%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG096+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:05:19 PM UTC 2026
% Result : Theorem 81.21s 52.52s
% Output : CNFRefutation 81.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 28
% Syntax : Number of formulae : 296 ( 120 unt; 0 def)
% Number of atoms : 746 ( 212 equ)
% Maximal formula atoms : 52 ( 2 avg)
% Number of connectives : 802 ( 352 ~; 345 |; 71 &)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-4 aty)
% Number of variables : 276 ( 0 sgn 101 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__1205,hypothesis,
( aSet0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X1] :
( aElementOf0(X1,xJ)
=> ( ! [X2] :
( aElementOf0(X2,xJ)
=> aElementOf0(sdtpldt0(X1,X2),xJ) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__1294,hypothesis,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mAddInvr,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
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(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mDefMod,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aIdeal0(X3) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aElementOf0(sdtpldt0(X1,smndt0(X2)),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMod) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mMulMnOne,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMnOne) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mCancel,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCancel) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(m__1205_03,hypothesis,
! [X1] :
( aElement0(X1)
=> ( ? [X2,X3] :
( aElementOf0(X2,xI)
& aElementOf0(X3,xJ)
& sdtpldt0(X2,X3) = X1 )
& aElementOf0(X1,sdtpldt1(xI,xJ)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205_03) ).
fof(mUnNeZr,axiom,
sz10 != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnNeZr) ).
fof(mDefSSum,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ! [X3] :
( X3 = sdtpldt1(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ? [X5,X6] :
( aElementOf0(X5,X1)
& aElementOf0(X6,X2)
& sdtpldt0(X5,X6) = X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSSum) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__,conjecture,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1319) ).
fof(m__1217,hypothesis,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(mIdeSum,axiom,
! [X1,X2] :
( ( aIdeal0(X1)
& aIdeal0(X2) )
=> aIdeal0(sdtpldt1(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIdeSum) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(c_0_28,hypothesis,
! [X138,X139,X140,X141,X142,X143] :
( aSet0(xI)
& ( ~ aElementOf0(X139,xI)
| aElementOf0(sdtpldt0(X138,X139),xI)
| ~ aElementOf0(X138,xI) )
& ( ~ aElement0(X140)
| aElementOf0(sdtasdt0(X140,X138),xI)
| ~ aElementOf0(X138,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ( ~ aElementOf0(X142,xJ)
| aElementOf0(sdtpldt0(X141,X142),xJ)
| ~ aElementOf0(X141,xJ) )
& ( ~ aElement0(X143)
| aElementOf0(sdtasdt0(X143,X141),xJ)
| ~ aElementOf0(X141,xJ) )
& aIdeal0(xJ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1205])])])]) ).
fof(c_0_29,plain,
! [X95,X96] :
( ~ aSet0(X95)
| ~ aElementOf0(X96,X95)
| aElement0(X96) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_30,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xJ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,hypothesis,
aElementOf0(xb,xJ),
inference(split_conjunct,[status(thm)],[m__1294]) ).
fof(c_0_32,plain,
! [X92] :
( ( sdtasdt0(X92,sz00) = sz00
| ~ aElement0(X92) )
& ( sz00 = sdtasdt0(sz00,X92)
| ~ aElement0(X92) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
cnf(c_0_33,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,hypothesis,
aSet0(xJ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_35,plain,
! [X77,X78,X79] :
( ~ aElement0(X77)
| ~ aElement0(X78)
| ~ aElement0(X79)
| sdtpldt0(sdtpldt0(X77,X78),X79) = sdtpldt0(X77,sdtpldt0(X78,X79)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_36,plain,
! [X81] :
( ( sdtpldt0(X81,smndt0(X81)) = sz00
| ~ aElement0(X81) )
& ( sz00 = sdtpldt0(smndt0(X81),X81)
| ~ aElement0(X81) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).
fof(c_0_37,plain,
! [X70] :
( ~ aElement0(X70)
| aElement0(smndt0(X70)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
cnf(c_0_38,hypothesis,
( aElementOf0(sdtpldt0(X2,X1),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X2,xJ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,hypothesis,
( aElementOf0(sdtasdt0(X1,xb),xJ)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_42,hypothesis,
aElement0(xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_31]),c_0_34])]) ).
cnf(c_0_43,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,hypothesis,
aElementOf0(xa,xI),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_47,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_48,hypothesis,
( aElementOf0(sdtpldt0(xb,X1),xJ)
| ~ aElementOf0(X1,xJ) ),
inference(spm,[status(thm)],[c_0_38,c_0_31]) ).
cnf(c_0_49,hypothesis,
aElementOf0(sz00,xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42])]) ).
fof(c_0_50,plain,
! [X75,X76] :
( ~ aElement0(X75)
| ~ aElement0(X76)
| sdtpldt0(X75,X76) = sdtpldt0(X76,X75) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_51,plain,
! [X80] :
( ( sdtpldt0(X80,sz00) = X80
| ~ aElement0(X80) )
& ( X80 = sdtpldt0(sz00,X80)
| ~ aElement0(X80) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_52,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_53,hypothesis,
sdtpldt0(xa,xb) = sz10,
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_54,hypothesis,
aElement0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_46]),c_0_47])]) ).
fof(c_0_55,plain,
! [X135,X136,X137] :
( ( ~ sdteqdtlpzmzozddtrp0(X135,X136,X137)
| aElementOf0(sdtpldt0(X135,smndt0(X136)),X137)
| ~ aElement0(X135)
| ~ aElement0(X136)
| ~ aIdeal0(X137) )
& ( ~ aElementOf0(sdtpldt0(X135,smndt0(X136)),X137)
| sdteqdtlpzmzozddtrp0(X135,X136,X137)
| ~ aElement0(X135)
| ~ aElement0(X136)
| ~ aIdeal0(X137) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefMod])])]) ).
