%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG087+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 : n026.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 05:05:17 PM UTC 2026
% Result : Theorem 0.30s 1.62s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 49)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& xy = sdtpldt0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
fof(mDefSInt,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ! [X3] :
( X3 = sdtasasdt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElementOf0(X4,X1)
& aElementOf0(X4,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSInt) ).
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/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(mSetEq,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ( ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(X3,X2) )
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetEq) ).
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(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(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(m__870,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__870) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mCancel,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__901,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = xx )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = xy )
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
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(mAddInvr,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
fof(m__934,hypothesis,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mUnNeZr,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
fof(i_0_26,negated_conjecture,
~ ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& xy = sdtpldt0(X1,X2) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(i_0_27,plain,
! [X97,X98,X99,X100,X103,X104,X105,X106,X108,X109] :
( ( aSet0(X99)
| X99 != sdtpldt1(X97,X98)
| ~ aSet0(X97)
| ~ aSet0(X98) )
& ( aElementOf0(esk3_4(X97,X98,X99,X100),X97)
| ~ aElementOf0(X100,X99)
| X99 != sdtpldt1(X97,X98)
| ~ aSet0(X97)
| ~ aSet0(X98) )
& ( aElementOf0(esk4_4(X97,X98,X99,X100),X98)
| ~ aElementOf0(X100,X99)
| X99 != sdtpldt1(X97,X98)
| ~ aSet0(X97)
| ~ aSet0(X98) )
& ( sdtpldt0(esk3_4(X97,X98,X99,X100),esk4_4(X97,X98,X99,X100)) = X100
| ~ aElementOf0(X100,X99)
| X99 != sdtpldt1(X97,X98)
| ~ aSet0(X97)
| ~ aSet0(X98) )
& ( ~ aElementOf0(X104,X97)
| ~ aElementOf0(X105,X98)
| sdtpldt0(X104,X105) != X103
| aElementOf0(X103,X99)
| X99 != sdtpldt1(X97,X98)
| ~ aSet0(X97)
| ~ aSet0(X98) )
& ( ~ aElementOf0(esk5_3(X97,X98,X106),X106)
| ~ aElementOf0(X108,X97)
| ~ aElementOf0(X109,X98)
| sdtpldt0(X108,X109) != esk5_3(X97,X98,X106)
| ~ aSet0(X106)
| X106 = sdtpldt1(X97,X98)
| ~ aSet0(X97)
| ~ aSet0(X98) )
& ( aElementOf0(esk6_3(X97,X98,X106),X97)
| aElementOf0(esk5_3(X97,X98,X106),X106)
| ~ aSet0(X106)
| X106 = sdtpldt1(X97,X98)
| ~ aSet0(X97)
| ~ aSet0(X98) )
& ( aElementOf0(esk7_3(X97,X98,X106),X98)
| aElementOf0(esk5_3(X97,X98,X106),X106)
| ~ aSet0(X106)
| X106 = sdtpldt1(X97,X98)
| ~ aSet0(X97)
| ~ aSet0(X98) )
& ( sdtpldt0(esk6_3(X97,X98,X106),esk7_3(X97,X98,X106)) = esk5_3(X97,X98,X106)
| aElementOf0(esk5_3(X97,X98,X106),X106)
| ~ aSet0(X106)
| X106 = sdtpldt1(X97,X98)
| ~ aSet0(X97)
| ~ aSet0(X98) ) ),
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])])])])])]) ).
