TSTP Solution File: RNG087+2 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : RNG087+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n018.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 : 600s
% DateTime : Mon Jul 18 20:30:23 EDT 2022
% Result : Theorem 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
fof(mDefIdeal,axiom,
! [W0] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
input ).
fof(mDefIdeal_0,plain,
! [W0] :
( aIdeal0(W0)
| ~ ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(orientation,[status(thm)],[mDefIdeal]) ).
fof(mDefIdeal_1,plain,
! [W0] :
( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(orientation,[status(thm)],[mDefIdeal]) ).
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
input ).
fof(mEOfElem_0,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
inference(orientation,[status(thm)],[mEOfElem]) ).
fof(mSetSort,axiom,
! [W0] :
( aSet0(W0)
=> $true ),
input ).
fof(mSetSort_0,plain,
! [W0] :
( ~ aSet0(W0)
| $true ),
inference(orientation,[status(thm)],[mSetSort]) ).
fof(mUnNeZr,axiom,
sz10 != sz00,
input ).
fof(mUnNeZr_0,plain,
( sz10 != sz00
| $false ),
inference(orientation,[status(thm)],[mUnNeZr]) ).
fof(mMulZero,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
input ).
fof(mMulZero_0,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
inference(orientation,[status(thm)],[mMulZero]) ).
fof(mMulMnOne,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
& smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ),
input ).
fof(mMulMnOne_0,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
& smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ),
inference(orientation,[status(thm)],[mMulMnOne]) ).
fof(mMulUnit,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
input ).
fof(mMulUnit_0,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
inference(orientation,[status(thm)],[mMulUnit]) ).
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
input ).
fof(mMulAsso_0,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) ) ),
inference(orientation,[status(thm)],[mMulAsso]) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
input ).
fof(mMulComm_0,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(orientation,[status(thm)],[mMulComm]) ).
fof(mAddInvr,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
input ).
fof(mAddInvr_0,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
inference(orientation,[status(thm)],[mAddInvr]) ).
fof(mAddZero,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
input ).
fof(mAddZero_0,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
inference(orientation,[status(thm)],[mAddZero]) ).
fof(mAddAsso,axiom,
! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
input ).
fof(mAddAsso_0,plain,
! [W0,W1,W2] :
( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2))
| ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) ) ),
inference(orientation,[status(thm)],[mAddAsso]) ).
fof(mAddComm,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
input ).
fof(mAddComm_0,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(orientation,[status(thm)],[mAddComm]) ).
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) ),
input ).
fof(mSortsB_02_0,plain,
! [W0,W1] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(orientation,[status(thm)],[mSortsB_02]) ).
fof(mSortsB,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) ),
input ).
fof(mSortsB_0,plain,
! [W0,W1] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(orientation,[status(thm)],[mSortsB]) ).
fof(mSortsU,axiom,
! [W0] :
( aElement0(W0)
=> aElement0(smndt0(W0)) ),
input ).
fof(mSortsU_0,plain,
! [W0] :
( ~ aElement0(W0)
| aElement0(smndt0(W0)) ),
inference(orientation,[status(thm)],[mSortsU]) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
input ).
fof(mSortsC_01_0,plain,
( aElement0(sz10)
| $false ),
inference(orientation,[status(thm)],[mSortsC_01]) ).
fof(mSortsC,axiom,
aElement0(sz00),
input ).
fof(mSortsC_0,plain,
( aElement0(sz00)
| $false ),
inference(orientation,[status(thm)],[mSortsC]) ).
fof(mElmSort,axiom,
! [W0] :
( aElement0(W0)
=> $true ),
input ).
fof(mElmSort_0,plain,
! [W0] :
( ~ aElement0(W0)
| $true ),
inference(orientation,[status(thm)],[mElmSort]) ).
fof(def_lhs_atom1,axiom,
! [W0] :
( lhs_atom1(W0)
<=> ~ aElement0(W0) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [W0] :
( lhs_atom1(W0)
| $true ),
inference(fold_definition,[status(thm)],[mElmSort_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
( lhs_atom2
<=> aElement0(sz00) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
( lhs_atom2
| $false ),
inference(fold_definition,[status(thm)],[mSortsC_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
( lhs_atom3
<=> aElement0(sz10) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
( lhs_atom3
| $false ),
inference(fold_definition,[status(thm)],[mSortsC_01_0,def_lhs_atom3]) ).
fof(to_be_clausified_3,plain,
! [W0] :
( lhs_atom1(W0)
| aElement0(smndt0(W0)) ),
inference(fold_definition,[status(thm)],[mSortsU_0,def_lhs_atom1]) ).
fof(def_lhs_atom4,axiom,
! [W1,W0] :
( lhs_atom4(W1,W0)
<=> aElement0(sdtpldt0(W0,W1)) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [W0,W1] :
( lhs_atom4(W1,W0)
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(fold_definition,[status(thm)],[mSortsB_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [W1,W0] :
( lhs_atom5(W1,W0)
<=> aElement0(sdtasdt0(W0,W1)) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [W0,W1] :
( lhs_atom5(W1,W0)
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(fold_definition,[status(thm)],[mSortsB_02_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [W1,W0] :
( lhs_atom6(W1,W0)
<=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [W0,W1] :
( lhs_atom6(W1,W0)
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(fold_definition,[status(thm)],[mAddComm_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [W2,W1,W0] :
( lhs_atom7(W2,W1,W0)
<=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [W0,W1,W2] :
( lhs_atom7(W2,W1,W0)
| ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) ) ),
inference(fold_definition,[status(thm)],[mAddAsso_0,def_lhs_atom7]) ).
fof(to_be_clausified_8,plain,
! [W0] :
( lhs_atom1(W0)
| ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
inference(fold_definition,[status(thm)],[mAddZero_0,def_lhs_atom1]) ).
fof(to_be_clausified_9,plain,
! [W0] :
( lhs_atom1(W0)
| ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
inference(fold_definition,[status(thm)],[mAddInvr_0,def_lhs_atom1]) ).
fof(def_lhs_atom8,axiom,
! [W1,W0] :
( lhs_atom8(W1,W0)
<=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [W0,W1] :
( lhs_atom8(W1,W0)
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(fold_definition,[status(thm)],[mMulComm_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [W2,W1,W0] :
( lhs_atom9(W2,W1,W0)
<=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [W0,W1,W2] :
( lhs_atom9(W2,W1,W0)
| ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) ) ),
inference(fold_definition,[status(thm)],[mMulAsso_0,def_lhs_atom9]) ).
fof(to_be_clausified_12,plain,
! [W0] :
( lhs_atom1(W0)
| ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
inference(fold_definition,[status(thm)],[mMulUnit_0,def_lhs_atom1]) ).
fof(to_be_clausified_13,plain,
! [W0] :
( lhs_atom1(W0)
| ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
& smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ),
inference(fold_definition,[status(thm)],[mMulMnOne_0,def_lhs_atom1]) ).
fof(to_be_clausified_14,plain,
! [W0] :
( lhs_atom1(W0)
| ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
inference(fold_definition,[status(thm)],[mMulZero_0,def_lhs_atom1]) ).
fof(def_lhs_atom10,axiom,
( lhs_atom10
<=> sz10 != sz00 ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
( lhs_atom10
| $false ),
inference(fold_definition,[status(thm)],[mUnNeZr_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [W0] :
( lhs_atom11(W0)
<=> ~ aSet0(W0) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
! [W0] :
( lhs_atom11(W0)
| $true ),
inference(fold_definition,[status(thm)],[mSetSort_0,def_lhs_atom11]) ).
fof(to_be_clausified_17,plain,
! [W0] :
( lhs_atom11(W0)
| ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
inference(fold_definition,[status(thm)],[mEOfElem_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [W0] :
( lhs_atom12(W0)
<=> ~ aIdeal0(W0) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
! [W0] :
( lhs_atom12(W0)
| ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(fold_definition,[status(thm)],[mDefIdeal_1,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [W0] :
( lhs_atom13(W0)
<=> aIdeal0(W0) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
! [W0] :
( lhs_atom13(W0)
| ~ ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(fold_definition,[status(thm)],[mDefIdeal_0,def_lhs_atom13]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X1] :
( lhs_atom13(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('<stdin>',to_be_clausified_19) ).
fof(c_0_1,axiom,
! [X1] :
( lhs_atom12(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('<stdin>',to_be_clausified_18) ).
fof(c_0_2,axiom,
! [X3,X2,X1] :
( lhs_atom9(X3,X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) ) ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_3,axiom,
! [X3,X2,X1] :
( lhs_atom7(X3,X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) ) ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_4,axiom,
! [X1] :
( lhs_atom11(X1)
| ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_5,axiom,
! [X2,X1] :
( lhs_atom8(X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2) ) ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_6,axiom,
! [X2,X1] :
( lhs_atom6(X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2) ) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_7,axiom,
! [X2,X1] :
( lhs_atom5(X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2) ) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_8,axiom,
! [X2,X1] :
( lhs_atom4(X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2) ) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_9,axiom,
! [X1] :
( lhs_atom1(X1)
| ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_10,axiom,
! [X1] :
( lhs_atom1(X1)
| ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_11,axiom,
! [X1] :
( lhs_atom1(X1)
| ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_12,axiom,
! [X1] :
( lhs_atom1(X1)
| ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_13,axiom,
! [X1] :
( lhs_atom1(X1)
| ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_14,axiom,
! [X1] :
( lhs_atom1(X1)
| aElement0(smndt0(X1)) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_15,axiom,
! [X1] :
( lhs_atom11(X1)
| $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_16,axiom,
( lhs_atom10
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_17,axiom,
( lhs_atom3
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_18,axiom,
( lhs_atom2
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_19,axiom,
! [X1] :
( lhs_atom1(X1)
| $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_20,axiom,
! [X1] :
( lhs_atom13(X1)
| ~ ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
c_0_0 ).
fof(c_0_21,axiom,
! [X1] :
( lhs_atom12(X1)
| ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
c_0_1 ).
fof(c_0_22,axiom,
! [X3,X2,X1] :
( lhs_atom9(X3,X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) ) ),
c_0_2 ).
fof(c_0_23,axiom,
! [X3,X2,X1] :
( lhs_atom7(X3,X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) ) ),
c_0_3 ).
fof(c_0_24,axiom,
! [X1] :
( lhs_atom11(X1)
| ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
c_0_4 ).
fof(c_0_25,axiom,
! [X2,X1] :
( lhs_atom8(X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2) ) ),
c_0_5 ).
fof(c_0_26,axiom,
! [X2,X1] :
( lhs_atom6(X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2) ) ),
c_0_6 ).
fof(c_0_27,axiom,
! [X2,X1] :
( lhs_atom5(X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2) ) ),
c_0_7 ).
fof(c_0_28,axiom,
! [X2,X1] :
( lhs_atom4(X2,X1)
| ~ ( aElement0(X1)
& aElement0(X2) ) ),
c_0_8 ).
fof(c_0_29,axiom,
! [X1] :
( lhs_atom1(X1)
| ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
c_0_9 ).
fof(c_0_30,axiom,
! [X1] :
( lhs_atom1(X1)
| ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
c_0_10 ).
fof(c_0_31,axiom,
! [X1] :
( lhs_atom1(X1)
| ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
c_0_11 ).
fof(c_0_32,axiom,
! [X1] :
( lhs_atom1(X1)
| ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
c_0_12 ).
fof(c_0_33,axiom,
! [X1] :
( lhs_atom1(X1)
| ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
c_0_13 ).
fof(c_0_34,axiom,
! [X1] :
( lhs_atom1(X1)
| aElement0(smndt0(X1)) ),
c_0_14 ).