cnf(c_0_56,hypothesis,
aElementOf0(sdtpldt0(xb,sz00),xJ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,hypothesis,
sdtpldt0(sz00,xb) = sdtpldt0(smndt0(xa),sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_42]),c_0_54])]) ).
cnf(c_0_60,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,hypothesis,
aElementOf0(sdtpldt0(sz00,xb),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_41]),c_0_42])]) ).
cnf(c_0_62,hypothesis,
xb = sdtpldt0(smndt0(xa),sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_42])]) ).
cnf(c_0_63,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aIdeal0(X3)
| ~ aElementOf0(sdtpldt0(smndt0(X2),X1),X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_57]),c_0_45]) ).
cnf(c_0_64,hypothesis,
aElementOf0(sdtpldt0(smndt0(xa),sz10),xJ),
inference(rw,[status(thm)],[c_0_61,c_0_59]) ).
cnf(c_0_65,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_66,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_67,hypothesis,
sdtpldt0(xa,sdtpldt0(smndt0(xa),sz10)) = sz10,
inference(rw,[status(thm)],[c_0_53,c_0_62]) ).
cnf(c_0_68,plain,
( aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_69,hypothesis,
sdteqdtlpzmzozddtrp0(sz10,xa,xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_54]),c_0_66])]) ).
cnf(c_0_70,hypothesis,
( sdtpldt0(xa,sdtpldt0(sz10,smndt0(xa))) = sz10
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_57]),c_0_66])]) ).
cnf(c_0_71,hypothesis,
aElementOf0(sdtpldt0(sz10,smndt0(xa)),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_65]),c_0_54]),c_0_66])]) ).
fof(c_0_72,plain,
! [X91] :
( ( sdtasdt0(smndt0(sz10),X91) = smndt0(X91)
| ~ aElement0(X91) )
& ( smndt0(X91) = sdtasdt0(X91,smndt0(sz10))
| ~ aElement0(X91) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])]) ).
cnf(c_0_73,hypothesis,
sdtpldt0(xa,sdtpldt0(sz10,smndt0(xa))) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_45]),c_0_54])]) ).
cnf(c_0_74,hypothesis,
aElement0(sdtpldt0(sz10,smndt0(xa))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_71]),c_0_34])]) ).
cnf(c_0_75,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
fof(c_0_76,plain,
! [X87] :
( ( sdtasdt0(X87,sz10) = X87
| ~ aElement0(X87) )
& ( X87 = sdtasdt0(sz10,X87)
| ~ aElement0(X87) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).
cnf(c_0_77,hypothesis,
sdtpldt0(sz00,sdtpldt0(smndt0(xa),sz10)) = sdtpldt0(smndt0(xa),sz10),
inference(rw,[status(thm)],[c_0_59,c_0_62]) ).
cnf(c_0_78,hypothesis,
sdtpldt0(smndt0(xa),sz10) = sdtpldt0(sz00,sdtpldt0(sz10,smndt0(xa))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_73]),c_0_74]),c_0_54])]) ).
fof(c_0_79,plain,
! [X71,X72] :
( ~ aElement0(X71)
| ~ aElement0(X72)
| aElement0(sdtpldt0(X71,X72)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_80,plain,
( sdtpldt0(sdtasdt0(X1,smndt0(sz10)),X1) = sz00
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_75]) ).
cnf(c_0_81,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_82,hypothesis,
( sdtpldt0(xa,sdtpldt0(xb,X1)) = sdtpldt0(sz10,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_53]),c_0_42]),c_0_54])]) ).
cnf(c_0_83,hypothesis,
sdtpldt0(sz00,sdtpldt0(sz00,sdtpldt0(sz10,smndt0(xa)))) = sdtpldt0(sz00,sdtpldt0(sz10,smndt0(xa))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78]),c_0_78]) ).
cnf(c_0_84,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_85,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_86,plain,
( sdtpldt0(smndt0(sz10),sz10) = sz00
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_66])]) ).
cnf(c_0_87,hypothesis,
( sdtpldt0(xa,sdtpldt0(sdtpldt0(sz00,sdtpldt0(sz10,smndt0(xa))),X1)) = sdtpldt0(sz10,X1)
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_62]),c_0_78]) ).
cnf(c_0_88,hypothesis,
sdtpldt0(sz00,sdtpldt0(sz10,smndt0(xa))) = sdtpldt0(sz10,smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_58]),c_0_74])]) ).
cnf(c_0_89,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_43]),c_0_41])]),c_0_85]) ).
cnf(c_0_90,plain,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_45]),c_0_66])]) ).
cnf(c_0_91,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_43]),c_0_85]) ).
cnf(c_0_92,hypothesis,
( sdtpldt0(xa,sdtpldt0(sdtpldt0(sz10,smndt0(xa)),X1)) = sdtpldt0(sz10,X1)
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_93,hypothesis,
sdtpldt0(sz10,sz00) = sz10,
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_89,c_0_82]),c_0_53]),c_0_42]),c_0_54]),c_0_41])]) ).
cnf(c_0_94,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(X2,X3)))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_43]),c_0_85]) ).
fof(c_0_95,plain,
! [X93,X94] :
( ~ aElement0(X93)
| ~ aElement0(X94)
| sdtasdt0(X93,X94) != sz00
| X93 = sz00
| X94 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCancel])]) ).
fof(c_0_96,plain,
! [X88,X89,X90] :
( ( sdtasdt0(X88,sdtpldt0(X89,X90)) = sdtpldt0(sdtasdt0(X88,X89),sdtasdt0(X88,X90))
| ~ aElement0(X88)
| ~ aElement0(X89)
| ~ aElement0(X90) )
& ( sdtasdt0(sdtpldt0(X89,X90),X88) = sdtpldt0(sdtasdt0(X89,X88),sdtasdt0(X90,X88))
| ~ aElement0(X88)
| ~ aElement0(X89)
| ~ aElement0(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_97,plain,
( sdtpldt0(sz10,smndt0(sz10)) = sz00
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_90]),c_0_66])]) ).
