%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG097+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.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 16.84s 11.18s
% Output : CNFRefutation 16.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 20
% Syntax : Number of formulae : 112 ( 44 unt; 0 def)
% Number of atoms : 266 ( 82 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 254 ( 100 ~; 96 |; 38 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 102 ( 1 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
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/sandbox2/benchmark/theBenchmark.p',m__1205) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(m__1294,hypothesis,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1294) ).
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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mAddInvr,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1319) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(m__1217,hypothesis,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1217) ).
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/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(mMulMnOne,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
fof(m__,conjecture,
aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_20,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])])]) ).
fof(c_0_21,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_22,plain,
! [X75,X76] :
( ~ aElement0(X75)
| ~ aElement0(X76)
| sdtpldt0(X75,X76) = sdtpldt0(X76,X75) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_23,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,hypothesis,
aElementOf0(xa,xI),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_25,hypothesis,
aSet0(xI),
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_21]) ).
fof(c_0_28,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])]) ).
cnf(c_0_29,hypothesis,
sdtpldt0(xa,xb) = sz10,
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_30,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,hypothesis,
aElement0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_32,hypothesis,
aElement0(xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_26]),c_0_27])]) ).
cnf(c_0_33,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,hypothesis,
sdtpldt0(xb,xa) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
fof(c_0_35,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_36,hypothesis,
( sdtpldt0(xb,sdtpldt0(xa,X1)) = sdtpldt0(sz10,X1)
| ~ aElement0(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_31]),c_0_32])]) ).
cnf(c_0_37,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_38,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_39,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_36,c_0_37]),c_0_34]),c_0_38]),c_0_31])]) ).
cnf(c_0_40,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_41,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_42,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_43,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_39]),c_0_38]),c_0_40])]) ).
cnf(c_0_44,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_33,c_0_29]),c_0_32]),c_0_31])]) ).
cnf(c_0_45,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_46,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])]) ).
fof(c_0_47,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_48,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(split_conjunct,[status(thm)],[m__1319]) ).
fof(c_0_50,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_51,hypothesis,
( sdtpldt0(sz00,sdtpldt0(sz10,X1)) = sdtpldt0(sz10,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_43]),c_0_40]),c_0_38])]) ).
cnf(c_0_52,hypothesis,
( sdtpldt0(sz10,smndt0(xb)) = sdtpldt0(xa,sz00)
| ~ aElement0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_32])]) ).
fof(c_0_53,plain,
! [X70] :
( ~ aElement0(X70)
| aElement0(smndt0(X70)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
cnf(c_0_54,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_56,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_57,hypothesis,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__1217]) ).
fof(c_0_60,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_61,hypothesis,
( sdtpldt0(sz00,sdtpldt0(xa,sz00)) = sdtpldt0(xa,sz00)
| ~ aElement0(smndt0(xb)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_62,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_40])]) ).
cnf(c_0_64,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_65,hypothesis,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_31]),c_0_59])]) ).
cnf(c_0_66,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__1217]) ).
fof(c_0_67,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_68,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_60]) ).
cnf(c_0_69,hypothesis,
sdtpldt0(sz00,sdtpldt0(xa,sz00)) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_32])]) ).
cnf(c_0_70,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_38])]) ).
cnf(c_0_71,hypothesis,
aElement0(xw),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_58]),c_0_32]),c_0_66])]) ).
cnf(c_0_72,hypothesis,
( sdtpldt0(sz10,smndt0(xa)) = sdtpldt0(xb,sz00)
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_45]),c_0_31])]) ).
cnf(c_0_73,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_74,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_75,plain,
( sdtasdt0(sz10,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz10,X1),X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_55]),c_0_40])]) ).
cnf(c_0_76,hypothesis,
sdtpldt0(sz00,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_37]),c_0_31])]) ).
cnf(c_0_77,hypothesis,
sdtasdt0(sz10,sz00) = sz00,
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_78,hypothesis,
( sdtpldt0(sz00,sdtpldt0(xb,sz00)) = sdtpldt0(xb,sz00)
| ~ aElement0(smndt0(xa)) ),
inference(spm,[status(thm)],[c_0_51,c_0_72]) ).
cnf(c_0_79,plain,
( smndt0(sz00) = sz00
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_64]),c_0_38])]) ).