fof(c_0_35,plain,
! [X1] : $true,
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_36,plain,
lhs_atom10,
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_37,plain,
lhs_atom3,
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_38,plain,
lhs_atom2,
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_39,plain,
! [X1] : $true,
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_40,plain,
! [X4] :
( ( aElementOf0(esk1_1(X4),X4)
| ~ aSet0(X4)
| lhs_atom13(X4) )
& ( aElement0(esk3_1(X4))
| aElementOf0(esk2_1(X4),X4)
| ~ aSet0(X4)
| lhs_atom13(X4) )
& ( ~ aElementOf0(sdtasdt0(esk3_1(X4),esk1_1(X4)),X4)
| aElementOf0(esk2_1(X4),X4)
| ~ aSet0(X4)
| lhs_atom13(X4) )
& ( aElement0(esk3_1(X4))
| ~ aElementOf0(sdtpldt0(esk1_1(X4),esk2_1(X4)),X4)
| ~ aSet0(X4)
| lhs_atom13(X4) )
& ( ~ aElementOf0(sdtasdt0(esk3_1(X4),esk1_1(X4)),X4)
| ~ aElementOf0(sdtpldt0(esk1_1(X4),esk2_1(X4)),X4)
| ~ aSet0(X4)
| lhs_atom13(X4) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
fof(c_0_41,plain,
! [X4,X5,X6,X7] :
( ( aSet0(X4)
| lhs_atom12(X4) )
& ( ~ aElementOf0(X6,X4)
| aElementOf0(sdtpldt0(X5,X6),X4)
| ~ aElementOf0(X5,X4)
| lhs_atom12(X4) )
& ( ~ aElement0(X7)
| aElementOf0(sdtasdt0(X7,X5),X4)
| ~ aElementOf0(X5,X4)
| lhs_atom12(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
fof(c_0_42,plain,
! [X4,X5,X6] :
( lhs_atom9(X4,X5,X6)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ aElement0(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])]) ).
fof(c_0_43,plain,
! [X4,X5,X6] :
( lhs_atom7(X4,X5,X6)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ aElement0(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
fof(c_0_44,plain,
! [X3,X4] :
( lhs_atom11(X3)
| ~ aElementOf0(X4,X3)
| aElement0(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
fof(c_0_45,plain,
! [X3,X4] :
( lhs_atom8(X3,X4)
| ~ aElement0(X4)
| ~ aElement0(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
fof(c_0_46,plain,
! [X3,X4] :
( lhs_atom6(X3,X4)
| ~ aElement0(X4)
| ~ aElement0(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
fof(c_0_47,plain,
! [X3,X4] :
( lhs_atom5(X3,X4)
| ~ aElement0(X4)
| ~ aElement0(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
fof(c_0_48,plain,
! [X3,X4] :
( lhs_atom4(X3,X4)
| ~ aElement0(X4)
| ~ aElement0(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).
fof(c_0_49,plain,
! [X2] :
( ( sdtasdt0(smndt0(sz10),X2) = smndt0(X2)
| lhs_atom1(X2) )
& ( smndt0(X2) = sdtasdt0(X2,smndt0(sz10))
| lhs_atom1(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
fof(c_0_50,plain,
! [X2] :
( ( sdtpldt0(X2,smndt0(X2)) = sz00
| lhs_atom1(X2) )
& ( sz00 = sdtpldt0(smndt0(X2),X2)
| lhs_atom1(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
fof(c_0_51,plain,
! [X2] :
( ( sdtasdt0(X2,sz10) = X2
| lhs_atom1(X2) )
& ( X2 = sdtasdt0(sz10,X2)
| lhs_atom1(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
fof(c_0_52,plain,
! [X2] :
( ( sdtpldt0(X2,sz00) = X2
| lhs_atom1(X2) )
& ( X2 = sdtpldt0(sz00,X2)
| lhs_atom1(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_32])]) ).
fof(c_0_53,plain,
! [X2] :
( ( sdtasdt0(X2,sz00) = sz00
| lhs_atom1(X2) )
& ( sz00 = sdtasdt0(sz00,X2)
| lhs_atom1(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])]) ).
fof(c_0_54,plain,
! [X2] :
( lhs_atom1(X2)
| aElement0(smndt0(X2)) ),
inference(variable_rename,[status(thm)],[c_0_34]) ).
fof(c_0_55,plain,
! [X2] : $true,
inference(variable_rename,[status(thm)],[c_0_35]) ).
fof(c_0_56,plain,
lhs_atom10,
c_0_36 ).
fof(c_0_57,plain,
lhs_atom3,
c_0_37 ).
fof(c_0_58,plain,
lhs_atom2,
c_0_38 ).
fof(c_0_59,plain,
! [X2] : $true,
inference(variable_rename,[status(thm)],[c_0_39]) ).
cnf(c_0_60,plain,
( lhs_atom13(X1)
| ~ aSet0(X1)
| ~ aElementOf0(sdtpldt0(esk1_1(X1),esk2_1(X1)),X1)
| ~ aElementOf0(sdtasdt0(esk3_1(X1),esk1_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_61,plain,
( lhs_atom13(X1)
| aElementOf0(esk2_1(X1),X1)
| ~ aSet0(X1)
| ~ aElementOf0(sdtasdt0(esk3_1(X1),esk1_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_62,plain,
( lhs_atom13(X1)
| aElement0(esk3_1(X1))
| ~ aSet0(X1)
| ~ aElementOf0(sdtpldt0(esk1_1(X1),esk2_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_63,plain,
( lhs_atom12(X1)
| aElementOf0(sdtpldt0(X2,X3),X1)
| ~ aElementOf0(X2,X1)
| ~ aElementOf0(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_64,plain,
( lhs_atom9(X1,X2,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_65,plain,
( lhs_atom7(X1,X2,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_66,plain,
( lhs_atom12(X1)
| aElementOf0(sdtasdt0(X3,X2),X1)
| ~ aElementOf0(X2,X1)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_67,plain,
( lhs_atom13(X1)
| aElementOf0(esk2_1(X1),X1)
| aElement0(esk3_1(X1))
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_68,plain,
( lhs_atom13(X1)
| aElementOf0(esk1_1(X1),X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_69,plain,
( aElement0(X1)
| lhs_atom11(X2)
| ~ aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_70,plain,
( lhs_atom8(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_71,plain,
( lhs_atom6(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_72,plain,
( lhs_atom5(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_73,plain,
( lhs_atom4(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_74,plain,
( lhs_atom1(X1)
| sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_75,plain,
( lhs_atom1(X1)
| smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_76,plain,
( lhs_atom1(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_77,plain,
( lhs_atom1(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_78,plain,
( lhs_atom1(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_79,plain,
( lhs_atom1(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_80,plain,
( lhs_atom1(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_81,plain,
( lhs_atom1(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_82,plain,
( lhs_atom1(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_83,plain,
( lhs_atom1(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_84,plain,
( aElement0(smndt0(X1))
| lhs_atom1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_85,plain,
( lhs_atom12(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_86,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_87,plain,
lhs_atom10,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_88,plain,
lhs_atom3,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_89,plain,
lhs_atom2,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_90,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_91,plain,
( lhs_atom13(X1)
| ~ aSet0(X1)
| ~ aElementOf0(sdtpldt0(esk1_1(X1),esk2_1(X1)),X1)
| ~ aElementOf0(sdtasdt0(esk3_1(X1),esk1_1(X1)),X1) ),
c_0_60,
[final] ).
cnf(c_0_92,plain,
( lhs_atom13(X1)
| aElementOf0(esk2_1(X1),X1)
| ~ aSet0(X1)
| ~ aElementOf0(sdtasdt0(esk3_1(X1),esk1_1(X1)),X1) ),
c_0_61,
[final] ).
cnf(c_0_93,plain,
( lhs_atom13(X1)
| aElement0(esk3_1(X1))
| ~ aSet0(X1)
| ~ aElementOf0(sdtpldt0(esk1_1(X1),esk2_1(X1)),X1) ),
c_0_62,
[final] ).
cnf(c_0_94,plain,
( lhs_atom12(X1)
| aElementOf0(sdtpldt0(X2,X3),X1)
| ~ aElementOf0(X2,X1)
| ~ aElementOf0(X3,X1) ),
c_0_63,
[final] ).
cnf(c_0_95,plain,
( lhs_atom9(X1,X2,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
c_0_64,
[final] ).
cnf(c_0_96,plain,
( lhs_atom7(X1,X2,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
c_0_65,
[final] ).
cnf(c_0_97,plain,
( lhs_atom12(X1)
| aElementOf0(sdtasdt0(X3,X2),X1)
| ~ aElementOf0(X2,X1)
| ~ aElement0(X3) ),
c_0_66,
[final] ).
cnf(c_0_98,plain,
( lhs_atom13(X1)
| aElementOf0(esk2_1(X1),X1)
| aElement0(esk3_1(X1))
| ~ aSet0(X1) ),
c_0_67,
[final] ).
cnf(c_0_99,plain,
( lhs_atom13(X1)
| aElementOf0(esk1_1(X1),X1)
| ~ aSet0(X1) ),
c_0_68,
[final] ).
cnf(c_0_100,plain,
( aElement0(X1)
| lhs_atom11(X2)
| ~ aElementOf0(X1,X2) ),
c_0_69,
[final] ).
cnf(c_0_101,plain,
( lhs_atom8(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
c_0_70,
[final] ).
cnf(c_0_102,plain,
( lhs_atom6(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
c_0_71,
[final] ).
cnf(c_0_103,plain,
( lhs_atom5(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
c_0_72,
[final] ).
cnf(c_0_104,plain,
( lhs_atom4(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
c_0_73,
[final] ).
cnf(c_0_105,plain,
( lhs_atom1(X1)
| sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ),
c_0_74,
[final] ).
cnf(c_0_106,plain,
( lhs_atom1(X1)
| sdtasdt0(X1,smndt0(sz10)) = smndt0(X1) ),
c_0_75,
[final] ).
cnf(c_0_107,plain,
( lhs_atom1(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
c_0_76,
[final] ).
cnf(c_0_108,plain,
( lhs_atom1(X1)
| sdtpldt0(smndt0(X1),X1) = sz00 ),
c_0_77,
[final] ).
cnf(c_0_109,plain,
( lhs_atom1(X1)
| sdtasdt0(X1,sz10) = X1 ),
c_0_78,
[final] ).
cnf(c_0_110,plain,
( lhs_atom1(X1)
| sdtasdt0(sz10,X1) = X1 ),
c_0_79,
[final] ).
cnf(c_0_111,plain,
( lhs_atom1(X1)
| sdtpldt0(X1,sz00) = X1 ),
c_0_80,
[final] ).
cnf(c_0_112,plain,
( lhs_atom1(X1)
| sdtpldt0(sz00,X1) = X1 ),
c_0_81,
[final] ).
cnf(c_0_113,plain,
( lhs_atom1(X1)
| sdtasdt0(X1,sz00) = sz00 ),
c_0_82,
[final] ).
cnf(c_0_114,plain,
( lhs_atom1(X1)
| sdtasdt0(sz00,X1) = sz00 ),
c_0_83,
[final] ).
cnf(c_0_115,plain,
( aElement0(smndt0(X1))
| lhs_atom1(X1) ),
c_0_84,
[final] ).
cnf(c_0_116,plain,
( lhs_atom12(X1)
| aSet0(X1) ),
c_0_85,
[final] ).
cnf(c_0_117,plain,
$true,
c_0_86,
[final] ).
cnf(c_0_118,plain,
lhs_atom10,
c_0_87,
[final] ).
cnf(c_0_119,plain,
lhs_atom3,
c_0_88,
[final] ).
cnf(c_0_120,plain,
lhs_atom2,
c_0_89,
[final] ).
cnf(c_0_121,plain,
$true,
c_0_90,
[final] ).