cnf(c_0_98,hypothesis,
( sdtpldt0(sz10,X1) = sdtpldt0(X1,sz10)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_73]),c_0_74]),c_0_54])]) ).
cnf(c_0_99,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_93]),c_0_41]),c_0_66])]) ).
cnf(c_0_100,hypothesis,
( aElement0(sdtpldt0(X1,sz10))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_53]),c_0_42]),c_0_54])]) ).
cnf(c_0_101,plain,
( X1 = sz00
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_102,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
fof(c_0_103,hypothesis,
! [X144] :
( ( aElementOf0(esk12_1(X144),xI)
| ~ aElement0(X144) )
& ( aElementOf0(esk13_1(X144),xJ)
| ~ aElement0(X144) )
& ( sdtpldt0(esk12_1(X144),esk13_1(X144)) = X144
| ~ aElement0(X144) )
& ( aElementOf0(X144,sdtpldt1(xI,xJ))
| ~ aElement0(X144) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1205_03])])])]) ).
cnf(c_0_104,plain,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_45]),c_0_66])]) ).
cnf(c_0_105,hypothesis,
( sdtpldt0(smndt0(X1),sdtpldt0(sz10,X1)) = sz10
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_98]),c_0_99]),c_0_66])]) ).
cnf(c_0_106,hypothesis,
( aElement0(sdtpldt0(sz10,X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_57]),c_0_66])]) ).
cnf(c_0_107,plain,
( sdtpldt0(X1,X2) = sz00
| X3 = sz00
| sdtpldt0(sdtasdt0(X3,X1),sdtasdt0(X3,X2)) != sz00
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_85]) ).
cnf(c_0_108,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mUnNeZr]) ).
cnf(c_0_109,hypothesis,
( aElementOf0(X1,sdtpldt1(xI,xJ))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_110,plain,
( sdtpldt0(smndt0(sz10),sz00) = sdtpldt0(sz00,smndt0(sz10))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_104]),c_0_66])]) ).
cnf(c_0_111,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_112,hypothesis,
sdtpldt0(smndt0(sz10),sdtpldt0(sz10,sz10)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_98]),c_0_66])]) ).
cnf(c_0_113,hypothesis,
aElement0(sdtpldt0(sz10,sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_98]),c_0_66])]) ).
cnf(c_0_114,plain,
( sdtpldt0(X1,X2) = sz00
| sdtpldt0(sdtasdt0(sz10,X1),X2) != sz00
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_81]),c_0_66])]),c_0_108]) ).
cnf(c_0_115,hypothesis,
( aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_109,c_0_85]) ).
cnf(c_0_116,plain,
sdtpldt0(smndt0(sz10),sz00) = sdtpldt0(sz00,smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_45]),c_0_66])]) ).
cnf(c_0_117,plain,
( sdtpldt0(sdtasdt0(smndt0(sz10),X1),X1) = sz00
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_111]) ).
cnf(c_0_118,hypothesis,
( sdtpldt0(sdtpldt0(sz10,sz10),smndt0(sz10)) = sz10
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_112]),c_0_113])]) ).
cnf(c_0_119,hypothesis,
( sdtpldt0(X1,sz10) = sz00
| sdtpldt0(sz10,sdtasdt0(sz10,X1)) != sz00
| ~ aElement0(sdtasdt0(sz10,X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_98]),c_0_66])]) ).
cnf(c_0_120,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_121,hypothesis,
( aElementOf0(sdtpldt0(sz00,smndt0(sz10)),sdtpldt1(xI,xJ))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_41])]) ).
fof(c_0_122,plain,
! [X101,X102,X103,X104,X107,X108,X109,X110,X112,X113] :
( ( aSet0(X103)
| X103 != sdtpldt1(X101,X102)
| ~ aSet0(X101)
| ~ aSet0(X102) )
& ( aElementOf0(esk3_4(X101,X102,X103,X104),X101)
| ~ aElementOf0(X104,X103)
| X103 != sdtpldt1(X101,X102)
| ~ aSet0(X101)
| ~ aSet0(X102) )
& ( aElementOf0(esk4_4(X101,X102,X103,X104),X102)
| ~ aElementOf0(X104,X103)
| X103 != sdtpldt1(X101,X102)
| ~ aSet0(X101)
| ~ aSet0(X102) )
& ( sdtpldt0(esk3_4(X101,X102,X103,X104),esk4_4(X101,X102,X103,X104)) = X104
| ~ aElementOf0(X104,X103)
| X103 != sdtpldt1(X101,X102)
| ~ aSet0(X101)
| ~ aSet0(X102) )
& ( ~ aElementOf0(X108,X101)
| ~ aElementOf0(X109,X102)
| sdtpldt0(X108,X109) != X107
| aElementOf0(X107,X103)
| X103 != sdtpldt1(X101,X102)
| ~ aSet0(X101)
| ~ aSet0(X102) )
& ( ~ aElementOf0(esk5_3(X101,X102,X110),X110)
| ~ aElementOf0(X112,X101)
| ~ aElementOf0(X113,X102)
| sdtpldt0(X112,X113) != esk5_3(X101,X102,X110)
| ~ aSet0(X110)
| X110 = sdtpldt1(X101,X102)
| ~ aSet0(X101)
| ~ aSet0(X102) )
& ( aElementOf0(esk6_3(X101,X102,X110),X101)
| aElementOf0(esk5_3(X101,X102,X110),X110)
| ~ aSet0(X110)
| X110 = sdtpldt1(X101,X102)
| ~ aSet0(X101)
| ~ aSet0(X102) )
& ( aElementOf0(esk7_3(X101,X102,X110),X102)
| aElementOf0(esk5_3(X101,X102,X110),X110)
| ~ aSet0(X110)
| X110 = sdtpldt1(X101,X102)
| ~ aSet0(X101)
| ~ aSet0(X102) )
& ( sdtpldt0(esk6_3(X101,X102,X110),esk7_3(X101,X102,X110)) = esk5_3(X101,X102,X110)
| aElementOf0(esk5_3(X101,X102,X110),X110)
| ~ aSet0(X110)
| X110 = sdtpldt1(X101,X102)
| ~ aSet0(X101)
| ~ aSet0(X102) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSSum])])])])])]) ).