cnf(c_0_80,hypothesis,
( aElementOf0(sdtasdt0(X1,sdtasdt0(X2,X3)),xI)
| ~ aElementOf0(X3,xI)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_54]),c_0_58]) ).
cnf(c_0_81,hypothesis,
sdtasdt0(sz10,xa) = xa,
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_75,c_0_76]),c_0_77]),c_0_76]),c_0_31]),c_0_38])]) ).
cnf(c_0_82,hypothesis,
sdtpldt0(sz00,sdtpldt0(xb,sz00)) = sdtpldt0(xb,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_62]),c_0_31])]) ).
cnf(c_0_83,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_84,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_37,c_0_33]),c_0_38])]),c_0_48]) ).
cnf(c_0_85,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_62]),c_0_40])]) ).
cnf(c_0_86,hypothesis,
( aElementOf0(sdtasdt0(X1,xa),xI)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_24]),c_0_31]),c_0_40])]) ).
cnf(c_0_87,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_88,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_37]),c_0_32])]) ).
cnf(c_0_89,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_83]),c_0_62]) ).
cnf(c_0_90,hypothesis,
sdtpldt0(xa,sz00) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_84]),c_0_76]),c_0_31]),c_0_38])]) ).
cnf(c_0_91,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_85]),c_0_38])]) ).
cnf(c_0_92,hypothesis,
( aElementOf0(smndt0(xa),xI)
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_31])]) ).
cnf(c_0_93,hypothesis,
( sdtpldt0(sz00,sdtpldt0(xb,X1)) = sdtpldt0(xb,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_88]),c_0_32]),c_0_38])]) ).
cnf(c_0_94,hypothesis,
sdtpldt0(smndt0(xa),xa) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_38]),c_0_31])]) ).
cnf(c_0_95,hypothesis,
aElementOf0(smndt0(xa),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_62]),c_0_40])]) ).
cnf(c_0_96,hypothesis,
sdtpldt0(xb,sz00) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_84]),c_0_88]),c_0_38]),c_0_32])]) ).
cnf(c_0_97,hypothesis,
( sdtpldt0(xa,smndt0(xa)) = sz00
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_94]),c_0_31])]) ).
cnf(c_0_98,hypothesis,
aElement0(smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_95]),c_0_25])]) ).
cnf(c_0_99,hypothesis,
( sdtpldt0(sz10,smndt0(xa)) = xb
| ~ aElement0(smndt0(xa)) ),
inference(rw,[status(thm)],[c_0_72,c_0_96]) ).
cnf(c_0_100,hypothesis,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
cnf(c_0_101,hypothesis,
sdtpldt0(sz10,smndt0(xa)) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_98])]) ).
cnf(c_0_102,hypothesis,
sdtpldt0(smndt0(xa),sz00) = sdtpldt0(sz00,smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_100]),c_0_98]),c_0_31])]) ).
fof(c_0_103,negated_conjecture,
~ aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_104,hypothesis,
sdtpldt0(smndt0(sz10),xb) = sdtpldt0(sz00,smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_101]),c_0_98]),c_0_40])]) ).
cnf(c_0_105,hypothesis,
sdtpldt0(sz00,smndt0(xa)) = smndt0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_102]),c_0_98])]) ).
cnf(c_0_106,negated_conjecture,
~ aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_107,hypothesis,
sdtpldt0(smndt0(sz10),xb) = smndt0(xa),
inference(rw,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_108,negated_conjecture,
~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_74]),c_0_66])]) ).
cnf(c_0_109,hypothesis,
( sdtpldt0(xb,smndt0(sz10)) = smndt0(xa)
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_107]),c_0_32])]) ).
cnf(c_0_110,negated_conjecture,
~ aElement0(smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_95])]) ).
cnf(c_0_111,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_62]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG097+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n009.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 01:51:56 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 16.84/11.18 % Version : CSE_E---1.7
% 16.84/11.18 % Problem : theBenchmark.p
% 16.84/11.18 % SZS status Theorem for theBenchmark.p
% 16.84/11.18 % SZS output start CNFRefutation
% See solution above
% 16.91/11.24 % Total time : 8.381s
%------------------------------------------------------------------------------