% End CNF derivation
cnf(c_0_91_0,axiom,
( aIdeal0(X1)
| ~ aSet0(X1)
| ~ aElementOf0(sdtpldt0(sk1_esk1_1(X1),sk1_esk2_1(X1)),X1)
| ~ aElementOf0(sdtasdt0(sk1_esk3_1(X1),sk1_esk1_1(X1)),X1) ),
inference(unfold_definition,[status(thm)],[c_0_91,def_lhs_atom13]) ).
cnf(c_0_92_0,axiom,
( aIdeal0(X1)
| aElementOf0(sk1_esk2_1(X1),X1)
| ~ aSet0(X1)
| ~ aElementOf0(sdtasdt0(sk1_esk3_1(X1),sk1_esk1_1(X1)),X1) ),
inference(unfold_definition,[status(thm)],[c_0_92,def_lhs_atom13]) ).
cnf(c_0_93_0,axiom,
( aIdeal0(X1)
| aElement0(sk1_esk3_1(X1))
| ~ aSet0(X1)
| ~ aElementOf0(sdtpldt0(sk1_esk1_1(X1),sk1_esk2_1(X1)),X1) ),
inference(unfold_definition,[status(thm)],[c_0_93,def_lhs_atom13]) ).
cnf(c_0_94_0,axiom,
( ~ aIdeal0(X1)
| aElementOf0(sdtpldt0(X2,X3),X1)
| ~ aElementOf0(X2,X1)
| ~ aElementOf0(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_94,def_lhs_atom12]) ).
cnf(c_0_95_0,axiom,
( sdtasdt0(sdtasdt0(X3,X2),X1) = sdtasdt0(X3,sdtasdt0(X2,X1))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(unfold_definition,[status(thm)],[c_0_95,def_lhs_atom9]) ).
cnf(c_0_96_0,axiom,
( sdtpldt0(sdtpldt0(X3,X2),X1) = sdtpldt0(X3,sdtpldt0(X2,X1))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(unfold_definition,[status(thm)],[c_0_96,def_lhs_atom7]) ).
cnf(c_0_97_0,axiom,
( ~ aIdeal0(X1)
| aElementOf0(sdtasdt0(X3,X2),X1)
| ~ aElementOf0(X2,X1)
| ~ aElement0(X3) ),
inference(unfold_definition,[status(thm)],[c_0_97,def_lhs_atom12]) ).
cnf(c_0_98_0,axiom,
( aIdeal0(X1)
| aElementOf0(sk1_esk2_1(X1),X1)
| aElement0(sk1_esk3_1(X1))
| ~ aSet0(X1) ),
inference(unfold_definition,[status(thm)],[c_0_98,def_lhs_atom13]) ).
cnf(c_0_99_0,axiom,
( aIdeal0(X1)
| aElementOf0(sk1_esk1_1(X1),X1)
| ~ aSet0(X1) ),
inference(unfold_definition,[status(thm)],[c_0_99,def_lhs_atom13]) ).
cnf(c_0_100_0,axiom,
( ~ aSet0(X2)
| aElement0(X1)
| ~ aElementOf0(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_100,def_lhs_atom11]) ).
cnf(c_0_101_0,axiom,
( sdtasdt0(X2,X1) = sdtasdt0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(unfold_definition,[status(thm)],[c_0_101,def_lhs_atom8]) ).
cnf(c_0_102_0,axiom,
( sdtpldt0(X2,X1) = sdtpldt0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(unfold_definition,[status(thm)],[c_0_102,def_lhs_atom6]) ).
cnf(c_0_103_0,axiom,
( aElement0(sdtasdt0(X2,X1))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(unfold_definition,[status(thm)],[c_0_103,def_lhs_atom5]) ).
cnf(c_0_104_0,axiom,
( aElement0(sdtpldt0(X2,X1))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(unfold_definition,[status(thm)],[c_0_104,def_lhs_atom4]) ).
cnf(c_0_105_0,axiom,
( ~ aElement0(X1)
| sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ),
inference(unfold_definition,[status(thm)],[c_0_105,def_lhs_atom1]) ).
cnf(c_0_106_0,axiom,
( ~ aElement0(X1)
| sdtasdt0(X1,smndt0(sz10)) = smndt0(X1) ),
inference(unfold_definition,[status(thm)],[c_0_106,def_lhs_atom1]) ).
cnf(c_0_107_0,axiom,
( ~ aElement0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(unfold_definition,[status(thm)],[c_0_107,def_lhs_atom1]) ).
cnf(c_0_108_0,axiom,
( ~ aElement0(X1)
| sdtpldt0(smndt0(X1),X1) = sz00 ),
inference(unfold_definition,[status(thm)],[c_0_108,def_lhs_atom1]) ).
cnf(c_0_109_0,axiom,
( ~ aElement0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_109,def_lhs_atom1]) ).
cnf(c_0_110_0,axiom,
( ~ aElement0(X1)
| sdtasdt0(sz10,X1) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_110,def_lhs_atom1]) ).
cnf(c_0_111_0,axiom,
( ~ aElement0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_111,def_lhs_atom1]) ).
cnf(c_0_112_0,axiom,
( ~ aElement0(X1)
| sdtpldt0(sz00,X1) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_112,def_lhs_atom1]) ).
cnf(c_0_113_0,axiom,
( ~ aElement0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(unfold_definition,[status(thm)],[c_0_113,def_lhs_atom1]) ).
cnf(c_0_114_0,axiom,
( ~ aElement0(X1)
| sdtasdt0(sz00,X1) = sz00 ),
inference(unfold_definition,[status(thm)],[c_0_114,def_lhs_atom1]) ).
cnf(c_0_115_0,axiom,
( ~ aElement0(X1)
| aElement0(smndt0(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_115,def_lhs_atom1]) ).
cnf(c_0_116_0,axiom,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(unfold_definition,[status(thm)],[c_0_116,def_lhs_atom12]) ).
cnf(c_0_117_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_117,def_true]) ).
cnf(c_0_118_0,axiom,
sz10 != sz00,
inference(unfold_definition,[status(thm)],[c_0_118,def_lhs_atom10]) ).
cnf(c_0_119_0,axiom,
aElement0(sz10),
inference(unfold_definition,[status(thm)],[c_0_119,def_lhs_atom3]) ).
cnf(c_0_120_0,axiom,
aElement0(sz00),
inference(unfold_definition,[status(thm)],[c_0_120,def_lhs_atom2]) ).
cnf(c_0_121_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_121,def_true]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,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('<stdin>',mDefSSum) ).
fof(c_0_1_002,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('<stdin>',mDefSInt) ).
fof(c_0_2_003,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ( ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(X3,X2) )
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) )
=> X1 = X2 ) ),
file('<stdin>',mSetEq) ).
fof(c_0_3_004,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('<stdin>',mAMDistr) ).
fof(c_0_4_005,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('<stdin>',mCancel) ).
fof(c_0_5_006,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 ) ) ) ) ),
c_0_0 ).
fof(c_0_6_007,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ! [X3] :
( X3 = sdtasasdt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElementOf0(X4,X1)
& aElementOf0(X4,X2) ) ) ) ) ),
c_0_1 ).
fof(c_0_7_008,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ( ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(X3,X2) )
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) )
=> X1 = X2 ) ),
c_0_2 ).
fof(c_0_8_009,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)) ) ),
c_0_3 ).
fof(c_0_9_010,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
c_0_4 ).
fof(c_0_10_011,plain,
! [X7,X8,X9,X10,X13,X14,X15,X16,X18,X19] :
( ( aSet0(X9)
| X9 != sdtpldt1(X7,X8)
| ~ aSet0(X7)
| ~ aSet0(X8) )
& ( aElementOf0(esk2_4(X7,X8,X9,X10),X7)
| ~ aElementOf0(X10,X9)
| X9 != sdtpldt1(X7,X8)
| ~ aSet0(X7)
| ~ aSet0(X8) )
& ( aElementOf0(esk3_4(X7,X8,X9,X10),X8)
| ~ aElementOf0(X10,X9)
| X9 != sdtpldt1(X7,X8)
| ~ aSet0(X7)
| ~ aSet0(X8) )
& ( sdtpldt0(esk2_4(X7,X8,X9,X10),esk3_4(X7,X8,X9,X10)) = X10
| ~ aElementOf0(X10,X9)
| X9 != sdtpldt1(X7,X8)
| ~ aSet0(X7)
| ~ aSet0(X8) )
& ( ~ aElementOf0(X14,X7)
| ~ aElementOf0(X15,X8)
| sdtpldt0(X14,X15) != X13
| aElementOf0(X13,X9)
| X9 != sdtpldt1(X7,X8)
| ~ aSet0(X7)
| ~ aSet0(X8) )
& ( ~ aElementOf0(esk4_3(X7,X8,X16),X16)
| ~ aElementOf0(X18,X7)
| ~ aElementOf0(X19,X8)
| sdtpldt0(X18,X19) != esk4_3(X7,X8,X16)
| ~ aSet0(X16)
| X16 = sdtpldt1(X7,X8)
| ~ aSet0(X7)
| ~ aSet0(X8) )
& ( aElementOf0(esk5_3(X7,X8,X16),X7)
| aElementOf0(esk4_3(X7,X8,X16),X16)
| ~ aSet0(X16)
| X16 = sdtpldt1(X7,X8)
| ~ aSet0(X7)
| ~ aSet0(X8) )
& ( aElementOf0(esk6_3(X7,X8,X16),X8)
| aElementOf0(esk4_3(X7,X8,X16),X16)
| ~ aSet0(X16)
| X16 = sdtpldt1(X7,X8)
| ~ aSet0(X7)
| ~ aSet0(X8) )
& ( sdtpldt0(esk5_3(X7,X8,X16),esk6_3(X7,X8,X16)) = esk4_3(X7,X8,X16)
| aElementOf0(esk4_3(X7,X8,X16),X16)
| ~ aSet0(X16)
| X16 = sdtpldt1(X7,X8)
| ~ aSet0(X7)
| ~ aSet0(X8) ) ),
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)],[c_0_5])])])])])]) ).
fof(c_0_11_012,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( aSet0(X7)
| X7 != sdtasasdt0(X5,X6)
| ~ aSet0(X5)
| ~ aSet0(X6) )
& ( aElementOf0(X8,X5)
| ~ aElementOf0(X8,X7)
| X7 != sdtasasdt0(X5,X6)
| ~ aSet0(X5)
| ~ aSet0(X6) )
& ( aElementOf0(X8,X6)
| ~ aElementOf0(X8,X7)
| X7 != sdtasasdt0(X5,X6)
| ~ aSet0(X5)
| ~ aSet0(X6) )
& ( ~ aElementOf0(X9,X5)
| ~ aElementOf0(X9,X6)
| aElementOf0(X9,X7)
| X7 != sdtasasdt0(X5,X6)
| ~ aSet0(X5)
| ~ aSet0(X6) )
& ( ~ aElementOf0(esk1_3(X5,X6,X10),X10)
| ~ aElementOf0(esk1_3(X5,X6,X10),X5)
| ~ aElementOf0(esk1_3(X5,X6,X10),X6)
| ~ aSet0(X10)
| X10 = sdtasasdt0(X5,X6)
| ~ aSet0(X5)
| ~ aSet0(X6) )
& ( aElementOf0(esk1_3(X5,X6,X10),X5)
| aElementOf0(esk1_3(X5,X6,X10),X10)
| ~ aSet0(X10)
| X10 = sdtasasdt0(X5,X6)
| ~ aSet0(X5)
| ~ aSet0(X6) )
& ( aElementOf0(esk1_3(X5,X6,X10),X6)
| aElementOf0(esk1_3(X5,X6,X10),X10)
| ~ aSet0(X10)
| X10 = sdtasasdt0(X5,X6)
| ~ aSet0(X5)
| ~ aSet0(X6) ) ),
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)],[c_0_6])])])])])]) ).