cnf(c_0_123,plain,
( sdtasdt0(smndt0(sz10),sz00) = sz00
| ~ aElement0(sdtasdt0(smndt0(sz10),sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_117]),c_0_41])]) ).
cnf(c_0_124,plain,
( aElement0(sdtasdt0(smndt0(sz10),X1))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_111]) ).
cnf(c_0_125,hypothesis,
sdtpldt0(sdtpldt0(sz10,sz10),smndt0(sz10)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_45]),c_0_66])]) ).
cnf(c_0_126,hypothesis,
( sdtpldt0(X1,sz10) = sz00
| sdtpldt0(sz10,X1) != sz00
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_119,c_0_81]) ).
cnf(c_0_127,plain,
( sdtpldt0(X1,sdtasdt0(X1,smndt0(sz10))) = sz00
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_75]) ).
cnf(c_0_128,hypothesis,
aElementOf0(sdtpldt0(sz00,smndt0(sz10)),sdtpldt1(xI,xJ)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_45]),c_0_66])]) ).
cnf(c_0_129,plain,
( aSet0(X1)
| X1 != sdtpldt1(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_130,plain,
( sdtpldt0(sdtasdt0(X1,sz00),sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_58]),c_0_41])]) ).
cnf(c_0_131,plain,
sdtasdt0(smndt0(sz10),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_41])]) ).
cnf(c_0_132,hypothesis,
( sdtpldt0(smndt0(sdtpldt0(sz10,sz10)),sz10) = sdtpldt0(sz00,smndt0(sz10))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_125]),c_0_113])]) ).
cnf(c_0_133,hypothesis,
( sdtpldt0(sdtasdt0(sz10,smndt0(sz10)),sz10) = sz00
| ~ aElement0(sdtasdt0(sz10,smndt0(sz10))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_66])]) ).
cnf(c_0_134,plain,
( aElement0(sdtasdt0(X1,smndt0(sz10)))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_75]) ).
cnf(c_0_135,hypothesis,
( aElement0(sdtpldt0(sz00,smndt0(sz10)))
| ~ aSet0(sdtpldt1(xI,xJ)) ),
inference(spm,[status(thm)],[c_0_33,c_0_128]) ).
cnf(c_0_136,plain,
( aSet0(sdtpldt1(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_129]) ).
cnf(c_0_137,plain,
( sdtpldt0(sz00,smndt0(X1)) = smndt0(X1)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_111]),c_0_131]) ).
cnf(c_0_138,plain,
( sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_120]),c_0_45]) ).
cnf(c_0_139,hypothesis,
sdtpldt0(smndt0(sdtpldt0(sz10,sz10)),sz10) = sdtpldt0(sz00,smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_45]),c_0_66])]) ).
cnf(c_0_140,hypothesis,
sdtpldt0(sdtasdt0(sz10,smndt0(sz10)),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_66])]) ).
fof(c_0_141,plain,
! [X73,X74] :
( ~ aElement0(X73)
| ~ aElement0(X74)
| aElement0(sdtasdt0(X73,X74)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_142,hypothesis,
aElement0(sdtpldt0(sz00,smndt0(sz10))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_34]),c_0_47])]) ).
cnf(c_0_143,plain,
( sdtpldt0(sz00,smndt0(X1)) = smndt0(X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_45]),c_0_66])]) ).
cnf(c_0_144,hypothesis,
sdtpldt0(sdtpldt0(sz10,sz10),sdtpldt0(sz00,smndt0(sz10))) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_99]),c_0_66]),c_0_113])]) ).
cnf(c_0_145,hypothesis,
( sdtpldt0(sz10,sdtasdt0(sz10,smndt0(sz10))) = sz00
| ~ aElement0(sdtasdt0(sz10,smndt0(sz10))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_140]),c_0_66])]) ).
cnf(c_0_146,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_147,hypothesis,
aElement0(smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_66])]) ).
cnf(c_0_148,hypothesis,
sdtpldt0(sz00,sdtpldt0(sz00,smndt0(sz10))) = sdtpldt0(sz00,smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_144]),c_0_139]),c_0_142]),c_0_113])]) ).
cnf(c_0_149,hypothesis,
sdtpldt0(sz10,sdtasdt0(sz10,smndt0(sz10))) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147]),c_0_66])]) ).
cnf(c_0_150,hypothesis,
sdtpldt0(sz00,smndt0(sz10)) = smndt0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_143]),c_0_66])]) ).
cnf(c_0_151,plain,
( sdtpldt0(smndt0(smndt0(sz10)),sz00) = sz10
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_90]),c_0_99]),c_0_66])]) ).
cnf(c_0_152,plain,
( smndt0(sz00) = sz00
| ~ aElement0(smndt0(sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_44]),c_0_41])]) ).
cnf(c_0_153,hypothesis,
( sdtpldt0(sz00,sdtasdt0(sz10,smndt0(sz10))) = smndt0(sz10)
| ~ aElement0(sdtasdt0(sz10,smndt0(sz10))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_149]),c_0_116]),c_0_150]),c_0_66])]) ).