fof(i_0_28,plain,
! [X112,X113,X114,X115,X116,X117] :
( ( aSet0(X114)
| X114 != sdtasasdt0(X112,X113)
| ~ aSet0(X112)
| ~ aSet0(X113) )
& ( aElementOf0(X115,X112)
| ~ aElementOf0(X115,X114)
| X114 != sdtasasdt0(X112,X113)
| ~ aSet0(X112)
| ~ aSet0(X113) )
& ( aElementOf0(X115,X113)
| ~ aElementOf0(X115,X114)
| X114 != sdtasasdt0(X112,X113)
| ~ aSet0(X112)
| ~ aSet0(X113) )
& ( ~ aElementOf0(X116,X112)
| ~ aElementOf0(X116,X113)
| aElementOf0(X116,X114)
| X114 != sdtasasdt0(X112,X113)
| ~ aSet0(X112)
| ~ aSet0(X113) )
& ( ~ aElementOf0(esk8_3(X112,X113,X117),X117)
| ~ aElementOf0(esk8_3(X112,X113,X117),X112)
| ~ aElementOf0(esk8_3(X112,X113,X117),X113)
| ~ aSet0(X117)
| X117 = sdtasasdt0(X112,X113)
| ~ aSet0(X112)
| ~ aSet0(X113) )
& ( aElementOf0(esk8_3(X112,X113,X117),X112)
| aElementOf0(esk8_3(X112,X113,X117),X117)
| ~ aSet0(X117)
| X117 = sdtasasdt0(X112,X113)
| ~ aSet0(X112)
| ~ aSet0(X113) )
& ( aElementOf0(esk8_3(X112,X113,X117),X113)
| aElementOf0(esk8_3(X112,X113,X117),X117)
| ~ aSet0(X117)
| X117 = sdtasasdt0(X112,X113)
| ~ aSet0(X112)
| ~ aSet0(X113) ) ),
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)],[mDefSInt])])])])])]) ).
fof(i_0_29,plain,
! [X119,X120,X121,X122,X123] :
( ( aSet0(X119)
| ~ aIdeal0(X119) )
& ( ~ aElementOf0(X121,X119)
| aElementOf0(sdtpldt0(X120,X121),X119)
| ~ aElementOf0(X120,X119)
| ~ aIdeal0(X119) )
& ( ~ aElement0(X122)
| aElementOf0(sdtasdt0(X122,X120),X119)
| ~ aElementOf0(X120,X119)
| ~ aIdeal0(X119) )
& ( aElementOf0(esk9_1(X123),X123)
| ~ aSet0(X123)
| aIdeal0(X123) )
& ( aElement0(esk11_1(X123))
| aElementOf0(esk10_1(X123),X123)
| ~ aSet0(X123)
| aIdeal0(X123) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X123),esk9_1(X123)),X123)
| aElementOf0(esk10_1(X123),X123)
| ~ aSet0(X123)
| aIdeal0(X123) )
& ( aElement0(esk11_1(X123))
| ~ aElementOf0(sdtpldt0(esk9_1(X123),esk10_1(X123)),X123)
| ~ aSet0(X123)
| aIdeal0(X123) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X123),esk9_1(X123)),X123)
| ~ aElementOf0(sdtpldt0(esk9_1(X123),esk10_1(X123)),X123)
| ~ aSet0(X123)
| aIdeal0(X123) ) ),
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])])])])])]) ).
fof(i_0_30,plain,
! [X93,X94] :
( ( aElementOf0(esk2_2(X93,X94),X94)
| aElementOf0(esk1_2(X93,X94),X93)
| X93 = X94
| ~ aSet0(X93)
| ~ aSet0(X94) )
& ( ~ aElementOf0(esk2_2(X93,X94),X93)
| aElementOf0(esk1_2(X93,X94),X93)
| X93 = X94
| ~ aSet0(X93)
| ~ aSet0(X94) )
& ( aElementOf0(esk2_2(X93,X94),X94)
| ~ aElementOf0(esk1_2(X93,X94),X94)
| X93 = X94
| ~ aSet0(X93)
| ~ aSet0(X94) )
& ( ~ aElementOf0(esk2_2(X93,X94),X93)
| ~ aElementOf0(esk1_2(X93,X94),X94)
| X93 = X94
| ~ aSet0(X93)
| ~ aSet0(X94) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSetEq])])])]) ).