fof(c_0_12_013,plain,
! [X4,X5] :
( ( aElementOf0(esk8_2(X4,X5),X5)
| aElementOf0(esk7_2(X4,X5),X4)
| X4 = X5
| ~ aSet0(X4)
| ~ aSet0(X5) )
& ( ~ aElementOf0(esk8_2(X4,X5),X4)
| aElementOf0(esk7_2(X4,X5),X4)
| X4 = X5
| ~ aSet0(X4)
| ~ aSet0(X5) )
& ( aElementOf0(esk8_2(X4,X5),X5)
| ~ aElementOf0(esk7_2(X4,X5),X5)
| X4 = X5
| ~ aSet0(X4)
| ~ aSet0(X5) )
& ( ~ aElementOf0(esk8_2(X4,X5),X4)
| ~ aElementOf0(esk7_2(X4,X5),X5)
| X4 = X5
| ~ aSet0(X4)
| ~ aSet0(X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_13_014,plain,
! [X4,X5,X6] :
( ( sdtasdt0(X4,sdtpldt0(X5,X6)) = sdtpldt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
| ~ aElement0(X4)
| ~ aElement0(X5)
| ~ aElement0(X6) )
& ( sdtasdt0(sdtpldt0(X5,X6),X4) = sdtpldt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
| ~ aElement0(X4)
| ~ aElement0(X5)
| ~ aElement0(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_14_015,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| sdtasdt0(X3,X4) != sz00
| X3 = sz00
| X4 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
cnf(c_0_15_016,plain,
( sdtpldt0(esk2_4(X2,X1,X3,X4),esk3_4(X2,X1,X3,X4)) = X4
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16_017,plain,
( X3 = sdtasasdt0(X2,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aElementOf0(esk1_3(X2,X1,X3),X1)
| ~ aElementOf0(esk1_3(X2,X1,X3),X2)
| ~ aElementOf0(esk1_3(X2,X1,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17_018,plain,
( aElementOf0(esk2_4(X2,X1,X3,X4),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18_019,plain,
( aElementOf0(esk3_4(X2,X1,X3,X4),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19_020,plain,
( X3 = sdtpldt1(X2,X1)
| aElementOf0(esk4_3(X2,X1,X3),X3)
| sdtpldt0(esk5_3(X2,X1,X3),esk6_3(X2,X1,X3)) = esk4_3(X2,X1,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20_021,plain,
( X3 = sdtpldt1(X2,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| sdtpldt0(X4,X5) != esk4_3(X2,X1,X3)
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X2)
| ~ aElementOf0(esk4_3(X2,X1,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21_022,plain,
( X3 = sdtpldt1(X2,X1)
| aElementOf0(esk4_3(X2,X1,X3),X3)
| aElementOf0(esk5_3(X2,X1,X3),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22_023,plain,
( X3 = sdtpldt1(X2,X1)
| aElementOf0(esk4_3(X2,X1,X3),X3)
| aElementOf0(esk6_3(X2,X1,X3),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23_024,plain,
( X3 = sdtasasdt0(X2,X1)
| aElementOf0(esk1_3(X2,X1,X3),X3)
| aElementOf0(esk1_3(X2,X1,X3),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24_025,plain,
( X3 = sdtasasdt0(X2,X1)
| aElementOf0(esk1_3(X2,X1,X3),X3)
| aElementOf0(esk1_3(X2,X1,X3),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25_026,plain,
( X2 = X1
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk7_2(X2,X1),X1)
| ~ aElementOf0(esk8_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26_027,plain,
( sdtasdt0(X3,sdtpldt0(X2,X1)) = sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27_028,plain,
( sdtasdt0(sdtpldt0(X2,X1),X3) = sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28_029,plain,
( aElementOf0(X4,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,X1)
| ~ aElementOf0(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_29_030,plain,
( X2 = X1
| aElementOf0(esk7_2(X2,X1),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk8_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30_031,plain,
( X2 = X1
| aElementOf0(esk8_2(X2,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk7_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_31_032,plain,
( aElementOf0(X4,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32_033,plain,
( X2 = X1
| aElementOf0(esk7_2(X2,X1),X2)
| aElementOf0(esk8_2(X2,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_33_034,plain,
( aElementOf0(X4,X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34_035,plain,
( aElementOf0(X4,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_35_036,plain,
( aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_36_037,plain,
( aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_37_038,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_38_039,plain,
( sdtpldt0(esk2_4(X2,X1,X3,X4),esk3_4(X2,X1,X3,X4)) = X4
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
c_0_15,
[final] ).
cnf(c_0_39_040,plain,
( X3 = sdtasasdt0(X2,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aElementOf0(esk1_3(X2,X1,X3),X1)
| ~ aElementOf0(esk1_3(X2,X1,X3),X2)
| ~ aElementOf0(esk1_3(X2,X1,X3),X3) ),
c_0_16,
[final] ).
cnf(c_0_40_041,plain,
( aElementOf0(esk2_4(X2,X1,X3,X4),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
c_0_17,
[final] ).
cnf(c_0_41_042,plain,
( aElementOf0(esk3_4(X2,X1,X3,X4),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
c_0_18,
[final] ).
cnf(c_0_42_043,plain,
( X3 = sdtpldt1(X2,X1)
| aElementOf0(esk4_3(X2,X1,X3),X3)
| sdtpldt0(esk5_3(X2,X1,X3),esk6_3(X2,X1,X3)) = esk4_3(X2,X1,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
c_0_19,
[final] ).
cnf(c_0_43_044,plain,
( X3 = sdtpldt1(X2,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| sdtpldt0(X4,X5) != esk4_3(X2,X1,X3)
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X2)
| ~ aElementOf0(esk4_3(X2,X1,X3),X3) ),
c_0_20,
[final] ).
cnf(c_0_44_045,plain,
( X3 = sdtpldt1(X2,X1)
| aElementOf0(esk4_3(X2,X1,X3),X3)
| aElementOf0(esk5_3(X2,X1,X3),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
c_0_21,
[final] ).
cnf(c_0_45_046,plain,
( X3 = sdtpldt1(X2,X1)
| aElementOf0(esk4_3(X2,X1,X3),X3)
| aElementOf0(esk6_3(X2,X1,X3),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
c_0_22,
[final] ).
cnf(c_0_46_047,plain,
( X3 = sdtasasdt0(X2,X1)
| aElementOf0(esk1_3(X2,X1,X3),X3)
| aElementOf0(esk1_3(X2,X1,X3),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
c_0_23,
[final] ).
cnf(c_0_47_048,plain,
( X3 = sdtasasdt0(X2,X1)
| aElementOf0(esk1_3(X2,X1,X3),X3)
| aElementOf0(esk1_3(X2,X1,X3),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
c_0_24,
[final] ).
cnf(c_0_48_049,plain,
( X2 = X1
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk7_2(X2,X1),X1)
| ~ aElementOf0(esk8_2(X2,X1),X2) ),
c_0_25,
[final] ).
cnf(c_0_49_050,plain,
( sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1)) = sdtasdt0(X3,sdtpldt0(X2,X1))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
c_0_26,
[final] ).
cnf(c_0_50_051,plain,
( sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3)) = sdtasdt0(sdtpldt0(X2,X1),X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
c_0_27,
[final] ).
cnf(c_0_51_052,plain,
( aElementOf0(X4,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,X1)
| ~ aElementOf0(X5,X2) ),
c_0_28,
[final] ).
cnf(c_0_52_053,plain,
( X2 = X1
| aElementOf0(esk7_2(X2,X1),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk8_2(X2,X1),X2) ),
c_0_29,
[final] ).
cnf(c_0_53_054,plain,
( X2 = X1
| aElementOf0(esk8_2(X2,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk7_2(X2,X1),X1) ),
c_0_30,
[final] ).
cnf(c_0_54_055,plain,
( aElementOf0(X4,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2) ),
c_0_31,
[final] ).
cnf(c_0_55_056,plain,
( X2 = X1
| aElementOf0(esk7_2(X2,X1),X2)
| aElementOf0(esk8_2(X2,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
c_0_32,
[final] ).
cnf(c_0_56_057,plain,
( aElementOf0(X4,X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X3) ),
c_0_33,
[final] ).
cnf(c_0_57_058,plain,
( aElementOf0(X4,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X3) ),
c_0_34,
[final] ).
cnf(c_0_58_059,plain,
( aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1) ),
c_0_35,
[final] ).
cnf(c_0_59_060,plain,
( aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1) ),
c_0_36,
[final] ).
cnf(c_0_60_061,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
c_0_37,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_38_0,axiom,
( sdtpldt0(sk2_esk2_4(X2,X1,X3,X4),sk2_esk3_4(X2,X1,X3,X4)) = X4
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_38]) ).
cnf(c_0_38_1,axiom,
( ~ aSet0(X1)
| sdtpldt0(sk2_esk2_4(X2,X1,X3,X4),sk2_esk3_4(X2,X1,X3,X4)) = X4
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_38]) ).
cnf(c_0_38_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| sdtpldt0(sk2_esk2_4(X2,X1,X3,X4),sk2_esk3_4(X2,X1,X3,X4)) = X4
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_38]) ).
cnf(c_0_38_3,axiom,
( X3 != sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| sdtpldt0(sk2_esk2_4(X2,X1,X3,X4),sk2_esk3_4(X2,X1,X3,X4)) = X4
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_38]) ).
cnf(c_0_38_4,axiom,
( ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| sdtpldt0(sk2_esk2_4(X2,X1,X3,X4),sk2_esk3_4(X2,X1,X3,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_38]) ).
cnf(c_0_39_0,axiom,
( X3 = sdtasasdt0(X2,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_39]) ).
cnf(c_0_39_1,axiom,
( ~ aSet0(X1)
| X3 = sdtasasdt0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_39]) ).
cnf(c_0_39_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| X3 = sdtasasdt0(X2,X1)
| ~ aSet0(X3)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_39]) ).
cnf(c_0_39_3,axiom,
( ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X3 = sdtasasdt0(X2,X1)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_39]) ).
cnf(c_0_39_4,axiom,
( ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X3 = sdtasasdt0(X2,X1)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_39]) ).
cnf(c_0_39_5,axiom,
( ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X3 = sdtasasdt0(X2,X1)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_39]) ).
cnf(c_0_39_6,axiom,
( ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| ~ aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X3 = sdtasasdt0(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_39]) ).
cnf(c_0_40_0,axiom,
( aElementOf0(sk2_esk2_4(X2,X1,X3,X4),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_40]) ).
cnf(c_0_40_1,axiom,
( ~ aSet0(X1)
| aElementOf0(sk2_esk2_4(X2,X1,X3,X4),X2)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_40]) ).
cnf(c_0_40_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk2_4(X2,X1,X3,X4),X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_40]) ).
cnf(c_0_40_3,axiom,
( X3 != sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk2_4(X2,X1,X3,X4),X2)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_40]) ).
cnf(c_0_40_4,axiom,
( ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk2_4(X2,X1,X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_40]) ).
cnf(c_0_41_0,axiom,
( aElementOf0(sk2_esk3_4(X2,X1,X3,X4),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_41]) ).
cnf(c_0_41_1,axiom,
( ~ aSet0(X1)
| aElementOf0(sk2_esk3_4(X2,X1,X3,X4),X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_41]) ).
cnf(c_0_41_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk3_4(X2,X1,X3,X4),X1)
| X3 != sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_41]) ).
cnf(c_0_41_3,axiom,
( X3 != sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk3_4(X2,X1,X3,X4),X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_41]) ).
cnf(c_0_41_4,axiom,
( ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk3_4(X2,X1,X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_41]) ).
cnf(c_0_42_0,axiom,
( X3 = sdtpldt1(X2,X1)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| sdtpldt0(sk2_esk5_3(X2,X1,X3),sk2_esk6_3(X2,X1,X3)) = sk2_esk4_3(X2,X1,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_42]) ).
cnf(c_0_42_1,axiom,
( aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| sdtpldt0(sk2_esk5_3(X2,X1,X3),sk2_esk6_3(X2,X1,X3)) = sk2_esk4_3(X2,X1,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_42]) ).
cnf(c_0_42_2,axiom,
( sdtpldt0(sk2_esk5_3(X2,X1,X3),sk2_esk6_3(X2,X1,X3)) = sk2_esk4_3(X2,X1,X3)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_42]) ).
cnf(c_0_42_3,axiom,
( ~ aSet0(X1)
| sdtpldt0(sk2_esk5_3(X2,X1,X3),sk2_esk6_3(X2,X1,X3)) = sk2_esk4_3(X2,X1,X3)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_42]) ).
cnf(c_0_42_4,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| sdtpldt0(sk2_esk5_3(X2,X1,X3),sk2_esk6_3(X2,X1,X3)) = sk2_esk4_3(X2,X1,X3)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_42]) ).
cnf(c_0_42_5,axiom,
( ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| sdtpldt0(sk2_esk5_3(X2,X1,X3),sk2_esk6_3(X2,X1,X3)) = sk2_esk4_3(X2,X1,X3)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_42]) ).
cnf(c_0_43_0,axiom,
( X3 = sdtpldt1(X2,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| sdtpldt0(X4,X5) != sk2_esk4_3(X2,X1,X3)
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X2)
| ~ aElementOf0(sk2_esk4_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_43]) ).
cnf(c_0_43_1,axiom,
( ~ aSet0(X1)
| X3 = sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| sdtpldt0(X4,X5) != sk2_esk4_3(X2,X1,X3)
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X2)
| ~ aElementOf0(sk2_esk4_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_43]) ).
cnf(c_0_43_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| X3 = sdtpldt1(X2,X1)
| ~ aSet0(X3)
| sdtpldt0(X4,X5) != sk2_esk4_3(X2,X1,X3)
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X2)
| ~ aElementOf0(sk2_esk4_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_43]) ).