cnf(c_0_154,plain,
sdtpldt0(smndt0(smndt0(sz10)),sz00) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_45]),c_0_66])]) ).
cnf(c_0_155,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_45]),c_0_41])]) ).
cnf(c_0_156,hypothesis,
sdtpldt0(sz00,sdtasdt0(sz10,smndt0(sz10))) = smndt0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_146]),c_0_147]),c_0_66])]) ).
cnf(c_0_157,plain,
( smndt0(smndt0(sz10)) = sz10
| ~ aElement0(smndt0(smndt0(sz10))) ),
inference(spm,[status(thm)],[c_0_84,c_0_154]) ).
cnf(c_0_158,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_155]),c_0_41])]) ).
cnf(c_0_159,hypothesis,
( sdtasdt0(sz10,smndt0(sz10)) = smndt0(sz10)
| ~ aElement0(sdtasdt0(sz10,smndt0(sz10))) ),
inference(spm,[status(thm)],[c_0_58,c_0_156]) ).
cnf(c_0_160,plain,
( smndt0(smndt0(sz10)) = sz10
| ~ aElement0(smndt0(sz10)) ),
inference(spm,[status(thm)],[c_0_157,c_0_45]) ).
cnf(c_0_161,plain,
( sdtpldt0(sdtasdt0(sz10,X1),sdtasdt0(sz10,X2)) = sdtpldt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_102]),c_0_66])]),c_0_85]) ).
cnf(c_0_162,plain,
( sdtpldt0(sdtasdt0(X1,sz00),sdtasdt0(X1,sz00)) = sdtasdt0(X1,sz00)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_158]),c_0_41])]) ).
cnf(c_0_163,plain,
( sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,sz00)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_120]),c_0_45]) ).
cnf(c_0_164,hypothesis,
sdtasdt0(sz10,smndt0(sz10)) = smndt0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_146]),c_0_147]),c_0_66])]) ).
cnf(c_0_165,plain,
smndt0(smndt0(sz10)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_45]),c_0_66])]) ).
cnf(c_0_166,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_158]),c_0_41]),c_0_66])]) ).
cnf(c_0_167,hypothesis,
sdtpldt0(smndt0(sz10),sdtasdt0(sz10,sz10)) = sz00,
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_163,c_0_164]),c_0_165]),c_0_166]),c_0_147]),c_0_66])]) ).
cnf(c_0_168,hypothesis,
( sdtpldt0(sz00,sdtasdt0(sz10,sz10)) = sz10
| ~ aElement0(sdtasdt0(sz10,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_167]),c_0_165]),c_0_93]),c_0_147])]) ).
cnf(c_0_169,hypothesis,
sdtpldt0(sz00,sdtasdt0(sz10,sz10)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_146]),c_0_66])]) ).
fof(c_0_170,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_171,plain,
! [X84,X85,X86] :
( ~ aElement0(X84)
| ~ aElement0(X85)
| ~ aElement0(X86)
| sdtasdt0(sdtasdt0(X84,X85),X86) = sdtasdt0(X84,sdtasdt0(X85,X86)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_172,hypothesis,
( sdtasdt0(sz10,sz10) = sz10
| ~ aElement0(sdtasdt0(sz10,sz10)) ),
inference(spm,[status(thm)],[c_0_58,c_0_169]) ).
cnf(c_0_173,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_174,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(split_conjunct,[status(thm)],[m__1319]) ).
cnf(c_0_175,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_176,hypothesis,
sdtasdt0(sz10,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_146]),c_0_66])]) ).
cnf(c_0_177,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI),
inference(rw,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_178,hypothesis,
( sdtasdt0(sz10,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_66])]) ).
cnf(c_0_179,plain,
( sdtasdt0(sz10,X1) = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_130]),c_0_41]),c_0_66])]) ).
cnf(c_0_180,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),xI)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(smndt0(xx)) ),
inference(spm,[status(thm)],[c_0_177,c_0_43]) ).
cnf(c_0_181,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_182,hypothesis,
( sdtasdt0(sz10,sdtpldt0(sz00,X1)) = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_183,plain,
( aElementOf0(esk4_4(X1,X2,X3,X4),X2)
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_184,plain,
( aElementOf0(esk3_4(X1,X2,X3,X4),X1)
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_185,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),xI)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_45]),c_0_181])]) ).
cnf(c_0_186,hypothesis,
( sdtasdt0(sz10,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_57]),c_0_41])]) ).
cnf(c_0_187,plain,
( sdtpldt0(esk3_4(X1,X2,X3,X4),esk4_4(X1,X2,X3,X4)) = X4
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_188,plain,
( aElementOf0(esk4_4(X1,X2,sdtpldt1(X1,X2),X3),X2)
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_183]) ).
cnf(c_0_189,hypothesis,
aElementOf0(xx,sdtpldt1(xI,xJ)),
inference(spm,[status(thm)],[c_0_109,c_0_181]) ).
cnf(c_0_190,plain,
( aElementOf0(esk3_4(X1,X2,sdtpldt1(X1,X2),X3),X1)
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_184]) ).
cnf(c_0_191,plain,
( sdtpldt0(smndt0(smndt0(X1)),sz00) = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_44]),c_0_45]) ).
cnf(c_0_192,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),xI)
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_146]),c_0_42]),c_0_181])]) ).
cnf(c_0_193,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_194,hypothesis,
( sdtpldt0(sdtasdt0(sz10,X1),sz00) = sdtpldt0(X1,sz00)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_186]),c_0_166]),c_0_41]),c_0_66])]) ).
cnf(c_0_195,plain,
( sdtpldt0(sz00,sdtpldt0(sz00,X1)) = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_158]),c_0_41])]) ).