fof(i_0_31,plain,
! [X84,X85,X86] :
( ( sdtasdt0(X84,sdtpldt0(X85,X86)) = sdtpldt0(sdtasdt0(X84,X85),sdtasdt0(X84,X86))
| ~ aElement0(X84)
| ~ aElement0(X85)
| ~ aElement0(X86) )
& ( sdtasdt0(sdtpldt0(X85,X86),X84) = sdtpldt0(sdtasdt0(X85,X84),sdtasdt0(X86,X84))
| ~ aElement0(X84)
| ~ aElement0(X85)
| ~ aElement0(X86) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
fof(i_0_32,plain,
! [X80,X81,X82] :
( ~ aElement0(X80)
| ~ aElement0(X81)
| ~ aElement0(X82)
| sdtasdt0(sdtasdt0(X80,X81),X82) = sdtasdt0(X80,sdtasdt0(X81,X82)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(i_0_33,plain,
! [X73,X74,X75] :
( ~ aElement0(X73)
| ~ aElement0(X74)
| ~ aElement0(X75)
| sdtpldt0(sdtpldt0(X73,X74),X75) = sdtpldt0(X73,sdtpldt0(X74,X75)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(i_0_34,hypothesis,
! [X127,X128,X129,X130,X131,X132] :
( aSet0(xI)
& ( ~ aElementOf0(X128,xI)
| aElementOf0(sdtpldt0(X127,X128),xI)
| ~ aElementOf0(X127,xI) )
& ( ~ aElement0(X129)
| aElementOf0(sdtasdt0(X129,X127),xI)
| ~ aElementOf0(X127,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ( ~ aElementOf0(X131,xJ)
| aElementOf0(sdtpldt0(X130,X131),xJ)
| ~ aElementOf0(X130,xJ) )
& ( ~ aElement0(X132)
| aElementOf0(sdtasdt0(X132,X130),xJ)
| ~ aElementOf0(X130,xJ) )
& aIdeal0(xJ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__870])])])]) ).
fof(i_0_35,negated_conjecture,
! [X137,X138] :
( ~ aElementOf0(X137,xI)
| ~ aElementOf0(X138,xJ)
| xy != sdtpldt0(X137,X138) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_26])]) ).
fof(i_0_36,plain,
! [X69,X70] :
( ~ aElement0(X69)
| ~ aElement0(X70)
| aElement0(sdtasdt0(X69,X70)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(i_0_37,plain,
! [X67,X68] :
( ~ aElement0(X67)
| ~ aElement0(X68)
| aElement0(sdtpldt0(X67,X68)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(i_0_38,plain,
! [X78,X79] :
( ~ aElement0(X78)
| ~ aElement0(X79)
| sdtasdt0(X78,X79) = sdtasdt0(X79,X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(i_0_39,plain,
! [X71,X72] :
( ~ aElement0(X71)
| ~ aElement0(X72)
| sdtpldt0(X71,X72) = sdtpldt0(X72,X71) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(i_0_40,plain,
! [X89,X90] :
( ~ aElement0(X89)
| ~ aElement0(X90)
| sdtasdt0(X89,X90) != sz00
| X89 = sz00
| X90 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCancel])]) ).
fof(i_0_41,plain,
! [X91,X92] :
( ~ aSet0(X91)
| ~ aElementOf0(X92,X91)
| aElement0(X92) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(i_0_42,hypothesis,
( aElementOf0(esk12_0,xI)
& aElementOf0(esk13_0,xJ)
& sdtpldt0(esk12_0,esk13_0) = xx
& aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(esk14_0,xI)
& aElementOf0(esk15_0,xJ)
& sdtpldt0(esk14_0,esk15_0) = xy
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__901])]) ).
fof(i_0_43,plain,
! [X87] :
( ( sdtasdt0(smndt0(sz10),X87) = smndt0(X87)
| ~ aElement0(X87) )
& ( smndt0(X87) = sdtasdt0(X87,smndt0(sz10))
| ~ aElement0(X87) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])]) ).
fof(i_0_44,plain,
! [X77] :
( ( sdtpldt0(X77,smndt0(X77)) = sz00
| ~ aElement0(X77) )
& ( sz00 = sdtpldt0(smndt0(X77),X77)
| ~ aElement0(X77) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).
fof(i_0_45,plain,
! [X83] :
( ( sdtasdt0(X83,sz10) = X83
| ~ aElement0(X83) )
& ( X83 = sdtasdt0(sz10,X83)
| ~ aElement0(X83) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).