cnf(c_0_43_3,axiom,
( ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X3 = sdtpldt1(X2,X1)
| sdtpldt0(X4,X5) != sk2_esk4_3(X2,X1,X3)
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X2)
| ~ aElementOf0(sk2_esk4_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_43]) ).
cnf(c_0_43_4,axiom,
( sdtpldt0(X4,X5) != sk2_esk4_3(X2,X1,X3)
| ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X3 = sdtpldt1(X2,X1)
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X2)
| ~ aElementOf0(sk2_esk4_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_43]) ).
cnf(c_0_43_5,axiom,
( ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != sk2_esk4_3(X2,X1,X3)
| ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X3 = sdtpldt1(X2,X1)
| ~ aElementOf0(X4,X2)
| ~ aElementOf0(sk2_esk4_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_43]) ).
cnf(c_0_43_6,axiom,
( ~ aElementOf0(X4,X2)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != sk2_esk4_3(X2,X1,X3)
| ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X3 = sdtpldt1(X2,X1)
| ~ aElementOf0(sk2_esk4_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_43]) ).
cnf(c_0_43_7,axiom,
( ~ aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| ~ aElementOf0(X4,X2)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != sk2_esk4_3(X2,X1,X3)
| ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X3 = sdtpldt1(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_43]) ).
cnf(c_0_44_0,axiom,
( X3 = sdtpldt1(X2,X1)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| aElementOf0(sk2_esk5_3(X2,X1,X3),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_44]) ).
cnf(c_0_44_1,axiom,
( aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| aElementOf0(sk2_esk5_3(X2,X1,X3),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_44]) ).
cnf(c_0_44_2,axiom,
( aElementOf0(sk2_esk5_3(X2,X1,X3),X2)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_44]) ).
cnf(c_0_44_3,axiom,
( ~ aSet0(X1)
| aElementOf0(sk2_esk5_3(X2,X1,X3),X2)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_44]) ).
cnf(c_0_44_4,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk5_3(X2,X1,X3),X2)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_44]) ).
cnf(c_0_44_5,axiom,
( ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk5_3(X2,X1,X3),X2)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_44]) ).
cnf(c_0_45_0,axiom,
( X3 = sdtpldt1(X2,X1)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| aElementOf0(sk2_esk6_3(X2,X1,X3),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_45]) ).
cnf(c_0_45_1,axiom,
( aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| aElementOf0(sk2_esk6_3(X2,X1,X3),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_45]) ).
cnf(c_0_45_2,axiom,
( aElementOf0(sk2_esk6_3(X2,X1,X3),X1)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_45]) ).
cnf(c_0_45_3,axiom,
( ~ aSet0(X1)
| aElementOf0(sk2_esk6_3(X2,X1,X3),X1)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_45]) ).
cnf(c_0_45_4,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk6_3(X2,X1,X3),X1)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_45]) ).
cnf(c_0_45_5,axiom,
( ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk6_3(X2,X1,X3),X1)
| aElementOf0(sk2_esk4_3(X2,X1,X3),X3)
| X3 = sdtpldt1(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_45]) ).
cnf(c_0_46_0,axiom,
( X3 = sdtasasdt0(X2,X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_46]) ).
cnf(c_0_46_1,axiom,
( aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| X3 = sdtasasdt0(X2,X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_46]) ).
cnf(c_0_46_2,axiom,
( aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| X3 = sdtasasdt0(X2,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_46]) ).
cnf(c_0_46_3,axiom,
( ~ aSet0(X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| X3 = sdtasasdt0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_46]) ).
cnf(c_0_46_4,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| X3 = sdtasasdt0(X2,X1)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_46]) ).
cnf(c_0_46_5,axiom,
( ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X2)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| X3 = sdtasasdt0(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_46]) ).
cnf(c_0_47_0,axiom,
( X3 = sdtasasdt0(X2,X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_47]) ).
cnf(c_0_47_1,axiom,
( aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| X3 = sdtasasdt0(X2,X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_47]) ).
cnf(c_0_47_2,axiom,
( aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| X3 = sdtasasdt0(X2,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_47]) ).
cnf(c_0_47_3,axiom,
( ~ aSet0(X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| X3 = sdtasasdt0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_47]) ).
cnf(c_0_47_4,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| X3 = sdtasasdt0(X2,X1)
| ~ aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_47]) ).
cnf(c_0_47_5,axiom,
( ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X1)
| aElementOf0(sk2_esk1_3(X2,X1,X3),X3)
| X3 = sdtasasdt0(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_47]) ).
cnf(c_0_48_0,axiom,
( X2 = X1
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sk2_esk7_2(X2,X1),X1)
| ~ aElementOf0(sk2_esk8_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_48]) ).
cnf(c_0_48_1,axiom,
( ~ aSet0(X1)
| X2 = X1
| ~ aSet0(X2)
| ~ aElementOf0(sk2_esk7_2(X2,X1),X1)
| ~ aElementOf0(sk2_esk8_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_48]) ).
cnf(c_0_48_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| X2 = X1
| ~ aElementOf0(sk2_esk7_2(X2,X1),X1)
| ~ aElementOf0(sk2_esk8_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_48]) ).
cnf(c_0_48_3,axiom,
( ~ aElementOf0(sk2_esk7_2(X2,X1),X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X2 = X1
| ~ aElementOf0(sk2_esk8_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_48]) ).
cnf(c_0_48_4,axiom,
( ~ aElementOf0(sk2_esk8_2(X2,X1),X2)
| ~ aElementOf0(sk2_esk7_2(X2,X1),X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_48]) ).
cnf(c_0_49_0,axiom,
( sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1)) = sdtasdt0(X3,sdtpldt0(X2,X1))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_49]) ).
cnf(c_0_49_1,axiom,
( ~ aElement0(X1)
| sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1)) = sdtasdt0(X3,sdtpldt0(X2,X1))
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_49]) ).
cnf(c_0_49_2,axiom,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1)) = sdtasdt0(X3,sdtpldt0(X2,X1))
| ~ aElement0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_49]) ).
cnf(c_0_49_3,axiom,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1)) = sdtasdt0(X3,sdtpldt0(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_49]) ).
cnf(c_0_50_0,axiom,
( sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3)) = sdtasdt0(sdtpldt0(X2,X1),X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_50]) ).
cnf(c_0_50_1,axiom,
( ~ aElement0(X1)
| sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3)) = sdtasdt0(sdtpldt0(X2,X1),X3)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_50]) ).
cnf(c_0_50_2,axiom,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3)) = sdtasdt0(sdtpldt0(X2,X1),X3)
| ~ aElement0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_50]) ).
cnf(c_0_50_3,axiom,
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3)) = sdtasdt0(sdtpldt0(X2,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_50]) ).
cnf(c_0_51_0,axiom,
( aElementOf0(X4,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,X1)
| ~ aElementOf0(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_51]) ).
cnf(c_0_51_1,axiom,
( ~ aSet0(X1)
| aElementOf0(X4,X3)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1)
| sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,X1)
| ~ aElementOf0(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_51]) ).
cnf(c_0_51_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X3)
| X3 != sdtpldt1(X2,X1)
| sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,X1)
| ~ aElementOf0(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_51]) ).
cnf(c_0_51_3,axiom,
( X3 != sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X3)
| sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,X1)
| ~ aElementOf0(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_51]) ).
cnf(c_0_51_4,axiom,
( sdtpldt0(X5,X6) != X4
| X3 != sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X3)
| ~ aElementOf0(X6,X1)
| ~ aElementOf0(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_51]) ).
cnf(c_0_51_5,axiom,
( ~ aElementOf0(X6,X1)
| sdtpldt0(X5,X6) != X4
| X3 != sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X3)
| ~ aElementOf0(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_51]) ).
cnf(c_0_51_6,axiom,
( ~ aElementOf0(X5,X2)
| ~ aElementOf0(X6,X1)
| sdtpldt0(X5,X6) != X4
| X3 != sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_51]) ).
cnf(c_0_52_0,axiom,
( X2 = X1
| aElementOf0(sk2_esk7_2(X2,X1),X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sk2_esk8_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_52]) ).
cnf(c_0_52_1,axiom,
( aElementOf0(sk2_esk7_2(X2,X1),X2)
| X2 = X1
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sk2_esk8_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_52]) ).
cnf(c_0_52_2,axiom,
( ~ aSet0(X1)
| aElementOf0(sk2_esk7_2(X2,X1),X2)
| X2 = X1
| ~ aSet0(X2)
| ~ aElementOf0(sk2_esk8_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_52]) ).
cnf(c_0_52_3,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk7_2(X2,X1),X2)
| X2 = X1
| ~ aElementOf0(sk2_esk8_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_52]) ).
cnf(c_0_52_4,axiom,
( ~ aElementOf0(sk2_esk8_2(X2,X1),X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk7_2(X2,X1),X2)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_52]) ).
cnf(c_0_53_0,axiom,
( X2 = X1
| aElementOf0(sk2_esk8_2(X2,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sk2_esk7_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_53]) ).
cnf(c_0_53_1,axiom,
( aElementOf0(sk2_esk8_2(X2,X1),X1)
| X2 = X1
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sk2_esk7_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_53]) ).
cnf(c_0_53_2,axiom,
( ~ aSet0(X1)
| aElementOf0(sk2_esk8_2(X2,X1),X1)
| X2 = X1
| ~ aSet0(X2)
| ~ aElementOf0(sk2_esk7_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_53]) ).
cnf(c_0_53_3,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk8_2(X2,X1),X1)
| X2 = X1
| ~ aElementOf0(sk2_esk7_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_53]) ).
cnf(c_0_53_4,axiom,
( ~ aElementOf0(sk2_esk7_2(X2,X1),X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk8_2(X2,X1),X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_53]) ).
cnf(c_0_54_0,axiom,
( aElementOf0(X4,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_54]) ).
cnf(c_0_54_1,axiom,
( ~ aSet0(X1)
| aElementOf0(X4,X3)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_54]) ).
cnf(c_0_54_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X3)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_54]) ).
cnf(c_0_54_3,axiom,
( X3 != sdtasasdt0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X3)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_54]) ).
cnf(c_0_54_4,axiom,
( ~ aElementOf0(X4,X1)
| X3 != sdtasasdt0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X3)
| ~ aElementOf0(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_54]) ).
cnf(c_0_54_5,axiom,
( ~ aElementOf0(X4,X2)
| ~ aElementOf0(X4,X1)
| X3 != sdtasasdt0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_54]) ).
cnf(c_0_55_0,axiom,
( X2 = X1
| aElementOf0(sk2_esk7_2(X2,X1),X2)
| aElementOf0(sk2_esk8_2(X2,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_55]) ).
cnf(c_0_55_1,axiom,
( aElementOf0(sk2_esk7_2(X2,X1),X2)
| X2 = X1
| aElementOf0(sk2_esk8_2(X2,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_55]) ).
cnf(c_0_55_2,axiom,
( aElementOf0(sk2_esk8_2(X2,X1),X1)
| aElementOf0(sk2_esk7_2(X2,X1),X2)
| X2 = X1
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_55]) ).
cnf(c_0_55_3,axiom,
( ~ aSet0(X1)
| aElementOf0(sk2_esk8_2(X2,X1),X1)
| aElementOf0(sk2_esk7_2(X2,X1),X2)
| X2 = X1
| ~ aSet0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_55]) ).
cnf(c_0_55_4,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(sk2_esk8_2(X2,X1),X1)
| aElementOf0(sk2_esk7_2(X2,X1),X2)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_55]) ).
cnf(c_0_56_0,axiom,
( aElementOf0(X4,X2)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_56]) ).
cnf(c_0_56_1,axiom,
( ~ aSet0(X1)
| aElementOf0(X4,X2)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_56]) ).
cnf(c_0_56_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_56]) ).
cnf(c_0_56_3,axiom,
( X3 != sdtasasdt0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X2)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_56]) ).
cnf(c_0_56_4,axiom,
( ~ aElementOf0(X4,X3)
| X3 != sdtasasdt0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_56]) ).
cnf(c_0_57_0,axiom,
( aElementOf0(X4,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_57]) ).
cnf(c_0_57_1,axiom,
( ~ aSet0(X1)
| aElementOf0(X4,X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_57]) ).