cnf(c_0_196,plain,
( sdtpldt0(esk3_4(X1,X2,sdtpldt1(X1,X2),X3),esk4_4(X1,X2,sdtpldt1(X1,X2),X3)) = X3
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_187]) ).
cnf(c_0_197,hypothesis,
aElementOf0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),xx),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_34]),c_0_47])]) ).
cnf(c_0_198,hypothesis,
aElementOf0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xx),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_189]),c_0_34]),c_0_47])]) ).
cnf(c_0_199,plain,
( sdtpldt0(sdtasdt0(smndt0(sz10),X1),sdtasdt0(smndt0(sz10),X2)) = smndt0(sdtpldt0(X1,X2))
| ~ aElement0(smndt0(sz10))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_102]),c_0_85]) ).
cnf(c_0_200,plain,
( smndt0(smndt0(X1)) = sdtpldt0(sz00,X1)
| ~ aElement0(smndt0(smndt0(X1)))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_191]) ).
cnf(c_0_201,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_146]),c_0_54]),c_0_193])]) ).
cnf(c_0_202,hypothesis,
( sdtasdt0(sz10,X1) = sdtpldt0(X1,sz00)
| ~ aElement0(sdtasdt0(sz10,X1))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_194]) ).
cnf(c_0_203,hypothesis,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(spm,[status(thm)],[c_0_109,c_0_193]) ).
cnf(c_0_204,plain,
( sdtpldt0(sz00,X1) = sdtpldt0(X1,sz00)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_195]),c_0_158]),c_0_41])]) ).
cnf(c_0_205,plain,
( sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_58]),c_0_41])]) ).
cnf(c_0_206,hypothesis,
sdtpldt0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xx),esk4_4(xI,xJ,sdtpldt1(xI,xJ),xx)) = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_189]),c_0_34]),c_0_47])]) ).
cnf(c_0_207,hypothesis,
aElement0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_197]),c_0_34])]) ).
cnf(c_0_208,hypothesis,
aElement0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_198]),c_0_47])]) ).
cnf(c_0_209,plain,
( aElement0(sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
| ~ aElement0(X1)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_102]),c_0_85]) ).
cnf(c_0_210,plain,
( sdtpldt0(sdtasdt0(smndt0(sz10),X1),sdtasdt0(smndt0(sz10),X2)) = smndt0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_199,c_0_147])]) ).
cnf(c_0_211,plain,
( smndt0(smndt0(X1)) = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_45]),c_0_45]) ).
cnf(c_0_212,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,sdtpldt0(smndt0(xa),sz10)),smndt0(xx))),xI),
inference(rw,[status(thm)],[c_0_201,c_0_62]) ).
cnf(c_0_213,hypothesis,
( sdtasdt0(sz10,X1) = sdtpldt0(X1,sz00)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_146]),c_0_66])]) ).
cnf(c_0_214,hypothesis,
aElementOf0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),xy),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_203]),c_0_34]),c_0_47])]) ).
cnf(c_0_215,hypothesis,
aElementOf0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xy),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_203]),c_0_34]),c_0_47])]) ).
cnf(c_0_216,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(sz00,X1)) = sz00
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_204]),c_0_158]),c_0_41])]) ).
cnf(c_0_217,hypothesis,
sdtpldt0(sz00,xx) = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_207]),c_0_208])]) ).
cnf(c_0_218,plain,
( aElement0(smndt0(sdtpldt0(X1,X2)))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_147])]) ).
cnf(c_0_219,plain,
( smndt0(sdtpldt0(sz00,X1)) = sdtpldt0(sz00,smndt0(X1))
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_211]),c_0_45]) ).
fof(c_0_220,plain,
! [X123,X124,X125,X126,X127] :
( ( aSet0(X123)
| ~ aIdeal0(X123) )
& ( ~ aElementOf0(X125,X123)
| aElementOf0(sdtpldt0(X124,X125),X123)
| ~ aElementOf0(X124,X123)
| ~ aIdeal0(X123) )
& ( ~ aElement0(X126)
| aElementOf0(sdtasdt0(X126,X124),X123)
| ~ aElementOf0(X124,X123)
| ~ aIdeal0(X123) )
& ( aElementOf0(esk9_1(X127),X127)
| ~ aSet0(X127)
| aIdeal0(X127) )
& ( aElement0(esk11_1(X127))
| aElementOf0(esk10_1(X127),X127)
| ~ aSet0(X127)
| aIdeal0(X127) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X127),esk9_1(X127)),X127)
| aElementOf0(esk10_1(X127),X127)
| ~ aSet0(X127)
| aIdeal0(X127) )
& ( aElement0(esk11_1(X127))
| ~ aElementOf0(sdtpldt0(esk9_1(X127),esk10_1(X127)),X127)
| ~ aSet0(X127)
| aIdeal0(X127) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X127),esk9_1(X127)),X127)
| ~ aElementOf0(sdtpldt0(esk9_1(X127),esk10_1(X127)),X127)
| ~ aSet0(X127)
| aIdeal0(X127) ) ),
inference(distribute,[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_221,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtpldt0(sdtasdt0(xx,smndt0(xa)),sdtasdt0(xx,sz10)),smndt0(xx))),xI)
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_102]),c_0_66]),c_0_181])]) ).
cnf(c_0_222,hypothesis,
( sdtpldt0(sdtpldt0(X1,sz00),sz00) = sdtpldt0(X1,sz00)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_194,c_0_213]) ).
cnf(c_0_223,hypothesis,
sdtpldt0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xy),esk4_4(xI,xJ,sdtpldt1(xI,xJ),xy)) = xy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_203]),c_0_34]),c_0_47])]) ).