fof(i_0_46,plain,
! [X76] :
( ( sdtpldt0(X76,sz00) = X76
| ~ aElement0(X76) )
& ( X76 = sdtpldt0(sz00,X76)
| ~ aElement0(X76) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(i_0_47,plain,
! [X88] :
( ( sdtasdt0(X88,sz00) = sz00
| ~ aElement0(X88) )
& ( sz00 = sdtasdt0(sz00,X88)
| ~ aElement0(X88) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(i_0_48,plain,
! [X66] :
( ~ aElement0(X66)
| aElement0(smndt0(X66)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
cnf(i_0_49,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)],[i_0_27]),
[final] ).
cnf(i_0_50,plain,
( X3 = sdtasasdt0(X1,X2)
| ~ aElementOf0(esk8_3(X1,X2,X3),X3)
| ~ aElementOf0(esk8_3(X1,X2,X3),X1)
| ~ aElementOf0(esk8_3(X1,X2,X3),X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_51,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)],[i_0_27]),
[final] ).
cnf(i_0_52,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)],[i_0_27]),
[final] ).
cnf(i_0_53,plain,
( sdtpldt0(esk6_3(X1,X2,X3),esk7_3(X1,X2,X3)) = esk5_3(X1,X2,X3)
| aElementOf0(esk5_3(X1,X2,X3),X3)
| X3 = sdtpldt1(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_54,plain,
( X3 = sdtpldt1(X1,X2)
| ~ aElementOf0(esk5_3(X1,X2,X3),X3)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(X5,X2)
| sdtpldt0(X4,X5) != esk5_3(X1,X2,X3)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_55,plain,
( aElementOf0(esk8_3(X1,X2,X3),X1)
| aElementOf0(esk8_3(X1,X2,X3),X3)
| X3 = sdtasasdt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_56,plain,
( aElementOf0(esk8_3(X1,X2,X3),X2)
| aElementOf0(esk8_3(X1,X2,X3),X3)
| X3 = sdtasasdt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_57,plain,
( aElementOf0(esk7_3(X1,X2,X3),X2)
| aElementOf0(esk5_3(X1,X2,X3),X3)
| X3 = sdtpldt1(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_58,plain,
( aElementOf0(esk6_3(X1,X2,X3),X1)
| aElementOf0(esk5_3(X1,X2,X3),X3)
| X3 = sdtpldt1(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_59,plain,
( aIdeal0(X1)
| ~ aElementOf0(sdtasdt0(esk11_1(X1),esk9_1(X1)),X1)
| ~ aElementOf0(sdtpldt0(esk9_1(X1),esk10_1(X1)),X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_60,plain,
( X1 = X2
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aElementOf0(esk1_2(X1,X2),X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_61,plain,
( aElementOf0(esk10_1(X1),X1)
| aIdeal0(X1)
| ~ aElementOf0(sdtasdt0(esk11_1(X1),esk9_1(X1)),X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_62,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_63,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_64,plain,
( aElement0(esk11_1(X1))
| aIdeal0(X1)
| ~ aElementOf0(sdtpldt0(esk9_1(X1),esk10_1(X1)),X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_65,plain,
( aElementOf0(X5,X6)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X4)
| sdtpldt0(X1,X3) != X5
| X6 != sdtpldt1(X2,X4)
| ~ aSet0(X2)
| ~ aSet0(X4) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_66,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| X1 = X2
| ~ aElementOf0(esk1_2(X1,X2),X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_67,plain,
( aElementOf0(esk1_2(X1,X2),X1)
| X1 = X2
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_68,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_69,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_70,plain,
( aElementOf0(X1,X4)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X4 != sdtasasdt0(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_71,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aElementOf0(esk1_2(X1,X2),X1)
| X1 = X2
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_72,plain,
( aElementOf0(sdtpldt0(X3,X1),X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X2)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_73,hypothesis,
( aElementOf0(sdtpldt0(X2,X1),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X2,xJ) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_74,hypothesis,
( aElementOf0(sdtpldt0(X2,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_75,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_76,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtasasdt0(X2,X4)
| ~ aSet0(X2)
| ~ aSet0(X4) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_77,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtasasdt0(X4,X2)
| ~ aSet0(X4)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_78,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xJ) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_79,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_80,negated_conjecture,
( ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xJ)
| xy != sdtpldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_81,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_82,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_83,plain,
( aElement0(esk11_1(X1))
| aElementOf0(esk10_1(X1),X1)
| aIdeal0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_84,plain,
( aSet0(X1)
| X1 != sdtasasdt0(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_85,plain,
( aSet0(X1)
| X1 != sdtpldt1(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_86,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_87,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_88,plain,
( X1 = sz00
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_89,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_90,hypothesis,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_91,hypothesis,
aElementOf0(xx,sdtpldt1(xI,xJ)),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_92,plain,
( aElementOf0(esk9_1(X1),X1)
| aIdeal0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_93,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_94,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_95,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_96,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_97,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_98,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_99,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_100,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_101,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_102,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_103,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_104,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_105,hypothesis,
aElementOf0(esk15_0,xJ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_106,hypothesis,
aElementOf0(esk14_0,xI),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_107,hypothesis,
aElementOf0(esk13_0,xJ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_108,hypothesis,
aElementOf0(esk12_0,xI),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_109,hypothesis,
aElementOf0(xl,xJ),
inference(split_conjunct,[status(thm)],[m__934]),
[final] ).
cnf(i_0_110,hypothesis,
aElementOf0(xk,xI),
inference(split_conjunct,[status(thm)],[m__934]),
[final] ).
cnf(i_0_111,hypothesis,
sdtpldt0(esk14_0,esk15_0) = xy,
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_112,hypothesis,
sdtpldt0(esk12_0,esk13_0) = xx,
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_113,hypothesis,
xx = sdtpldt0(xk,xl),
inference(split_conjunct,[status(thm)],[m__934]),
[final] ).
cnf(i_0_114,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_115,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_116,hypothesis,
aSet0(xJ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_117,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_118,hypothesis,
aElement0(xz),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_119,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_120,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]),
[final] ).
cnf(i_0_121,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mUnNeZr]),
[final] ).
cnf(i_0_122,axiom,
X1 = X1 ).
cnf(i_0_123,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_124,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_125,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_126,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_127,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_128,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_129,axiom,
( X1 != X2
| smndt0(X1) = smndt0(X2) ) ).
cnf(i_0_130,axiom,
( X1 != X2
| sdtpldt1(X1,X3) = sdtpldt1(X2,X3) ) ).
cnf(i_0_131,axiom,
( X1 != X2
| sdtpldt1(X3,X1) = sdtpldt1(X3,X2) ) ).
cnf(i_0_132,axiom,
( X1 != X2
| sdtasasdt0(X1,X3) = sdtasasdt0(X2,X3) ) ).
cnf(i_0_133,axiom,
( X1 != X2
| sdtasasdt0(X3,X1) = sdtasasdt0(X3,X2) ) ).
cnf(i_0_134,axiom,
( X1 != X2
| esk5_3(X1,X3,X4) = esk5_3(X2,X3,X4) ) ).
cnf(i_0_135,axiom,
( X1 != X2
| esk5_3(X3,X1,X4) = esk5_3(X3,X2,X4) ) ).
cnf(i_0_136,axiom,
( X1 != X2
| esk5_3(X3,X4,X1) = esk5_3(X3,X4,X2) ) ).
cnf(i_0_137,axiom,
( X1 != X2
| ~ aElementOf0(X1,X3)
| aElementOf0(X2,X3) ) ).
cnf(i_0_138,axiom,
( X1 != X2
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X2) ) ).
cnf(i_0_139,axiom,
( X1 != X2
| ~ aSet0(X1)
| aSet0(X2) ) ).
cnf(i_0_140,axiom,
( X1 != X2
| ~ aIdeal0(X1)
| aIdeal0(X2) ) ).
cnf(i_0_141,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_122_001,axiom,
X1 = X1 ).