cnf(c_0_57_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X1)
| X3 != sdtasasdt0(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_57]) ).
cnf(c_0_57_3,axiom,
( X3 != sdtasasdt0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X1)
| ~ aElementOf0(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_57]) ).
cnf(c_0_57_4,axiom,
( ~ aElementOf0(X4,X3)
| X3 != sdtasasdt0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aElementOf0(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_57]) ).
cnf(c_0_58_0,axiom,
( aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_58]) ).
cnf(c_0_58_1,axiom,
( ~ aSet0(X1)
| aSet0(X3)
| ~ aSet0(X2)
| X3 != sdtpldt1(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_58]) ).
cnf(c_0_58_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aSet0(X3)
| X3 != sdtpldt1(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_58]) ).
cnf(c_0_58_3,axiom,
( X3 != sdtpldt1(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_58]) ).
cnf(c_0_59_0,axiom,
( aSet0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_59]) ).
cnf(c_0_59_1,axiom,
( ~ aSet0(X1)
| aSet0(X3)
| ~ aSet0(X2)
| X3 != sdtasasdt0(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_59]) ).
cnf(c_0_59_2,axiom,
( ~ aSet0(X2)
| ~ aSet0(X1)
| aSet0(X3)
| X3 != sdtasasdt0(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_59]) ).
cnf(c_0_59_3,axiom,
( X3 != sdtasasdt0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aSet0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_59]) ).
cnf(c_0_60_0,axiom,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_60]) ).
cnf(c_0_60_1,axiom,
( X2 = sz00
| X1 = sz00
| sdtasdt0(X2,X1) != sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_60]) ).
cnf(c_0_60_2,axiom,
( sdtasdt0(X2,X1) != sz00
| X2 = sz00
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_60]) ).
cnf(c_0_60_3,axiom,
( ~ aElement0(X1)
| sdtasdt0(X2,X1) != sz00
| X2 = sz00
| X1 = sz00
| ~ aElement0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_60]) ).
cnf(c_0_60_4,axiom,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(X2,X1) != sz00
| X2 = sz00
| X1 = sz00 ),
inference(literals_permutation,[status(thm)],[c_0_60]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_062,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('<stdin>',m__870) ).
fof(c_0_1_063,conjecture,
? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& xy = sdtpldt0(X1,X2) ),
file('<stdin>',m__) ).
fof(c_0_2_064,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('<stdin>',m__901) ).
fof(c_0_3_065,hypothesis,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('<stdin>',m__934) ).
fof(c_0_4_066,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) ),
c_0_0 ).
fof(c_0_5_067,negated_conjecture,
~ ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& xy = sdtpldt0(X1,X2) ),
inference(assume_negation,[status(cth)],[c_0_1]) ).
fof(c_0_6_068,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) ),
c_0_2 ).
fof(c_0_7_069,hypothesis,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
c_0_3 ).
fof(c_0_8_070,hypothesis,
! [X3,X4,X5,X6,X7,X8] :
( aSet0(xI)
& ( ~ aElementOf0(X4,xI)
| aElementOf0(sdtpldt0(X3,X4),xI)
| ~ aElementOf0(X3,xI) )
& ( ~ aElement0(X5)
| aElementOf0(sdtasdt0(X5,X3),xI)
| ~ aElementOf0(X3,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ( ~ aElementOf0(X7,xJ)
| aElementOf0(sdtpldt0(X6,X7),xJ)
| ~ aElementOf0(X6,xJ) )
& ( ~ aElement0(X8)
| aElementOf0(sdtasdt0(X8,X6),xJ)
| ~ aElementOf0(X6,xJ) )
& aIdeal0(xJ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_9_071,negated_conjecture,
! [X3,X4] :
( ~ aElementOf0(X3,xI)
| ~ aElementOf0(X4,xJ)
| xy != sdtpldt0(X3,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_10_072,hypothesis,
( aElementOf0(esk1_0,xI)
& aElementOf0(esk2_0,xJ)
& sdtpldt0(esk1_0,esk2_0) = xx
& aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(esk3_0,xI)
& aElementOf0(esk4_0,xJ)
& sdtpldt0(esk3_0,esk4_0) = xy
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_6])])]) ).
fof(c_0_11_073,hypothesis,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
c_0_7 ).
cnf(c_0_12_074,hypothesis,
( aElementOf0(sdtpldt0(X1,X2),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13_075,hypothesis,
( aElementOf0(sdtpldt0(X1,X2),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X2,xJ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14_076,hypothesis,
( aElementOf0(sdtasdt0(X2,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15_077,hypothesis,
( aElementOf0(sdtasdt0(X2,X1),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16_078,negated_conjecture,
( xy != sdtpldt0(X1,X2)
| ~ aElementOf0(X2,xJ)
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17_079,hypothesis,
aElementOf0(xx,sdtpldt1(xI,xJ)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18_080,hypothesis,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19_081,hypothesis,
aElementOf0(xk,xI),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20_082,hypothesis,
aElementOf0(xl,xJ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21_083,hypothesis,
xx = sdtpldt0(xk,xl),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22_084,hypothesis,
aElementOf0(esk1_0,xI),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23_085,hypothesis,
aElementOf0(esk2_0,xJ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24_086,hypothesis,
sdtpldt0(esk1_0,esk2_0) = xx,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25_087,hypothesis,
aElementOf0(esk3_0,xI),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26_088,hypothesis,
aElementOf0(esk4_0,xJ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27_089,hypothesis,
sdtpldt0(esk3_0,esk4_0) = xy,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28_090,hypothesis,
aElement0(xz),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_29_091,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_30_092,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_31_093,hypothesis,
aSet0(xJ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32_094,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_33_095,hypothesis,
( aElementOf0(sdtpldt0(X1,X2),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xI) ),
c_0_12,
[final] ).
cnf(c_0_34_096,hypothesis,
( aElementOf0(sdtpldt0(X1,X2),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X2,xJ) ),
c_0_13,
[final] ).
cnf(c_0_35_097,hypothesis,
( aElementOf0(sdtasdt0(X2,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(X2) ),
c_0_14,
[final] ).
cnf(c_0_36_098,hypothesis,
( aElementOf0(sdtasdt0(X2,X1),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElement0(X2) ),
c_0_15,
[final] ).
cnf(c_0_37_099,negated_conjecture,
( sdtpldt0(X1,X2) != xy
| ~ aElementOf0(X2,xJ)
| ~ aElementOf0(X1,xI) ),
c_0_16,
[final] ).
cnf(c_0_38_100,hypothesis,
aElementOf0(xx,sdtpldt1(xI,xJ)),
c_0_17,
[final] ).
cnf(c_0_39_101,hypothesis,
aElementOf0(xy,sdtpldt1(xI,xJ)),
c_0_18,
[final] ).
cnf(c_0_40_102,hypothesis,
aElementOf0(xk,xI),
c_0_19,
[final] ).
cnf(c_0_41_103,hypothesis,
aElementOf0(xl,xJ),
c_0_20,
[final] ).
cnf(c_0_42_104,hypothesis,
sdtpldt0(xk,xl) = xx,
c_0_21,
[final] ).
cnf(c_0_43_105,hypothesis,
aElementOf0(esk1_0,xI),
c_0_22,
[final] ).
cnf(c_0_44_106,hypothesis,
aElementOf0(esk2_0,xJ),
c_0_23,
[final] ).
cnf(c_0_45_107,hypothesis,
sdtpldt0(esk1_0,esk2_0) = xx,
c_0_24,
[final] ).
cnf(c_0_46_108,hypothesis,
aElementOf0(esk3_0,xI),
c_0_25,
[final] ).
cnf(c_0_47_109,hypothesis,
aElementOf0(esk4_0,xJ),
c_0_26,
[final] ).
cnf(c_0_48_110,hypothesis,
sdtpldt0(esk3_0,esk4_0) = xy,
c_0_27,
[final] ).
cnf(c_0_49_111,hypothesis,
aElement0(xz),
c_0_28,
[final] ).
cnf(c_0_50_112,hypothesis,
aSet0(xI),
c_0_29,
[final] ).
cnf(c_0_51_113,hypothesis,
aIdeal0(xI),
c_0_30,
[final] ).
cnf(c_0_52_114,hypothesis,
aSet0(xJ),
c_0_31,
[final] ).
cnf(c_0_53_115,hypothesis,
aIdeal0(xJ),
c_0_32,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_170,plain,
sdtpldt0(sk3_esk3_0,sk3_esk4_0) = xy,
file('/export/starexec/sandbox2/tmp/iprover_modulo_689881.p',c_0_48) ).
cnf(c_249,plain,
sdtpldt0(sk3_esk3_0,sk3_esk4_0) = xy,
inference(copy,[status(esa)],[c_170]) ).
cnf(c_280,plain,
sdtpldt0(sk3_esk3_0,sk3_esk4_0) = xy,
inference(copy,[status(esa)],[c_249]) ).
cnf(c_291,plain,
sdtpldt0(sk3_esk3_0,sk3_esk4_0) = xy,
inference(copy,[status(esa)],[c_280]) ).
cnf(c_343,plain,
sdtpldt0(sk3_esk3_0,sk3_esk4_0) = xy,
inference(copy,[status(esa)],[c_291]) ).
cnf(c_850,plain,
sdtpldt0(sk3_esk3_0,sk3_esk4_0) = xy,
inference(copy,[status(esa)],[c_343]) ).
cnf(c_159,negated_conjecture,
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != xy ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_689881.p',c_0_37) ).
cnf(c_261,negated_conjecture,
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != xy ),
inference(copy,[status(esa)],[c_159]) ).
cnf(c_269,negated_conjecture,
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != xy ),
inference(copy,[status(esa)],[c_261]) ).
cnf(c_302,negated_conjecture,
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != xy ),
inference(copy,[status(esa)],[c_269]) ).
cnf(c_347,negated_conjecture,
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != xy ),
inference(copy,[status(esa)],[c_302]) ).
cnf(c_858,negated_conjecture,
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != xy ),
inference(copy,[status(esa)],[c_347]) ).
cnf(c_2351,plain,
( ~ aElementOf0(sk3_esk3_0,xI)
| ~ aElementOf0(sk3_esk4_0,xJ) ),
inference(resolution,[status(thm)],[c_850,c_858]) ).
cnf(c_2352,plain,
( ~ aElementOf0(sk3_esk3_0,xI)
| ~ aElementOf0(sk3_esk4_0,xJ) ),
inference(rewriting,[status(thm)],[c_2351]) ).
cnf(c_169,plain,
aElementOf0(sk3_esk4_0,xJ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_689881.p',c_0_47) ).
cnf(c_247,plain,
aElementOf0(sk3_esk4_0,xJ),
inference(copy,[status(esa)],[c_169]) ).
cnf(c_279,plain,
aElementOf0(sk3_esk4_0,xJ),
inference(copy,[status(esa)],[c_247]) ).
cnf(c_292,plain,
aElementOf0(sk3_esk4_0,xJ),
inference(copy,[status(esa)],[c_279]) ).
cnf(c_342,plain,
aElementOf0(sk3_esk4_0,xJ),
inference(copy,[status(esa)],[c_292]) ).
cnf(c_848,plain,
aElementOf0(sk3_esk4_0,xJ),
inference(copy,[status(esa)],[c_342]) ).
cnf(c_168,plain,
aElementOf0(sk3_esk3_0,xI),
file('/export/starexec/sandbox2/tmp/iprover_modulo_689881.p',c_0_46) ).
cnf(c_245,plain,
aElementOf0(sk3_esk3_0,xI),
inference(copy,[status(esa)],[c_168]) ).
cnf(c_278,plain,
aElementOf0(sk3_esk3_0,xI),
inference(copy,[status(esa)],[c_245]) ).
cnf(c_293,plain,
aElementOf0(sk3_esk3_0,xI),
inference(copy,[status(esa)],[c_278]) ).
cnf(c_341,plain,
aElementOf0(sk3_esk3_0,xI),
inference(copy,[status(esa)],[c_293]) ).
cnf(c_846,plain,
aElementOf0(sk3_esk3_0,xI),
inference(copy,[status(esa)],[c_341]) ).
cnf(c_2439,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2352,c_848,c_846]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : RNG087+2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 13:31:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.20/0.42 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.42 % FOF problem with conjecture
% 0.20/0.42 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_7ef782.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_689881.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_d36faa | grep -v "SZS"
% 0.20/0.44
% 0.20/0.44 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.44
% 0.20/0.44 %
% 0.20/0.44 % ------ iProver source info
% 0.20/0.44
% 0.20/0.44 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.44 % git: non_committed_changes: true
% 0.20/0.44 % git: last_make_outside_of_git: true
% 0.20/0.44
% 0.20/0.44 %
% 0.20/0.44 % ------ Input Options
% 0.20/0.44
% 0.20/0.44 % --out_options all
% 0.20/0.44 % --tptp_safe_out true
% 0.20/0.44 % --problem_path ""
% 0.20/0.44 % --include_path ""
% 0.20/0.44 % --clausifier .//eprover
% 0.20/0.44 % --clausifier_options --tstp-format
% 0.20/0.44 % --stdin false
% 0.20/0.44 % --dbg_backtrace false
% 0.20/0.44 % --dbg_dump_prop_clauses false
% 0.20/0.44 % --dbg_dump_prop_clauses_file -
% 0.20/0.44 % --dbg_out_stat false
% 0.20/0.44
% 0.20/0.44 % ------ General Options
% 0.20/0.44
% 0.20/0.44 % --fof false
% 0.20/0.44 % --time_out_real 150.