cnf(c_0_224,hypothesis,
aElement0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_214]),c_0_34])]) ).
cnf(c_0_225,hypothesis,
aElement0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_215]),c_0_47])]) ).
cnf(c_0_226,plain,
( sdtasdt0(smndt0(sz10),smndt0(sz10)) = sz10
| ~ aElement0(smndt0(sz10)) ),
inference(spm,[status(thm)],[c_0_75,c_0_165]) ).
cnf(c_0_227,hypothesis,
sdtpldt0(smndt0(xx),xx) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_217]),c_0_181])]) ).
cnf(c_0_228,hypothesis,
aElement0(smndt0(xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_206]),c_0_207]),c_0_208])]) ).
cnf(c_0_229,hypothesis,
sdtpldt0(sz00,smndt0(xx)) = smndt0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_217]),c_0_181])]) ).
cnf(c_0_230,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_220]) ).
fof(c_0_231,plain,
! [X131,X132] :
( ~ aIdeal0(X131)
| ~ aIdeal0(X132)
| aIdeal0(sdtpldt1(X131,X132)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIdeSum])]) ).
cnf(c_0_232,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtpldt0(sdtasdt0(xx,smndt0(xa)),sdtasdt0(xx,sz10)),smndt0(xx))),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_45]),c_0_54])]) ).
cnf(c_0_233,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_234,hypothesis,
( sdtpldt0(sdtpldt0(sz00,X1),sz00) = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_57]),c_0_41])]) ).
cnf(c_0_235,hypothesis,
sdtpldt0(sz00,xy) = xy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_223]),c_0_224]),c_0_225])]) ).
cnf(c_0_236,plain,
( smndt0(sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtasdt0(X2,smndt0(sz10)))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_175]),c_0_147])]),c_0_146]) ).
cnf(c_0_237,plain,
sdtasdt0(smndt0(sz10),smndt0(sz10)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_45]),c_0_66])]) ).
cnf(c_0_238,hypothesis,
sdtpldt0(smndt0(smndt0(xx)),sz00) = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_227]),c_0_217]),c_0_181]),c_0_228])]) ).
cnf(c_0_239,hypothesis,
aElement0(smndt0(smndt0(xx))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_229]),c_0_228]),c_0_41])]) ).
cnf(c_0_240,hypothesis,
( aElementOf0(sdtasdt0(X1,xx),sdtpldt1(xI,xJ))
| ~ aIdeal0(sdtpldt1(xI,xJ))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_230,c_0_189]) ).
cnf(c_0_241,plain,
( aIdeal0(sdtpldt1(X1,X2))
| ~ aIdeal0(X1)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_242,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_243,plain,
! [X82,X83] :
( ~ aElement0(X82)
| ~ aElement0(X83)
| sdtasdt0(X82,X83) = sdtasdt0(X83,X82) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_244,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtpldt0(sdtasdt0(xx,smndt0(xa)),xx),smndt0(xx))),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_233]),c_0_181])]) ).
cnf(c_0_245,plain,
( smndt0(sdtpldt0(X1,sz00)) = sdtpldt0(sz00,smndt0(X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_57]),c_0_41])]) ).
cnf(c_0_246,hypothesis,
sdtpldt0(xy,sz00) = xy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_235]),c_0_193])]) ).
cnf(c_0_247,plain,
( smndt0(smndt0(X1)) = sdtasdt0(X1,sz10)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_75]),c_0_237]),c_0_147])]) ).
cnf(c_0_248,hypothesis,
smndt0(smndt0(xx)) = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_238]),c_0_239])]) ).
cnf(c_0_249,hypothesis,
( aElementOf0(sdtasdt0(X1,xx),sdtpldt1(xI,xJ))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_241]),c_0_65]),c_0_242])]) ).
cnf(c_0_250,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_251,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,smndt0(xa)),sdtpldt0(xx,smndt0(xx)))),xI)
| ~ aElement0(sdtasdt0(xx,smndt0(xa)))
| ~ aElement0(smndt0(xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_43]),c_0_181])]) ).
cnf(c_0_252,hypothesis,
sdtpldt0(smndt0(xy),xy) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_235]),c_0_193])]) ).
cnf(c_0_253,hypothesis,
aElement0(smndt0(xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_223]),c_0_224]),c_0_225])]) ).
cnf(c_0_254,hypothesis,
sdtpldt0(sz00,smndt0(xy)) = smndt0(xy),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_246]),c_0_193])]) ).
cnf(c_0_255,hypothesis,
sdtasdt0(xx,sz10) = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_248]),c_0_181])]) ).
cnf(c_0_256,hypothesis,
( aElementOf0(sdtasdt0(xx,X1),sdtpldt1(xI,xJ))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_250]),c_0_181])]) ).
cnf(c_0_257,plain,
( sdtasdt0(smndt0(sz10),X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_111]) ).
cnf(c_0_258,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,smndt0(xa)),sdtpldt0(xx,smndt0(xx)))),xI)
| ~ aElement0(sdtasdt0(xx,smndt0(xa))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_45]),c_0_181])]) ).
cnf(c_0_259,hypothesis,
sdtpldt0(smndt0(smndt0(xy)),sz00) = xy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_252]),c_0_235]),c_0_193]),c_0_253])]) ).
cnf(c_0_260,hypothesis,
aElement0(smndt0(smndt0(xy))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_254]),c_0_253]),c_0_41])]) ).
cnf(c_0_261,hypothesis,
smndt0(xx) = sdtasdt0(xx,smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_255]),c_0_164]),c_0_66]),c_0_181])]) ).
cnf(c_0_262,hypothesis,
aElementOf0(sdtasdt0(smndt0(sz10),xx),sdtpldt1(xI,xJ)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_257]),c_0_147]),c_0_181])]) ).
