c_0_35])]) ).
cnf(c_0_104,negated_conjecture,
~ aElement0(sdtasdt0(xa,xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_103])]) ).
cnf(c_0_105,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_83]),c_0_51]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG096+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.86 % Computer : n005.cluster.edu
% 0.19/0.86 % Model : x86_64 x86_64
% 0.19/0.86 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.86 % Memory : 8046.5625MB
% 0.19/0.86 % OS : Linux 6.8.0-71-generic
% 0.19/0.86 % CPULimit : 300
% 0.19/0.86 % WCLimit : 300
% 0.19/0.86 % DateTime : Mon Sep 21 04:19:19 UTC 2026
% 0.19/0.86 % CPUTime :
% 0.19/0.86 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.92 Running first-order theorem proving
% 0.24/0.92 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
% 2.67/1.35 % Version: 3.5.1
% 2.67/1.35 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.67/1.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.67/1.35 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.67/1.35 % Starting new_bool_3 with 300s (1) cores
% 2.67/1.35 % Starting new_bool_1 with 300s (1) cores
% 2.67/1.35 % Starting sh5l with 300s (1) cores
% 2.67/1.35 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 2534915 completed with status 0
% 2.67/1.35 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 2.67/1.35 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.67/1.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.67/1.35 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.67/1.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.67/1.35 % No SInE strategy applied
% 2.67/1.35 % Search class: FGUSF-FFMM32-SFFFFFNN
% 2.67/1.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.67/1.35 % Starting SubtermCWHack with 136s (1) cores
% 2.67/1.35 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.67/1.35 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.67/1.35 % Starting new_bool_3 with 136s (1) cores
% 2.67/1.35 % Starting new_bool_1 with 136s (1) cores
% 2.67/1.35 % G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2534921 completed with status 0
% 2.67/1.35 % Result found by G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 2.67/1.35 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.67/1.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.67/1.35 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.67/1.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.67/1.35 % No SInE strategy applied
% 2.67/1.35 % Search class: FGUSF-FFMM32-SFFFFFNN
% 2.67/1.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.67/1.35 % Starting SubtermCWHack with 136s (1) cores
% 2.67/1.35 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.67/1.35 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.67/1.35 % Preprocessing time : 0.003 s
% 2.67/1.35 % Presaturation interreduction done
% 2.67/1.35
% 2.67/1.35 % Proof found!
% 2.67/1.35 % SZS status Theorem
% 2.67/1.35 % SZS output start CNFRefutation
% See solution above
% 2.67/1.35 % Parsed axioms : 33
% 2.67/1.35 % Removed by relevancy pruning/SinE : 0
% 2.67/1.35 % Initial clauses : 77
% 2.67/1.35 % Removed in clause preprocessing : 2
% 2.67/1.35 % Initial clauses in saturation : 75
% 2.67/1.35 % Processed clauses : 1966
% 2.67/1.35 % ...of these trivial : 57
% 2.67/1.35 % ...subsumed : 1095
% 2.67/1.35 % ...remaining for further processing : 814
% 2.67/1.35 % Other redundant clauses eliminated : 10
% 2.67/1.35 % Clauses deleted for lack of memory : 0
% 2.67/1.35 % Backward-subsumed : 115
% 2.67/1.35 % Backward-rewritten : 50
% 2.67/1.35 % Generated clauses : 9241
% 2.67/1.35 % ...of the previous two non-redundant : 7863
% 2.67/1.35 % ...aggressively subsumed : 0
% 2.67/1.35 % Contextual simplify-reflections : 38
% 2.67/1.35 % Paramodulations : 9232
% 2.67/1.35 % Factorizations : 0
% 2.67/1.35 % NegExts : 0
% 2.67/1.35 % Equation resolutions : 10
% 2.67/1.35 % Disequality decompositions : 0
% 2.67/1.35 % Total rewrite steps : 8009
% 2.67/1.35 % ...of those cached : 7891
% 2.67/1.35 % Propositional unsat checks : 0
% 2.67/1.35 % Propositional check models : 0
% 2.67/1.35 % Propositional check unsatisfiable : 0
% 2.67/1.35 % Propositional clauses : 0
% 2.67/1.35 % Propositional clauses after purity: 0
% 2.67/1.35 % Propositional unsat core size : 0
% 2.67/1.35 % Propositional preprocessing time : 0.000
% 2.67/1.35 % Propositional encoding time : 0.000
% 2.67/1.35 % Propositional solver time : 0.000
% 2.67/1.35 % Success case prop preproc time : 0.000
% 2.67/1.35 % Success case prop encoding time : 0.000
% 2.67/1.35 % Success case prop solver time : 0.000
% 2.67/1.35 % Current number of processed clauses : 565
% 2.67/1.35 % Positive orientable unit clauses : 119
% 2.67/1.35 % Positive unorientable unit clauses: 0
% 2.67/1.35 % Negative unit clauses : 19
% 2.67/1.35 % Non-unit-clauses : 427
% 2.67/1.35 % Current number of unprocessed clauses: 5942
% 2.67/1.35 % ...number of literals in the above : 25247
% 2.67/1.35 % Current number of archived formulas : 0
% 2.67/1.35 % Current number of archived clauses : 240
% 2.67/1.35 % Clause-clause subsumption calls (NU) : 78115
% 2.67/1.35 % Rec. Clause-clause subsumption calls : 17506
% 2.67/1.35 % Non-unit clause-clause subsumptions : 1028
% 2.67/1.35 % Unit Clause-clause subsumption calls : 3639
% 2.67/1.35 % Rewrite failures with RHS unbound : 0
% 2.67/1.35 % BW rewrite match attempts : 733
% 2.67/1.35 % BW rewrite match successes : 16
% 2.67/1.35 % Condensation attempts : 0
% 2.67/1.35 % Condensation successes : 0
% 2.67/1.35 % Termbank termtop insertions : 157697
% 2.67/1.35 % Search garbage collected termcells : 1209
% 2.67/1.35
% 2.67/1.35 % -------------------------------------------------
% 2.67/1.35 % User time : 0.368 s
% 2.67/1.35 % System time : 0.011 s
% 2.67/1.35 % Total time : 0.379 s
% 2.67/1.35 % Maximum resident set size: 3420 pages
% 2.67/1.35
% 2.67/1.35 % -------------------------------------------------
% 2.67/1.35 % User time : 1.647 s
% 2.67/1.35 % System time : 0.103 s
% 2.67/1.35 % Total time : 1.750 s
% 2.67/1.35 % Maximum resident set size: 4864 pages
% 2.67/1.35 % E exiting
%------------------------------------------------------------------------------