% 0.20/0.44 % --time_out_prep_mult 0.2
% 0.20/0.44 % --time_out_virtual -1.
% 0.20/0.44 % --schedule none
% 0.20/0.44 % --ground_splitting input
% 0.20/0.44 % --splitting_nvd 16
% 0.20/0.44 % --non_eq_to_eq false
% 0.20/0.44 % --prep_gs_sim true
% 0.20/0.44 % --prep_unflatten false
% 0.20/0.44 % --prep_res_sim true
% 0.20/0.44 % --prep_upred true
% 0.20/0.44 % --res_sim_input true
% 0.20/0.44 % --clause_weak_htbl true
% 0.20/0.44 % --gc_record_bc_elim false
% 0.20/0.44 % --symbol_type_check false
% 0.20/0.44 % --clausify_out false
% 0.20/0.44 % --large_theory_mode false
% 0.20/0.44 % --prep_sem_filter none
% 0.20/0.44 % --prep_sem_filter_out false
% 0.20/0.44 % --preprocessed_out false
% 0.20/0.44 % --sub_typing false
% 0.20/0.44 % --brand_transform false
% 0.20/0.44 % --pure_diseq_elim true
% 0.20/0.44 % --min_unsat_core false
% 0.20/0.44 % --pred_elim true
% 0.20/0.44 % --add_important_lit false
% 0.20/0.44 % --soft_assumptions false
% 0.20/0.44 % --reset_solvers false
% 0.20/0.44 % --bc_imp_inh []
% 0.20/0.44 % --conj_cone_tolerance 1.5
% 0.20/0.44 % --prolific_symb_bound 500
% 0.20/0.44 % --lt_threshold 2000
% 0.20/0.44
% 0.20/0.44 % ------ SAT Options
% 0.20/0.44
% 0.20/0.44 % --sat_mode false
% 0.20/0.44 % --sat_fm_restart_options ""
% 0.20/0.44 % --sat_gr_def false
% 0.20/0.44 % --sat_epr_types true
% 0.20/0.44 % --sat_non_cyclic_types false
% 0.20/0.44 % --sat_finite_models false
% 0.20/0.44 % --sat_fm_lemmas false
% 0.20/0.44 % --sat_fm_prep false
% 0.20/0.44 % --sat_fm_uc_incr true
% 0.20/0.44 % --sat_out_model small
% 0.20/0.44 % --sat_out_clauses false
% 0.20/0.44
% 0.20/0.44 % ------ QBF Options
% 0.20/0.44
% 0.20/0.44 % --qbf_mode false
% 0.20/0.44 % --qbf_elim_univ true
% 0.20/0.44 % --qbf_sk_in true
% 0.20/0.44 % --qbf_pred_elim true
% 0.20/0.44 % --qbf_split 32
% 0.20/0.44
% 0.20/0.44 % ------ BMC1 Options
% 0.20/0.44
% 0.20/0.44 % --bmc1_incremental false
% 0.20/0.44 % --bmc1_axioms reachable_all
% 0.20/0.44 % --bmc1_min_bound 0
% 0.20/0.44 % --bmc1_max_bound -1
% 0.20/0.44 % --bmc1_max_bound_default -1
% 0.20/0.44 % --bmc1_symbol_reachability true
% 0.20/0.44 % --bmc1_property_lemmas false
% 0.20/0.44 % --bmc1_k_induction false
% 0.20/0.44 % --bmc1_non_equiv_states false
% 0.20/0.44 % --bmc1_deadlock false
% 0.20/0.44 % --bmc1_ucm false
% 0.20/0.44 % --bmc1_add_unsat_core none
% 0.20/0.44 % --bmc1_unsat_core_children false
% 0.20/0.44 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.44 % --bmc1_out_stat full
% 0.20/0.44 % --bmc1_ground_init false
% 0.20/0.44 % --bmc1_pre_inst_next_state false
% 0.20/0.44 % --bmc1_pre_inst_state false
% 0.20/0.44 % --bmc1_pre_inst_reach_state false
% 0.20/0.44 % --bmc1_out_unsat_core false
% 0.20/0.44 % --bmc1_aig_witness_out false
% 0.20/0.44 % --bmc1_verbose false
% 0.20/0.44 % --bmc1_dump_clauses_tptp false
% 0.20/0.47 % --bmc1_dump_unsat_core_tptp false
% 0.20/0.47 % --bmc1_dump_file -
% 0.20/0.47 % --bmc1_ucm_expand_uc_limit 128
% 0.20/0.47 % --bmc1_ucm_n_expand_iterations 6
% 0.20/0.47 % --bmc1_ucm_extend_mode 1
% 0.20/0.47 % --bmc1_ucm_init_mode 2
% 0.20/0.47 % --bmc1_ucm_cone_mode none
% 0.20/0.47 % --bmc1_ucm_reduced_relation_type 0
% 0.20/0.47 % --bmc1_ucm_relax_model 4
% 0.20/0.47 % --bmc1_ucm_full_tr_after_sat true
% 0.20/0.47 % --bmc1_ucm_expand_neg_assumptions false
% 0.20/0.47 % --bmc1_ucm_layered_model none
% 0.20/0.47 % --bmc1_ucm_max_lemma_size 10
% 0.20/0.47
% 0.20/0.47 % ------ AIG Options
% 0.20/0.47
% 0.20/0.47 % --aig_mode false
% 0.20/0.47
% 0.20/0.47 % ------ Instantiation Options
% 0.20/0.47
% 0.20/0.47 % --instantiation_flag true
% 0.20/0.47 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.47 % --inst_solver_per_active 750
% 0.20/0.47 % --inst_solver_calls_frac 0.5
% 0.20/0.47 % --inst_passive_queue_type priority_queues
% 0.20/0.47 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.47 % --inst_passive_queues_freq [25;2]
% 0.20/0.47 % --inst_dismatching true
% 0.20/0.47 % --inst_eager_unprocessed_to_passive true
% 0.20/0.47 % --inst_prop_sim_given true
% 0.20/0.47 % --inst_prop_sim_new false
% 0.20/0.47 % --inst_orphan_elimination true
% 0.20/0.47 % --inst_learning_loop_flag true
% 0.20/0.47 % --inst_learning_start 3000
% 0.20/0.47 % --inst_learning_factor 2
% 0.20/0.47 % --inst_start_prop_sim_after_learn 3
% 0.20/0.47 % --inst_sel_renew solver
% 0.20/0.47 % --inst_lit_activity_flag true
% 0.20/0.47 % --inst_out_proof true
% 0.20/0.47
% 0.20/0.47 % ------ Resolution Options
% 0.20/0.47
% 0.20/0.47 % --resolution_flag true
% 0.20/0.47 % --res_lit_sel kbo_max
% 0.20/0.47 % --res_to_prop_solver none
% 0.20/0.47 % --res_prop_simpl_new false
% 0.20/0.47 % --res_prop_simpl_given false
% 0.20/0.47 % --res_passive_queue_type priority_queues
% 0.20/0.47 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.20/0.47 % --res_passive_queues_freq [15;5]
% 0.20/0.47 % --res_forward_subs full
% 0.20/0.47 % --res_backward_subs full
% 0.20/0.47 % --res_forward_subs_resolution true
% 0.20/0.47 % --res_backward_subs_resolution true
% 0.20/0.47 % --res_orphan_elimination false
% 0.20/0.47 % --res_time_limit 1000.
% 0.20/0.47 % --res_out_proof true
% 0.20/0.47 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_7ef782.s
% 0.20/0.47 % --modulo true
% 0.20/0.47
% 0.20/0.47 % ------ Combination Options
% 0.20/0.47
% 0.20/0.47 % --comb_res_mult 1000
% 0.20/0.47 % --comb_inst_mult 300
% 0.20/0.47 % ------
% 0.20/0.47
% 0.20/0.47 % ------ Parsing...% successful
% 0.20/0.47
% 0.20/0.47 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe:1:0s pe:2:0s pe_e snvd_s sp: 0 0s snvd_e %
% 0.20/0.47
% 0.20/0.47 % ------ Proving...
% 0.20/0.47 % ------ Problem Properties
% 0.20/0.47
% 0.20/0.47 %
% 0.20/0.47 % EPR false
% 0.20/0.47 % Horn false
% 0.20/0.47 % Has equality true
% 0.20/0.47
% 0.20/0.47 % % ------ Input Options Time Limit: Unbounded
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 % % ------ Current options:
% 0.20/0.47
% 0.20/0.47 % ------ Input Options
% 0.20/0.47
% 0.20/0.47 % --out_options all
% 0.20/0.47 % --tptp_safe_out true
% 0.20/0.47 % --problem_path ""
% 0.20/0.47 % --include_path ""
% 0.20/0.47 % --clausifier .//eprover
% 0.20/0.47 % --clausifier_options --tstp-format
% 0.20/0.47 % --stdin false
% 0.20/0.47 % --dbg_backtrace false
% 0.20/0.47 % --dbg_dump_prop_clauses false
% 0.20/0.47 % --dbg_dump_prop_clauses_file -
% 0.20/0.47 % --dbg_out_stat false
% 0.20/0.47
% 0.20/0.47 % ------ General Options
% 0.20/0.47
% 0.20/0.47 % --fof false
% 0.20/0.47 % --time_out_real 150.
% 0.20/0.47 % --time_out_prep_mult 0.2
% 0.20/0.47 % --time_out_virtual -1.