cnf(c_0_263,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,smndt0(xa)),sdtpldt0(xx,smndt0(xx)))),xI)
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_146]),c_0_181])]) ).
cnf(c_0_264,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_265,hypothesis,
smndt0(smndt0(xy)) = xy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_259]),c_0_260])]) ).
cnf(c_0_266,hypothesis,
smndt0(sdtasdt0(xx,smndt0(sz10))) = xx,
inference(rw,[status(thm)],[c_0_248,c_0_261]) ).
cnf(c_0_267,hypothesis,
( aElement0(sdtasdt0(smndt0(sz10),xx))
| ~ aSet0(sdtpldt1(xI,xJ)) ),
inference(spm,[status(thm)],[c_0_33,c_0_262]) ).
cnf(c_0_268,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,smndt0(xa)),sdtpldt0(xx,smndt0(xx)))),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_263,c_0_45]),c_0_54])]) ).
cnf(c_0_269,hypothesis,
( aElementOf0(sdtasdt0(X1,xa),xI)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_264,c_0_46]) ).
cnf(c_0_270,hypothesis,
sdtasdt0(xy,sz10) = xy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_265]),c_0_193])]) ).
cnf(c_0_271,hypothesis,
sdtasdt0(xx,smndt0(sz10)) = sdtpldt0(sz00,sdtasdt0(smndt0(sz10),xx)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_217]),c_0_131]),c_0_181]),c_0_41])]),c_0_261]) ).
cnf(c_0_272,plain,
( smndt0(smndt0(X1)) = X1
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_233,c_0_247]) ).
cnf(c_0_273,hypothesis,
smndt0(sdtasdt0(smndt0(sz10),xx)) = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_250]),c_0_147]),c_0_181])]) ).
cnf(c_0_274,hypothesis,
aElement0(sdtasdt0(smndt0(sz10),xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_136]),c_0_34]),c_0_47])]) ).
cnf(c_0_275,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,smndt0(xa)),sz00)),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_268,c_0_120]),c_0_181])]) ).
cnf(c_0_276,hypothesis,
( aElementOf0(sdtasdt0(X1,sdtasdt0(X2,xa)),xI)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_269]),c_0_242])]) ).
cnf(c_0_277,plain,
( sdtasdt0(smndt0(X1),X2) = sdtasdt0(smndt0(sz10),sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_111]),c_0_147])]) ).
cnf(c_0_278,hypothesis,
smndt0(xy) = sdtasdt0(xy,smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_270]),c_0_164]),c_0_66]),c_0_193])]) ).
cnf(c_0_279,hypothesis,
smndt0(xx) = sdtpldt0(sz00,sdtasdt0(smndt0(sz10),xx)),
inference(rw,[status(thm)],[c_0_261,c_0_271]) ).
cnf(c_0_280,hypothesis,
sdtpldt0(sz00,sdtasdt0(smndt0(sz10),xx)) = sdtasdt0(smndt0(sz10),xx),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_273]),c_0_261]),c_0_274])]),c_0_271]) ).
cnf(c_0_281,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,smndt0(xa))),xI)
| ~ aElement0(sdtasdt0(xx,smndt0(xa))) ),
inference(spm,[status(thm)],[c_0_275,c_0_84]) ).
cnf(c_0_282,hypothesis,
( aElementOf0(sdtasdt0(smndt0(X1),xa),xI)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_276,c_0_277]),c_0_147]),c_0_54])]) ).
cnf(c_0_283,hypothesis,
smndt0(sdtasdt0(xy,smndt0(sz10))) = xy,
inference(rw,[status(thm)],[c_0_265,c_0_278]) ).
cnf(c_0_284,hypothesis,
aElement0(sdtasdt0(xy,smndt0(sz10))),
inference(rw,[status(thm)],[c_0_253,c_0_278]) ).
cnf(c_0_285,hypothesis,
smndt0(xx) = sdtasdt0(smndt0(sz10),xx),
inference(rw,[status(thm)],[c_0_279,c_0_280]) ).
cnf(c_0_286,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,smndt0(xa))),xI)
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_281,c_0_146]),c_0_181])]) ).
cnf(c_0_287,plain,
( aElementOf0(sdtpldt0(X3,X1),X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X2)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_220]) ).
cnf(c_0_288,hypothesis,
aElementOf0(sdtasdt0(xy,xa),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282,c_0_283]),c_0_284])]) ).
cnf(c_0_289,hypothesis,
aElementOf0(sdtasdt0(sdtasdt0(smndt0(sz10),xx),xa),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282,c_0_285]),c_0_181])]) ).
cnf(c_0_290,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X2,sdtasdt0(X1,X3))
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[c_0_175,c_0_250]) ).
cnf(c_0_291,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,smndt0(xa))),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_45]),c_0_54])]) ).
cnf(c_0_292,hypothesis,
( aElementOf0(sdtpldt0(sdtasdt0(xy,xa),X1),xI)
| ~ aElementOf0(X1,xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_288]),c_0_242])]) ).
cnf(c_0_293,hypothesis,
aElementOf0(sdtasdt0(xx,sdtasdt0(smndt0(sz10),xa)),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_290]),c_0_54]),c_0_147]),c_0_181])]) ).
cnf(c_0_294,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,sdtasdt0(smndt0(sz10),xa))),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_111]),c_0_54])]) ).
cnf(c_0_295,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_292,c_0_293]),c_0_294]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG096+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n008.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:52:13 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 81.21/52.52 % Version : CSE_E---1.7
% 81.21/52.52 % Problem : theBenchmark.p
% 81.21/52.52 % SZS status Theorem for theBenchmark.p
% 81.21/52.52 % SZS output start CNFRefutation
% See solution above
% 81.41/52.75 % Total time : 41.971s
%------------------------------------------------------------------------------