cnf(i_0_123_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_124_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_125_004,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_126_005,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_127_006,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_128_007,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_129_008,axiom,
( X1 != X2
| smndt0(X1) = smndt0(X2) ) ).
cnf(i_0_130_009,axiom,
( X1 != X2
| sdtpldt1(X1,X3) = sdtpldt1(X2,X3) ) ).
cnf(i_0_131_010,axiom,
( X1 != X2
| sdtpldt1(X3,X1) = sdtpldt1(X3,X2) ) ).
cnf(i_0_132_011,axiom,
( X1 != X2
| sdtasasdt0(X1,X3) = sdtasasdt0(X2,X3) ) ).
cnf(i_0_133_012,axiom,
( X1 != X2
| sdtasasdt0(X3,X1) = sdtasasdt0(X3,X2) ) ).
cnf(i_0_134_013,axiom,
( X1 != X2
| esk5_3(X1,X3,X4) = esk5_3(X2,X3,X4) ) ).
cnf(i_0_135_014,axiom,
( X1 != X2
| esk5_3(X3,X1,X4) = esk5_3(X3,X2,X4) ) ).
cnf(i_0_136_015,axiom,
( X1 != X2
| esk5_3(X3,X4,X1) = esk5_3(X3,X4,X2) ) ).
cnf(i_0_137_016,axiom,
( X1 != X2
| ~ aElementOf0(X1,X3)
| aElementOf0(X2,X3) ) ).
cnf(i_0_138_017,axiom,
( X1 != X2
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X2) ) ).
cnf(i_0_139_018,axiom,
( X1 != X2
| ~ aSet0(X1)
| aSet0(X2) ) ).
cnf(i_0_140_019,axiom,
( X1 != X2
| ~ aIdeal0(X1)
| aIdeal0(X2) ) ).
cnf(i_0_141_020,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_142,plain,
( ~ aElementOf0(X1,sdtpldt1(X2,X3))
| ~ aSet0(X2)
| ~ aSet0(X3)
| sdtpldt0(esk3_4(X2,X3,sdtpldt1(X2,X3),X1),esk4_4(X2,X3,sdtpldt1(X2,X3),X1)) = X1 ),
inference(equality_inference,[],[49]) ).
cnf(i_0_143,plain,
( ~ aElementOf0(X1,sdtpldt1(X2,X3))
| ~ aSet0(X2)
| ~ aSet0(X3)
| aElementOf0(esk4_4(X2,X3,sdtpldt1(X2,X3),X1),X3) ),
inference(equality_inference,[],[51]) ).
cnf(i_0_144,plain,
( ~ aElementOf0(X1,sdtpldt1(X2,X3))
| ~ aSet0(X2)
| ~ aSet0(X3)
| aElementOf0(esk3_4(X2,X3,sdtpldt1(X2,X3),X1),X2) ),
inference(equality_inference,[],[52]) ).
cnf(i_0_145,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,sdtasasdt0(X1,X2))
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) ),
inference(equality_inference,[],[70]) ).
cnf(i_0_146,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,X1)
| ~ aElementOf0(X3,sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[76]) ).
cnf(i_0_147,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(X3,X2)
| ~ aElementOf0(X3,sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[77]) ).
cnf(i_0_148,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSet0(sdtasasdt0(X1,X2)) ),
inference(equality_inference,[],[84]) ).
cnf(i_0_149,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSet0(sdtpldt1(X1,X2)) ),
inference(equality_inference,[],[85]) ).
cnf(i_0_150,plain,
xy = sdtpldt0(esk14_0,esk15_0),
inference(scs_inference,[],[i_0_111,i_0_123]) ).
cnf(i_0_151,plain,
$false,
inference(scs_inference,[],[i_0_106,i_0_105,i_0_111,i_0_123,i_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG087+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:50:23 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.30/1.62 % Version : CSE_E---1.7
% 0.30/1.62 % Problem : theBenchmark.p
% 0.30/1.62 % SZS status Theorem for theBenchmark.p
% 0.30/1.62 % SZS output start CNFRefutation
% See solution above
% 0.30/1.64 % Total time : 1.271s
%------------------------------------------------------------------------------