% 0.20/0.47 % --schedule none
% 0.20/0.47 % --ground_splitting input
% 0.20/0.47 % --splitting_nvd 16
% 0.20/0.47 % --non_eq_to_eq false
% 0.20/0.47 % --prep_gs_sim true
% 0.20/0.47 % --prep_unflatten false
% 0.20/0.47 % --prep_res_sim true
% 0.20/0.47 % --prep_upred true
% 0.20/0.47 % --res_sim_input true
% 0.20/0.47 % --clause_weak_htbl true
% 0.20/0.47 % --gc_record_bc_elim false
% 0.20/0.47 % --symbol_type_check false
% 0.20/0.47 % --clausify_out false
% 0.20/0.47 % --large_theory_mode false
% 0.20/0.47 % --prep_sem_filter none
% 0.20/0.47 % --prep_sem_filter_out false
% 0.20/0.47 % --preprocessed_out false
% 0.20/0.47 % --sub_typing false
% 0.20/0.47 % --brand_transform false
% 0.20/0.47 % --pure_diseq_elim true
% 0.20/0.47 % --min_unsat_core false
% 0.20/0.47 % --pred_elim true
% 0.20/0.47 % --add_important_lit false
% 0.20/0.47 % --soft_assumptions false
% 0.20/0.47 % --reset_solvers false
% 0.20/0.47 % --bc_imp_inh []
% 0.20/0.47 % --conj_cone_tolerance 1.5
% 0.20/0.47 % --prolific_symb_bound 500
% 0.20/0.47 % --lt_threshold 2000
% 0.20/0.47
% 0.20/0.47 % ------ SAT Options
% 0.20/0.47
% 0.20/0.47 % --sat_mode false
% 0.20/0.47 % --sat_fm_restart_options ""
% 0.20/0.47 % --sat_gr_def false
% 0.20/0.47 % --sat_epr_types true
% 0.20/0.47 % --sat_non_cyclic_types false
% 0.20/0.47 % --sat_finite_models false
% 0.20/0.47 % --sat_fm_lemmas false
% 0.20/0.47 % --sat_fm_prep false
% 0.20/0.47 % --sat_fm_uc_incr true
% 0.20/0.47 % --sat_out_model small
% 0.20/0.47 % --sat_out_clauses false
% 0.20/0.47
% 0.20/0.47 % ------ QBF Options
% 0.20/0.47
% 0.20/0.47 % --qbf_mode false
% 0.20/0.47 % --qbf_elim_univ true
% 0.20/0.47 % --qbf_sk_in true
% 0.20/0.47 % --qbf_pred_elim true
% 0.20/0.47 % --qbf_split 32
% 0.20/0.47
% 0.20/0.47 % ------ BMC1 Options
% 0.20/0.47
% 0.20/0.47 % --bmc1_incremental false
% 0.20/0.47 % --bmc1_axioms reachable_all
% 0.20/0.47 % --bmc1_min_bound 0
% 0.20/0.47 % --bmc1_max_bound -1
% 0.20/0.47 % --bmc1_max_bound_default -1
% 0.20/0.47 % --bmc1_symbol_reachability true
% 0.20/0.47 % --bmc1_property_lemmas false
% 0.20/0.47 % --bmc1_k_induction false
% 0.20/0.47 % --bmc1_non_equiv_states false
% 0.20/0.47 % --bmc1_deadlock false
% 0.20/0.47 % --bmc1_ucm false
% 0.20/0.47 % --bmc1_add_unsat_core none
% 0.20/0.47 % --bmc1_unsat_core_children false
% 0.20/0.47 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.47 % --bmc1_out_stat full
% 0.20/0.47 % --bmc1_ground_init false
% 0.20/0.47 % --bmc1_pre_inst_next_state false
% 0.20/0.47 % --bmc1_pre_inst_state false
% 0.20/0.47 % --bmc1_pre_inst_reach_state false
% 0.20/0.47 % --bmc1_out_unsat_core false
% 0.20/0.47 % --bmc1_aig_witness_out false
% 0.20/0.47 % --bmc1_verbose false
% 0.20/0.47 % --bmc1_dump_clauses_tptp false
% 0.20/0.47 % --bmc1_dump_unsat_core_tptp false
% 0.20/0.47 % --bmc1_dump_file -
% 0.20/0.47 % --bmc1_ucm_expand_uc_limit 128
% 0.20/0.47 % --bmc1_ucm_n_expand_iterations 6
% 0.20/0.47 % --bmc1_ucm_extend_mode 1
% 0.20/0.47 % --bmc1_ucm_init_mode 2
% 0.20/0.47 % --bmc1_ucm_cone_mode none
% 0.20/0.47 % --bmc1_ucm_reduced_relation_type 0
% 0.20/0.47 % --bmc1_ucm_relax_model 4
% 0.20/0.47 % --bmc1_ucm_full_tr_after_sat true
% 0.20/0.47 % --bmc1_ucm_expand_neg_assumptions false
% 0.20/0.47 % --bmc1_ucm_layered_model none
% 0.20/0.47 % --bmc1_ucm_max_lemma_size 10
% 0.20/0.47
% 0.20/0.47 % ------ AIG Options
% 0.20/0.47
% 0.20/0.47 % --aig_mode false
% 0.20/0.47
% 0.20/0.47 % ------ Instantiation Options
% 0.20/0.47
% 0.20/0.47 % --instantiation_flag true
% 0.20/0.47 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.47 % --inst_solver_per_active 750
% 0.20/0.47 % --inst_solver_calls_frac 0.5
% 0.20/0.47 % --inst_passive_queue_type priority_queues
% 0.20/0.47 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.47 % --inst_passive_queues_freq [25;2]
% 0.20/0.47 % --inst_dismatching true
% 0.20/0.47 % --inst_eager_unprocessed_to_passive true
% 0.20/0.47 % --inst_prop_sim_given true
% 0.20/0.57 % --inst_prop_sim_new false
% 0.20/0.57 % --inst_orphan_elimination true
% 0.20/0.57 % --inst_learning_loop_flag true
% 0.20/0.57 % --inst_learning_start 3000
% 0.20/0.57 % --inst_learning_factor 2
% 0.20/0.57 % --inst_start_prop_sim_after_learn 3
% 0.20/0.57 % --inst_sel_renew solver
% 0.20/0.57 % --inst_lit_activity_flag true
% 0.20/0.57 % --inst_out_proof true
% 0.20/0.57
% 0.20/0.57 % ------ Resolution Options
% 0.20/0.57
% 0.20/0.57 % --resolution_flag true
% 0.20/0.57 % --res_lit_sel kbo_max
% 0.20/0.57 % --res_to_prop_solver none
% 0.20/0.57 % --res_prop_simpl_new false
% 0.20/0.57 % --res_prop_simpl_given false
% 0.20/0.57 % --res_passive_queue_type priority_queues
% 0.20/0.57 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.20/0.57 % --res_passive_queues_freq [15;5]
% 0.20/0.57 % --res_forward_subs full
% 0.20/0.57 % --res_backward_subs full
% 0.20/0.57 % --res_forward_subs_resolution true
% 0.20/0.57 % --res_backward_subs_resolution true
% 0.20/0.57 % --res_orphan_elimination false
% 0.20/0.57 % --res_time_limit 1000.
% 0.20/0.57 % --res_out_proof true
% 0.20/0.57 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_7ef782.s
% 0.20/0.57 % --modulo true
% 0.20/0.57
% 0.20/0.57 % ------ Combination Options
% 0.20/0.57
% 0.20/0.57 % --comb_res_mult 1000
% 0.20/0.57 % --comb_inst_mult 300
% 0.20/0.57 % ------
% 0.20/0.57
% 0.20/0.57
% 0.20/0.57
% 0.20/0.57 % ------ Proving...
% 0.20/0.57 %
% 0.20/0.57
% 0.20/0.57
% 0.20/0.57 % Resolution empty clause
% 0.20/0.57
% 0.20/0.57 % ------ Statistics
% 0.20/0.57
% 0.20/0.57 % ------ General
% 0.20/0.57
% 0.20/0.57 % num_of_input_clauses: 176
% 0.20/0.57 % num_of_input_neg_conjectures: 1
% 0.20/0.57 % num_of_splits: 0
% 0.20/0.57 % num_of_split_atoms: 0
% 0.20/0.57 % num_of_sem_filtered_clauses: 0
% 0.20/0.57 % num_of_subtypes: 0
% 0.20/0.57 % monotx_restored_types: 0
% 0.20/0.57 % sat_num_of_epr_types: 0
% 0.20/0.57 % sat_num_of_non_cyclic_types: 0
% 0.20/0.57 % sat_guarded_non_collapsed_types: 0
% 0.20/0.57 % is_epr: 0
% 0.20/0.57 % is_horn: 0
% 0.20/0.57 % has_eq: 1
% 0.20/0.57 % num_pure_diseq_elim: 0
% 0.20/0.57 % simp_replaced_by: 0
% 0.20/0.57 % res_preprocessed: 22
% 0.20/0.57 % prep_upred: 0
% 0.20/0.57 % prep_unflattend: 2
% 0.20/0.57 % pred_elim_cands: 3
% 0.20/0.57 % pred_elim: 3
% 0.20/0.57 % pred_elim_cl: 5
% 0.20/0.57 % pred_elim_cycles: 4
% 0.20/0.57 % forced_gc_time: 0
% 0.20/0.57 % gc_basic_clause_elim: 0
% 0.20/0.57 % parsing_time: 0.01
% 0.20/0.57 % sem_filter_time: 0.
% 0.20/0.57 % pred_elim_time: 0.
% 0.20/0.57 % out_proof_time: 0.
% 0.20/0.57 % monotx_time: 0.
% 0.20/0.57 % subtype_inf_time: 0.
% 0.20/0.57 % unif_index_cands_time: 0.
% 0.20/0.57 % unif_index_add_time: 0.
% 0.20/0.57 % total_time: 0.151
% 0.20/0.57 % num_of_symbols: 58
% 0.20/0.57 % num_of_terms: 2161
% 0.20/0.57
% 0.20/0.57 % ------ Propositional Solver
% 0.20/0.57
% 0.20/0.57 % prop_solver_calls: 1
% 0.20/0.57 % prop_fast_solver_calls: 69
% 0.20/0.57 % prop_num_of_clauses: 139
% 0.20/0.57 % prop_preprocess_simplified: 670
% 0.20/0.57 % prop_fo_subsumed: 0
% 0.20/0.57 % prop_solver_time: 0.
% 0.20/0.57 % prop_fast_solver_time: 0.
% 0.20/0.57 % prop_unsat_core_time: 0.
% 0.20/0.57
% 0.20/0.57 % ------ QBF
% 0.20/0.57
% 0.20/0.57 % qbf_q_res: 0
% 0.20/0.57 % qbf_num_tautologies: 0
% 0.20/0.57 % qbf_prep_cycles: 0
% 0.20/0.57
% 0.20/0.57 % ------ BMC1
% 0.20/0.57
% 0.20/0.57 % bmc1_current_bound: -1
% 0.20/0.57 % bmc1_last_solved_bound: -1
% 0.20/0.57 % bmc1_unsat_core_size: -1
% 0.20/0.57 % bmc1_unsat_core_parents_size: -1
% 0.20/0.57 % bmc1_merge_next_fun: 0
% 0.20/0.57 % bmc1_unsat_core_clauses_time: 0.
% 0.20/0.57
% 0.20/0.57 % ------ Instantiation
% 0.20/0.57
% 0.20/0.57 % inst_num_of_clauses: 170
% 0.20/0.57 % inst_num_in_passive: 0
% 0.20/0.57 % inst_num_in_active: 0
% 0.20/0.57 % inst_num_in_unprocessed: 171
% 0.20/0.57 % inst_num_of_loops: 0
% 0.20/0.58 % inst_num_of_learning_restarts: 0
% 0.20/0.58 % inst_num_moves_active_passive: 0
% 0.20/0.58 % inst_lit_activity: 0
% 0.20/0.58 % inst_lit_activity_moves: 0
% 0.20/0.58 % inst_num_tautologies: 0
% 0.20/0.58 % inst_num_prop_implied: 0
% 0.20/0.58 % inst_num_existing_simplified: 0
% 0.20/0.58 % inst_num_eq_res_simplified: 0
% 0.20/0.58 % inst_num_child_elim: 0
% 0.20/0.58 % inst_num_of_dismatching_blockings: 0
% 0.20/0.58 % inst_num_of_non_proper_insts: 0
% 0.20/0.58 % inst_num_of_duplicates: 0
% 0.20/0.58 % inst_inst_num_from_inst_to_res: 0
% 0.20/0.58 % inst_dismatching_checking_time: 0.
% 0.20/0.58
% 0.20/0.58 % ------ Resolution
% 0.20/0.58
% 0.20/0.58 % res_num_of_clauses: 531
% 0.20/0.58 % res_num_in_passive: 246
% 0.20/0.58 % res_num_in_active: 149
% 0.20/0.58 % res_num_of_loops: 61
% 0.20/0.58 % res_forward_subset_subsumed: 89
% 0.20/0.58 % res_backward_subset_subsumed: 0
% 0.20/0.58 % res_forward_subsumed: 10
% 0.20/0.58 % res_backward_subsumed: 0
% 0.20/0.58 % res_forward_subsumption_resolution: 11
% 0.20/0.58 % res_backward_subsumption_resolution: 0
% 0.20/0.58 % res_clause_to_clause_subsumption: 1053
% 0.20/0.58 % res_orphan_elimination: 0
% 0.20/0.58 % res_tautology_del: 0
% 0.20/0.58 % res_num_eq_res_simplified: 0
% 0.20/0.58 % res_num_sel_changes: 0
% 0.20/0.58 % res_moves_from_active_to_pass: 0
% 0.20/0.58
% 0.20/0.58 % Status Unsatisfiable
% 0.20/0.58 % SZS status Theorem
% 0.20/0.58 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------